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| 0 Cooling a cup of coffee with help of a spoon | |
| 1 Can I compute the mass of a coin based on the sound of its fall? | |
| 2 How does light bend around my finger tip? | |
| 3 How does gravity escape a black hole? | |
| 4 Did the Big Bang happen at a point? | |
| 5 Why are mirror images flipped horizontally but not vertically? | |
| 6 Do we know why there is a speed limit in our universe? | |
| 7 Book recommendations | |
| 8 What experiment would disprove string theory? | |
| 9 Why dont metals bond when touched together? | |
| 10 Why do ballpoint pens write better on pages that have pages below them? | |
| 11 What is Chirped Pulse Amplification, and why is it important enough to warrant a Nobel Prize? | |
| 12 Why does kinetic energy increase quadratically, not linearly, with speed? | |
| 13 What really allows airplanes to fly? | |
| 14 Why are four-legged chairs so common? | |
| 15 If I sliced the universe in half, would the slice go through a star? | |
| 16 Dont heavier objects actually fall faster because they exert their own gravity? | |
| 17 How do towels stay on hooks? | |
| 18 What exactly is a photon? | |
| 19 Does Earth really have two high-tide bulges on opposite sides? | |
| 20 Strange ice found in my garden | |
| 21 Why is the detection of gravitational waves so significant? | |
| 22 Surviving under water in air bubble | |
| 23 Why do we bend a book to keep it straight? | |
| 24 If photons have no mass, how can they have momentum? | |
| 25 Why doesnt matter pass through other matter if atoms are 99.999% empty space? | |
| 26 Why is Googles quantum supremacy experiment impressive? | |
| 27 Are units of angle really dimensionless? | |
| 28 Why dont electrons crash into the nuclei they orbit? | |
| 29 Why does space expansion not expand matter? | |
| 30 When separating an Oreo cookie, why does the cream stick to just one side only? | |
| 31 Why does NASA use gold foil on equipment and gold-coated visors? | |
| 32 How do moving charges produce magnetic fields? | |
| 33 How does a knife cut things at the atomic level? | |
| 34 Why do we not have spin greater than 2? | |
| 35 Why do shadows from the sun join each other when near enough? | |
| 36 Gauge symmetry is not a symmetry? | |
| 37 Why do we actually see the sun? | |
| 38 Whats the point of Hamiltonian mechanics? | |
| 39 Could Legolas actually see that far? | |
| 40 How do you make more precise instruments while only using less precise instruments? | |
| 41 Why does holding something up cost energy while no work is being done? | |
| 42 What makes a theory Quantum? | |
| 43 Given Newtons third law, why are things capable of moving? | |
| 44 Why does Stephen Hawking say black holes dont exist? | |
| 45 Why do sunbeams diverge even though the sun is much more than a few kilometers away? | |
| 46 How do I explain to a six year old why people on the other side of the Earth dont fall off? | |
| 47 Simple check for the global shape of the Earth | |
| 48 Why are the harmonics of a piano tone not multiples of the base frequency? | |
| 49 What is a field, really? | |
| 50 Why are the wet patches on these floor tiles circular? | |
| 51 Why is nuclear waste more dangerous than the original nuclear fuel? | |
| 52 Is $\pi^2 \approx g$ a coincidence? | |
| 53 Why does a mirror split my laser beam? | |
| 54 Why is my hand not burned by the air in an oven at 200 °C? | |
| 55 Why would spacetime curvature cause gravity? | |
| 56 Does someone falling into a black hole see the end of the universe? | |
| 57 Why are the windows of bridges of ships always inclined? | |
| 58 Does the Planck scale imply that spacetime is discrete? | |
| 59 Is temperature a Lorentz invariant in relativity? | |
| 60 Why do people categorically dismiss some simple quantum models? | |
| 61 If you view the Earth from far enough away can you observe its past? | |
| 62 Is time continuous or discrete? | |
| 63 How can you weigh your own head in an accurate way? | |
| 64 Why does my tea periodically alternate its rotational speed after stirring? (Link to video below) | |
| 65 How fast does gravity propagate? | |
| 66 How do I experimentally measure the surface area of a rock? | |
| 67 Is the butterfly effect real? | |
| 68 Why doesnt water boil in the oven? | |
| 69 A list of inconveniences between quantum mechanics and (general) relativity? | |
| 70 Why are there only derivatives to the first order in the Lagrangian? | |
| 71 Reading the Feynman lectures in 2012 | |
| 72 Why is the vibration in my wire acting so oddly? | |
| 73 Why can I touch aluminum foil in the oven and not get burned? | |
| 74 Why does paper cut through things so well? | |
| 75 What does it mean for two objects to touch? | |
| 76 Why do spaceships heat up when entering earth but not when exiting? | |
| 77 Does a particle exert force on itself? | |
| 78 Why does Newtons Third Law actually work? | |
| 79 Why does ice cream get harder when colder? | |
| 80 Why does the humidifier make a stoves flame orange? | |
| 81 How does mass leave the body when you lose weight? | |
| 82 Is anti-matter matter going backwards in time? | |
| 83 Calculus of variations -- how does it make sense to vary the position and the velocity independently? | |
| 84 Why dont we use weights to store energy? | |
| 85 Why do wet objects become darker? | |
| 86 Why am I not burned by a strong wind? | |
| 87 The Role of Rigor | |
| 88 On this infinite grid of resistors, whats the equivalent resistance? | |
| 89 If all motion is relative, how does light have a finite speed? | |
| 90 Could we send a man safely to the Moon in a rocket without knowledge of general relativity? | |
| 91 Superfields and the Inconsistency of regularization by dimensional reduction | |
| 92 Is it necessary to consume energy to perform computation? | |
| 93 Toilet paper dilemma | |
| 94 Is it possible for information to be transmitted faster than light by using a rigid pole? | |
| 95 Why do electrons, according to my textbook, exist forever? | |
| 96 What happens to the energy when waves perfectly cancel each other? | |
| 97 Why does a helium filled balloon move forward in a car when the car is accelerating? | |
| 98 What is the actual significance of the amplituhedron? | |
| 99 Can the Heisenberg Uncertainty Principle be explained intuitively? | |
| 100 What, in simplest terms, is gauge invariance? | |
| 101 Can Maxwells equations be derived from Coulombs Law and Special Relativity? | |
| 102 Is the universe fundamentally deterministic? | |
| 103 Why are most metals gray/silver? | |
| 104 Is it possible to start fire using moonlight? | |
| 105 What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis? | |
| 106 Books for general relativity | |
| 107 Why is glass transparent? | |
| 108 How can anything ever fall into a black hole as seen from an outside observer? | |
| 109 Whats inside a proton? | |
| 110 Why is oil a better lubricant than water? | |
| 111 Why do tuning forks have two prongs? | |
| 112 Why do fusion and fission both release energy? | |
| 113 Why is quantum entanglement considered to be an active link between particles? | |
| 114 Why are some people are claiming that the Big Bang never happened? | |
| 115 How do we know that radioactive decay rates are constant over billions of years? | |
| 116 How can I stand on the ground? EM or/and Pauli? | |
| 117 Is Angular Momentum truly fundamental? | |
| 118 What is $\Delta t$ in the time-energy uncertainty principle? | |
| 119 Why the Principle of Least Action? | |
| 120 Why does the Suns (or other stars) nuclear reaction not use up all its fuel immediately? | |
| 121 Intuitively, why are bundles so important in Physics? | |
| 122 Why does a sticker slowly peel off, but if it is pulled quickly it tears? | |
| 123 What is known about the topological structure of spacetime? | |
| 124 Does the $\frac{4}{3}$ problem of classical electromagnetism remain in quantum mechanics? | |
| 125 How can we see an atom now? What was the scale of this equipment? | |
| 126 Is there such thing as imaginary time dilation? | |
| 127 Thought experiment - would you notice if you fell into a black hole? | |
| 128 Explain it to me like Im a physics grad: Greenhouse Effect | |
| 129 QM without complex numbers | |
| 130 What Is Energy? Where did it come from? | |
| 131 Why is filling a balloon from your mouth much harder initially? | |
| 132 If gravity isnt a force, then why do we learn in school that it is? | |
| 133 If I pull a metal bar for long enough with a constant small force, will it eventually break? | |
| 134 Which is stronger, a rope without knots or a rope with knots? | |
| 135 Would a pin head heated to 15 million degrees Celsius kill everyone in a 1000 mile radius? | |
| 136 Why is there a scarcity of lithium? | |
| 137 Why do most formulas in physics have integer and rational exponents? | |
| 138 Is there something similar to Noethers theorem for discrete symmetries? | |
| 139 What is a good introductory book on quantum mechanics? | |
| 140 Best books for mathematical background? | |
| 141 What is the physical meaning of commutators in quantum mechanics? | |
| 142 Differentiating Propagator, Greens function, Correlation function, etc | |
| 143 What justifies dimensional analysis? | |
| 144 How is a quantum superposition different from a mixed state? | |
| 145 Why dont miners get boiled to death at $4$ km deep? | |
| 146 Trace of a commutator is zero - but what about the commutator of $x$ and $p$? | |
| 147 About the complex nature of the wave function? | |
| 148 Why was carbon-12 chosen for the atomic mass unit? | |
| 149 Why does the shower curtain move towards me when I am taking a hot shower? | |
| 150 Where is the flaw in this machine that decreases the entropy of a closed system? | |
| 151 Why does the atmosphere rotate along with the earth? | |
| 152 Why does hot water clean better than cold water? | |
| 153 What is the speed of sound in space? | |
| 154 How can a black hole produce sound? | |
| 155 What is the proper way to explain the twin paradox? | |
| 156 Why are radiators always placed under windows? | |
| 157 Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip? | |
| 158 If Earth had rings? | |
| 159 How can time dilation be symmetric? | |
| 160 Quantum Entanglement - Whats the big deal? | |
| 161 If we had a perfectly efficient computer and all the energy in the Milky-way available, what number could it count to? | |
| 162 Why does the LIGO observation disprove higher dimensions? | |
| 163 Why does nature favour the Laplacian? | |
| 164 What software programs are used to draw physics diagrams, and what are their relative merits? | |
| 165 Why do same/opposite electric charges repel/attract each other, respectively? | |
| 166 What conservation law corresponds to Lorentz boosts? | |
| 167 Why quantum mechanics? | |
| 168 Does a gun exert enough gravity on the bullet it fired to stop it? | |
| 169 Why does my wooden door disperse light into a rainbow color spectrum? | |
| 170 What is the relation between electromagnetic wave and photon? | |
| 171 Why is the $S_{z} =0$ state forbidden for photons? | |
| 172 Seeing something from only one angle means you have only seen (what?)% of its surface area at most? | |
| 173 Are Newtons laws of motion laws or definitions of force and mass? | |
| 174 Does juggling balls reduce the total weight of the juggler and balls? | |
| 175 Why does a remote car key work when held to your head/body? | |
| 176 Why does matter exist in 3 states (liquids, solid, gas)? | |
| 177 How did Einstein know the speed of light was constant? | |
| 178 Why does a billiard ball stop when it hits another billiard ball head on? | |
| 179 Am I attracting Pluto? | |
| 180 Why does a yellow object turn white under a yellow light? Shouldnt it turn yellow instead? | |
| 181 Why is a laserpointer able to erase a glow-in-the-dark sticker? | |
| 182 Can tin foil hats block anything? | |
| 183 Why is a $5-60 mph$ time slower than a $0-60 mph$ time for some automobiles? | |
| 184 Why do scientists think that all the laws of physics that apply in our galaxy apply in other galaxies? | |
| 185 Why do phones land face down? | |
| 186 What is a manifold? | |
| 187 Why cant $ i\hbar\frac{\partial}{\partial t}$ be considered the Hamiltonian operator? | |
| 188 How does this baby rattle work? | |
| 189 Superluminal neutrinos | |
| 190 Why do metals only glow red, yellow and white and not through the full range of the spectrum? | |
| 191 What is time, does it flow, and if so what defines its direction? | |
| 192 How exactly do you avoid fooling yourself? | |
| 193 Why are differential equations for fields in physics of order two? | |
| 194 Quantum Field Theory from a mathematical point of view | |
| 195 Why is light bent but not accelerated? | |
| 196 Why can Hiroshima be inhabited when Chernobyl cannot? | |
| 197 What makes running so much less energy-efficient than bicycling? | |
| 198 Why is it bad taste to have a dimensional quantity in the argument of a logarithm or exponential function? | |
| 199 What is spontaneous symmetry breaking in quantum systems? | |
| 200 Why does a full moon seem uniformly bright from earth, shouldnt it be dimmer at the border? | |
| 201 Why is information indestructible? | |
| 202 Why dont fluorescent lights produce shadows? | |
| 203 If you are vacuuming your carpet and you wrap the cord around your body do you become a magnet? | |
| 204 When I walk down the stairs where does my potential energy go? | |
| 205 What is more fundamental, fields or particles? | |
| 206 Why does rainwater form moving waves on the ground? Is there a name for this effect? | |
| 207 List of freely available physics books | |
| 208 In the earths crust, why is there far more uranium than gold? | |
| 209 Could a living planet alter its own trajectory only by changing its shape? | |
| 210 Classical and quantum anomalies | |
| 211 What causes the water in this fountain to reverse direction? | |
| 212 What is spin as it relates to subatomic particles? | |
| 213 If dark matter only interacts with gravity, why doesnt it all clump together in a single point? | |
| 214 Why doesnt water actually perfectly wet glass? | |
| 215 Can photons be detected without being absorbed? | |
| 216 Is there a symmetry associated to the conservation of information? | |
| 217 What does one second after big bang mean? | |
| 218 What happened to David John Candlin? | |
| 219 Why do travelling waves continue after amplitude sum = 0? | |
| 220 Will a hole cut into a metal disk expand or shrink when the disc is heated? | |
| 221 Why does public mains power use 50-60 Hz and 100-240 V? | |
| 222 How can magnets be used to pick up pieces of metal when the force from a magnetic field does no work? | |
| 223 How do laser tape measures work? | |
| 224 Why must a physical theory be mathematically self-consistent? | |
| 225 Why does a rubber band become a lighter color when stretched? | |
| 226 Does centrifugal force exist? | |
| 227 Why does water stop boiling immediately after turning off the heat? | |
| 228 Why does fire make very little sound? | |
| 229 Where does the extra kinetic energy come from in a gravitational slingshot? | |
| 230 What was the major discovery on gravitational waves made March 17th, 2014, in the BICEP2 experiment? | |
| 231 Why doesnt the Moon fall onto the Earth? | |
| 232 How and why do accelerating charges radiate electromagnetic radiation? | |
| 233 Visually stunning math concepts which are easy to explain | |
| 234 Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio? | |
| 235 How long will it take Marie to saw another board into 3 pieces? | |
| 236 Can I use my powers for good? | |
| 237 The staircase paradox, or why $\pi\ne4$ | |
| 238 How to study math to really understand it and have a healthy lifestyle with free time? | |
| 239 Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem) | |
| 240 Whats an intuitive way to think about the determinant? | |
| 241 Does $\pi$ contain all possible number combinations? | |
| 242 Splitting a sandwich and not feeling deceived | |
| 243 What was the first bit of mathematics that made you realize that math is beautiful? (For childrens book) | |
| 244 Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real? | |
| 245 Why can you turn clothing right-side-out? | |
| 246 Examples of patterns that eventually fail | |
| 247 Mathematical difference between white and black notes in a piano | |
| 248 Do complex numbers really exist? | |
| 249 What are imaginary numbers? | |
| 250 How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? | |
| 251 Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$ | |
| 252 The Egg: Bizarre behavior of the roots of a family of polynomials. | |
| 253 Is this Batman equation for real? | |
| 254 Best Sets of Lecture Notes and Articles | |
| 255 My sons Sum of Some is beautiful! But what is the proof or explanation? | |
| 256 Proofs that every mathematician should know. | |
| 257 Why does $1+2+3+\cdots = -\frac{1}{12}$? | |
| 258 What is the intuitive relationship between SVD and PCA? | |
| 259 How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$? | |
| 260 On familiarity (or How to avoid going down the Math Rabbit Hole?) | |
| 261 Fourier transform for dummies | |
| 262 The Ring Game on $K[x,y,z]$ | |
| 263 Pedagogy: How to cure students of the law of universal linearity? | |
| 264 Find five positive integers whose reciprocals sum to $1$ | |
| 265 Can every proof by contradiction also be shown without contradiction? | |
| 266 Obvious theorems that are actually false | |
| 267 Zero to the zero power – is $0^0=1$? | |
| 268 If $AB = I$ then $BA = I$ | |
| 269 Calculating the length of the paper on a toilet paper roll | |
| 270 How can you prove that a function has no closed form integral? | |
| 271 A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language | |
| 272 Surprising identities / equations | |
| 273 Is it true that $0.999999999\ldots=1$? | |
| 274 Why dont we define imaginary numbers for every impossibility? | |
| 275 What is the importance of eigenvalues/eigenvectors? | |
| 276 Nice examples of groups which are not obviously groups | |
| 277 Multiple-choice question about the probability of a random answer to itself being correct | |
| 278 In Russian roulette, is it best to go first? | |
| 279 One question to know if the number is 1, 2 or 3 | |
| 280 Why does this innovative method of subtraction from a third grader always work? | |
| 281 Intuition for the definition of the Gamma function? | |
| 282 Why can ALL quadratic equations be solved by the quadratic formula? | |
| 283 Math without pencil and paper | |
| 284 V.I. Arnold says Russian students cant solve this problem, but American students can -- why? | |
| 285 Really advanced techniques of integration (definite or indefinite) | |
| 286 Is mathematics one big tautology? | |
| 287 Help with a prime number spiral which turns 90 degrees at each prime | |
| 288 Is $10$ a magical number or I am missing something? | |
| 289 Funny identities | |
| 290 Cant argue with success? Looking for bad math that gets away with it | |
| 291 Is $7$ the only prime followed by a cube? | |
| 292 In the history of mathematics, has there ever been a mistake? | |
| 293 The Mathematics of Tetris | |
| 294 Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet? | |
| 295 Why do mathematicians use single-letter variables? | |
| 296 How does one prove the determinant inequality $\det\left(6(A^3+B^3+C^3)+I_{n}\right)\ge 5^n\det(A^2+B^2+C^2)$? | |
| 297 Is a matrix multiplied with its transpose something special? | |
| 298 How discontinuous can a derivative be? | |
| 299 Too old to start math | |
| 300 Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$ | |
| 301 What is the maximum volume that can be contained by a sheet of paper? | |
| 302 Please explain the intuition behind the dual problem in optimization. | |
| 303 Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$? | |
| 304 Norms Induced by Inner Products and the Parallelogram Law | |
| 305 Fun but serious mathematics books to gift advanced undergraduates. | |
| 306 Which answer in this list is the correct answer to this question? | |
| 307 What is the practical difference between a differential and a derivative? | |
| 308 Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ | |
| 309 Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers | |
| 310 Can you answer my sons fourth-grade homework question: Which numbers are prime, have digits adding to ten and have a three in the tens place? | |
| 311 The Integral that Stumped Feynman? | |
| 312 In (relatively) simple words: What is an inverse limit? | |
| 313 What is the importance of the Collatz conjecture? | |
| 314 What are some examples of when Mathematics accidentally discovered something about the world? | |
| 315 Derivative of sigmoid function $\sigma (x) = \frac{1}{1+e^{-x}}$ | |
| 316 Conjectures that have been disproved with extremely large counterexamples? | |
| 317 Best Fake Proofs? (A M.SE April Fools Day collection) | |
| 318 Any open subset of $\Bbb R$ is a countable union of disjoint open intervals | |
| 319 Why study Algebraic Geometry? | |
| 320 Why are rings called rings? | |
| 321 What is the result of $\infty - \infty$? | |
| 322 Integral Milking | |
| 323 A 1,400 years old approximation to the sine function by Mahabhaskariya of Bhaskara I | |
| 324 How to read a book in mathematics? | |
| 325 Why do we care about dual spaces? | |
| 326 What are some counter-intuitive results in mathematics that involve only finite objects? | |
| 327 How many fours are needed to represent numbers up to $N$? | |
| 328 Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer? | |
| 329 Your favourite application of the Baire Category Theorem | |
| 330 What books must every math undergraduate read? | |
| 331 Proving you *cant* make $2011$ out of $1,2,3,4$: nice twist on the usual | |
| 332 Does the open mapping theorem imply the Baire category theorem? | |
| 333 Optimizing response times of an ambulance corp: short-term versus average | |
| 334 Is there a 0-1 law for the theory of groups? | |
| 335 How can a piece of A4 paper be folded in exactly three equal parts? | |
| 336 Eigenvectors of real symmetric matrices are orthogonal | |
| 337 Do men or women have more brothers? | |
| 338 In simple English, what does it mean to be transcendental? | |
| 339 How to check if a point is inside a rectangle? | |
| 340 Good books and lecture notes about category theory. | |
| 341 Why does this matrix give the derivative of a function? | |
| 342 Is it faster to count to the infinite going one by one or two by two? | |
| 343 What are the Differences Between a Matrix and a Tensor? | |
| 344 How do I convince someone that $1+1=2$ may not necessarily be true? | |
| 345 How do I sell out with abstract algebra? | |
| 346 Why can a Venn diagram for $4+$ sets not be constructed using circles? | |
| 347 Identification of a quadrilateral as a trapezoid, rectangle, or square | |
| 348 Meaning of Rays in Polar Plot of Prime Numbers | |
| 349 What does $2^x$ really mean when $x$ is not an integer? | |
| 350 What do modern-day analysts actually do? | |
| 351 Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$ | |
| 352 Is computer science a branch of mathematics? | |
| 353 What is the difference between linear and affine function | |
| 354 Which one result in mathematics has surprised you the most? | |
| 355 Books on Number Theory for Layman | |
| 356 Teaching myself differential topology and differential geometry | |
| 357 List of interesting math videos / documentaries | |
| 358 Exterior Derivative vs. Covariant Derivative vs. Lie Derivative | |
| 359 How to show $e^{e^{e^{79}}}$ is not an integer | |
| 360 Are $14$ and $21$ the only interesting numbers? | |
| 361 How could we define the factorial of a matrix? | |
| 362 When can you switch the order of limits? | |
| 363 List of Interesting Math Blogs | |
| 364 Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$ | |
| 365 How do we prove that something is unprovable? | |
| 366 How many sides does a circle have? | |
| 367 Whats the intuition behind Pythagoras theorem? | |
| 368 Why is compactness so important? | |
| 369 Can a coin with an unknown bias be treated as fair? | |
| 370 A Topology such that the continuous functions are exactly the polynomials | |
| 371 What is the geometric interpretation of the transpose? | |
| 372 Counterintuitive examples in probability | |
| 373 What is a good complex analysis textbook, barring Ahlforss? | |
| 374 What were some major mathematical breakthroughs in 2016? | |
| 375 How to intuitively understand eigenvalue and eigenvector? | |
| 376 Importance of Representation Theory | |
| 377 Advice to young mathematicians | |
| 378 Why cant differentiability be generalized as nicely as continuity? | |
| 379 How to define a bijection between $(0,1)$ and $(0,1]$? | |
| 380 Derivative of Softmax loss function | |
| 381 Some users are mind bogglingly skilled at integration. How did they get there? | |
| 382 How do people perform mental arithmetic for complicated expressions? | |
| 383 Can we ascertain that there exists an epimorphism $G\rightarrow H$? | |
| 384 What Does it Really Mean to Have Different Kinds of Infinities? | |
| 385 How do you revise material that you already half-know, without getting bored and demotivated? | |
| 386 Are there any series whose convergence is unknown? | |
| 387 When can a sum and integral be interchanged? | |
| 388 A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$ | |
| 389 Symmetry of function defined by integral | |
| 390 Why $\sqrt{-1 \cdot {-1}} \neq \sqrt{-1}^2$? | |
| 391 Self-Contained Proof that $\sum\limits_{n=1}^{\infty} \frac1{n^p}$ Converges for $p > 1$ | |
| 392 There are apparently $3072$ ways to draw this flower. But why? | |
| 393 Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction | |
| 394 Proof that the trace of a matrix is the sum of its eigenvalues | |
| 395 Limit of $L^p$ norm | |
| 396 Is there a categorical definition of submetry? | |
| 397 Deleting any digit yields a prime... is there a name for this? | |
| 398 Inverse of the sum of matrices | |
| 399 What is $dx$ in integration? | |
| 400 Is $2048$ the highest power of $2$ with all even digits (base ten)? | |
| 401 Why is Eulers Gamma function the best extension of the factorial function to the reals? | |
| 402 $L^p$ and $L^q$ space inclusion | |
| 403 Do we have negative prime numbers? | |
| 404 Why do people use it is easy to prove? | |
| 405 Taking Seats on a Plane | |
| 406 Why is $1^{\infty}$ considered to be an indeterminate form | |
| 407 Mathematical ideas that took long to define rigorously | |
| 408 Open problems in General Relativity | |
| 409 How far can one get in analysis without leaving $\mathbb{Q}$? | |
| 410 How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? | |
| 411 Rational roots of polynomials | |
| 412 Lesser-known integration tricks | |
| 413 A variation of Fermats little theorem in the form $a^{n-d}\equiv a$ (mod $p$). | |
| 414 Is there a homology theory that counts connected components of a space? | |
| 415 Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$ | |
| 416 An Introduction to Tensors | |
| 417 Transpose of inverse vs inverse of transpose | |
| 418 How to prove Eulers formula: $e^{i\varphi}=\cos(\varphi) +i\sin(\varphi)$? | |
| 419 Intuition behind Matrix Multiplication | |
| 420 Striking applications of integration by parts | |
| 421 Why is the Penrose triangle impossible? | |
| 422 Software for drawing geometry diagrams | |
| 423 How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number? | |
| 424 Examples of mathematical discoveries which were kept as a secret | |
| 425 What properties of busy beaver numbers are computable? | |
| 426 What happens when we (incorrectly) make improper fractions proper again? | |
| 427 Can you provide me historical examples of pure mathematics becoming useful? | |
| 428 What are the most overpowered theorems in mathematics? | |
| 429 Do we know if there exist true mathematical statements that can not be proven? | |
| 430 Is there any integral for the Golden Ratio? | |
| 431 Using proof by contradiction vs proof of the contrapositive | |
| 432 Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$ | |
| 433 Induction on Real Numbers | |
| 434 Proof that ${\left(\pi^\pi\right)}^{\pi^\pi}$ (and now $\pi^{\left(\pi^{\pi^\pi}\right)}$) is a noninteger. | |
| 435 The Hole in One Pizza | |
| 436 Proof of $\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=\frac{1}{24}$ | |
| 437 What functions can be made continuous by mixing up their domain? | |
| 438 Is there a general formula for solving 4th degree equations (quartic)? | |
| 439 Discontinuous derivative. | |
| 440 Monty hall problem extended. | |
| 441 The sum of an uncountable number of positive numbers | |
| 442 Is Apple ipad / tablet good for mathematics students? | |
| 443 Stopping the Will I need this for the test question | |
| 444 Are there any open mathematical puzzles? | |
| 445 Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$? | |
| 446 How to distinguish between walking on a sphere and walking on a torus? | |
| 447 Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional? | |
| 448 Is there another simpler method to solve this elementary school math problem? | |
| 449 Most ambiguous and inconsistent phrases and notations in maths | |
| 450 Why does factoring eliminate a hole in the limit? | |
| 451 Whats the point in being a skeptical learner | |
| 452 Good book for self study of a First Course in Real Analysis | |
| 453 Overview of basic results about images and preimages | |
| 454 How to determine with certainty that a function has no elementary antiderivative? | |
| 455 What actually is a polynomial? | |
| 456 Sum of random decreasing numbers between 0 and 1: does it converge?? | |
| 457 Are there real-life relations which are symmetric and reflexive but not transitive? | |
| 458 Calculate Rotation Matrix to align Vector A to Vector B in 3d? | |
| 459 Whats new in higher dimensions? | |
| 460 How do you describe your mathematical research in laymans terms? | |
| 461 Pythagorean triples that survive Eulers totient function | |
| 462 Whats the significance of Tates thesis? | |
| 463 What is the difference between singular value and eigenvalue? | |
| 464 Intuition of the meaning of homology groups | |
| 465 Why does the series $\sum_{n=1}^\infty\frac1n$ not converge? | |
| 466 Why does an argument similiar to 0.999...=1 show 999...=-1? | |
| 467 Does a cubic matrix exist? | |
| 468 Is the following matrix invertible? | |
| 469 Do most mathematicians know most topics in mathematics? | |
| 470 Slice of pizza with no crust | |
| 471 Has lack of mathematical rigour killed anybody before? | |
| 472 Alternative notation for exponents, logs and roots? | |
| 473 Math and mental fatigue | |
| 474 What is the Riemann-Zeta function? | |
| 475 Why do both sine and cosine exist? | |
| 476 What is the best book to learn probability? | |
| 477 The square roots of different primes are linearly independent over the field of rationals | |
| 478 Can someone explain the math behind tessellation? | |
| 479 Where to start learning Linear Algebra? | |
| 480 Intuitively, what is the difference between Eigendecomposition and Singular Value Decomposition? | |
| 481 Looking for an intuitive explanation why the row rank is equal to the column rank for a matrix | |
| 482 Example of infinite field of characteristic $p\neq 0$ | |
| 483 Is non-standard analysis worth learning? | |
| 484 Connection between Fourier transform and Taylor series | |
| 485 Are we allowed to compare infinities? | |
| 486 Online tool for making graphs (vertices and edges)? | |
| 487 Whats 4 times more likely than 80%? | |
| 488 Simple theorems that are instances of deep mathematics | |
| 489 Do Arithmetic Mean and Geometric Mean of Prime Numbers converge? | |
| 490 Partial derivative in gradient descent for two variables | |
| 491 Apparently sometimes $1/2 < 1/4$? | |
| 492 Is the product of two Gaussian random variables also a Gaussian? | |
| 493 Intuitive explanation of entropy | |
| 494 The Best of Dover Books (a.k.a the best cheap mathematical texts) | |
| 495 Are mathematical articles on Wikipedia reliable? | |
| 496 What are the differences between rings, groups, and fields? | |
| 497 Why do units (from physics) behave like numbers? | |
| 498 Studying Euclidean geometry using hyperbolic criteria | |
| 499 Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$ | |
| 500 Identification of a curious function | |
| 501 What is the difference between regression and classification? | |
| 502 How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen? | |
| 503 How do you respond to I was always bad at math? | |
| 504 What are the numbers before and after the decimal point referred to in mathematics? | |
| 505 Can you explain the Axiom of choice in simple terms? | |
| 506 Why do we use the word scalar and not number in Linear Algebra? | |
| 507 What is the difference between Fourier series and Fourier transformation? | |
| 508 What is the difference between a point and a vector? | |
| 509 The direct sum $\oplus$ versus the cartesian product $\times$ | |
| 510 Is the blue area greater than the red area? | |
| 511 Does $R[x] \cong S[x]$ imply $R \cong S$? | |
| 512 Why does mathematical convention deal so ineptly with multisets? | |
| 513 List of interesting math podcasts? | |
| 514 Can you raise a number to an irrational exponent? | |
| 515 Examples of mathematical results discovered late | |
| 516 $\pi$ in arbitrary metric spaces | |
| 517 Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$ | |
| 518 Is there any mathematical reason for this digit-repetition-show? | |
| 519 Visually deceptive proofs which are mathematically wrong | |
| 520 Best book of topology for beginner? | |
| 521 Can someone explain Gödels incompleteness theorems in layman terms? | |
| 522 Why is $1$ not a prime number? | |
| 523 Studying for the Putnam Exam | |
| 524 Intuitive interpretation of the Laplacian | |
| 525 what is expected from a PhD student? | |
| 526 Why is the eigenvector of a covariance matrix equal to a principal component? | |
| 527 Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$ | |
| 528 Is it possible for a function to be in $L^p$ for only one $p$? | |
| 529 What are some examples of notation that really improved mathematics? | |
| 530 Classification of prime ideals of $\mathbb{Z}[X]$ | |
| 531 Division by $0$ | |
| 532 Application of Hilberts basis theorem in representation theory | |
| 533 Is $0$ a natural number? | |
| 534 Why is negative times negative = positive? | |
| 535 On Ph.D. Qualifying Exams | |
| 536 Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$ | |
| 537 What are some examples of a mathematical result being counterintuitive? | |
| 538 Can you be 1/12th Cherokee? | |
| 539 Why did mathematicians take Russells paradox seriously? | |
| 540 Values of $\sum_{n=0}^\infty x^n$ and $\sum_{n=0}^N x^n$ | |
| 541 How to find ${\large\int}_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx$ | |
| 542 What is the probability that a point chosen randomly from inside an equilateral triangle is closer to the center than to any of the edges? | |
| 543 Why is learning modern algebraic geometry so complicated? | |
| 544 What should be the intuition when working with compactness? | |
| 545 Motivation of irrationality measure | |
| 546 Show that the determinant of $A$ is equal to the product of its eigenvalues | |
| 547 The median minimizes the sum of absolute deviations (the $ {\ell}_{1} $ norm) | |
| 548 Why is gradient the direction of steepest ascent? | |
| 549 Learning Lambda Calculus | |
| 550 Is there a function that grows faster than exponentially but slower than a factorial? | |
| 551 How to find solutions of linear Diophantine ax + by = c? | |
| 552 What is category theory useful for? | |
| 553 Are half of all numbers odd? | |
| 554 Can $x^{x^{x^x}}$ be a rational number? | |
| 555 Prove that $C\exp(x)$ is the only set of functions for which $f(x) = f(x)$ | |
| 556 Are if and iff interchangeable in definitions? | |
| 557 Is there an integral that proves $\pi > 333/106$? | |
| 558 Past open problems with sudden and easy-to-understand solutions | |
| 559 How to prove $\int_0^1\tan^{-1}\left[\frac{\tanh^{-1}x-\tan^{-1}x}{\pi+\tanh^{-1}x-\tan^{-1}x}\right]\frac{dx}{x}=\frac{\pi}{8}\ln\frac{\pi^2}{8}?$ | |
| 560 What remains in a students mind | |
| 561 Proof $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$ | |
| 562 Why is $\infty \cdot 0$ not clearly equal to $0$? | |
| 563 What are good books to learn graph theory? | |
| 564 Can an irrational number raised to an irrational power be rational? | |
| 565 Advantages of Mathematics competition/olympiad students in Mathematical Research | |
| 566 Whats the difference between predicate and propositional logic? | |
| 567 How can I find the surface area of a normal chicken egg? | |
| 568 Why does LHopitals rule fail in calculating $\lim_{x \to \infty} \frac{x}{x+\sin(x)}$? | |
| 569 Why study linear algebra? | |
| 570 Why is integration so much harder than differentiation? | |
| 571 Why is $\cos (90)=-0.4$ in WebGL? | |
| 572 Why “characteristic zero” and not “infinite characteristic”? | |
| 573 Why are the solutions of polynomial equations so unconstrained over the quaternions? | |
| 574 Making Friends around a Circular Table | |
| 575 Is There An Injective Cubic Polynomial $\mathbb Z^2 \rightarrow \mathbb Z$? | |
| 576 Real life applications of Topology | |
| 577 Whats your favorite proof accessible to a general audience? | |
| 578 Pullback and Pushforward Isomorphism of Sheaves | |
| 579 Physical meaning of the null space of a matrix | |
| 580 How do you explain to a 5th grader why division by zero is meaningless? | |
| 581 Overview of basic facts about Cauchy functional equation | |
| 582 Is 10 closer to infinity than 1? | |
| 583 Examples of problems that are easier in the infinite case than in the finite case. | |
| 584 Help find hard integrals that evaluate to $59$? | |
| 585 Is the inverse of a symmetric matrix also symmetric? | |
| 586 When to learn category theory? | |
| 587 In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False? | |
| 588 Modular exponentiation by hand ($a^b\bmod c$) | |
| 589 How were old-school mathematics graphics created? | |
| 590 Infiniteness of non-twin primes. | |
| 591 probability $2/4$ vs $3/6$ | |
| 592 Continuous projections on $\ell_1$ with norm $>1$ | |
| 593 Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$? | |
| 594 All real numbers in $[0,2]$ can be represented as $\sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \dots}}}$ | |
| 595 Olympiad Inequality $\sum\limits_{cyc} \frac{x^4}{8x^3+5y^3} \geqslant \frac{x+y+z}{13}$ | |
| 596 What is the difference between independent and mutually exclusive events? | |
| 597 What is the Jacobian matrix? | |
| 598 If squaring a number means multiplying that number with itself then shouldnt taking square root of a number mean to divide a number by itself? | |
| 599 Is there a known well ordering of the reals? | |
| 600 Intuition behind Conditional Expectation | |
| 601 Is there an inverted dot product? | |
| 602 Find the average of $\sin^{100} (x)$ in 5 minutes? | |
| 603 How to find the Galois group of a polynomial? | |
| 604 Strategies for Effective Self-Study | |
| 605 What did Alan Turing mean when he said he didnt fully understand dy/dx? | |
| 606 Is there a domain larger than (i.e., a supserset of) the complex number domain? | |
| 607 Motivation for the rigour of real analysis | |
| 608 Probability that a stick randomly broken in five places can form a tetrahedron | |
| 609 The deep reason why $\int \frac{1}{x}\operatorname{d}x$ is a transcendental function ($\log$) | |
| 610 Expected time to roll all 1 through 6 on a die | |
| 611 Proofs of AM-GM inequality | |
| 612 The math behind Warren Buffetts famous rule – never lose money | |
| 613 Compute $\int_0^{\pi/4}\frac{(1-x^2)\ln(1+x^2)+(1+x^2)-(1-x^2)\ln(1-x^2)}{(1-x^4)(1+x^2)} x\exp(\frac{x^2-1}{x^2+1}) dx$ | |
| 614 derivative of cost function for Logistic Regression | |
| 615 Construction of a Borel set with positive but not full measure in each interval | |
| 616 Are the proofs by contradiction weaker than other proofs? | |
| 617 Why are There No Triernions (3-dimensional analogue of complex numbers / quaternions)? | |
| 618 What parts of a pure mathematics undergraduate curriculum have been discovered since $1964?$ | |
| 619 Is black hole pattern possible in Conways Game of Life that eats/clears everything? | |
| 620 A multiplication algorithm found in a book by Paul Erdős: how does it work? | |
| 621 Are all limits solvable without LHôpital Rule or Series Expansion | |
| 622 $n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesnt use Chebyshevs theorem? | |
| 623 Convergence of $\sum_{n=1}^{\infty} \frac{\sin(n!)}{n}$ | |
| 624 When is matrix multiplication commutative? | |
| 625 What is the difference and relationship between the binomial and Bernoulli distributions? | |
| 626 Is infinity a number? | |
| 627 Am I just not smart enough? | |
| 628 What is the smallest unknown natural number? | |
| 629 Is there a positive definition for irrational numbers? | |
| 630 Solving Special Function Equations Using Lie Symmetries | |
| 631 Gross-Zagier formulae outside of number theory | |
| 632 Why is the derivative of a circles area its perimeter (and similarly for spheres)? | |
| 633 Getting better at proofs | |
| 634 Mathematical equivalent of Feynmans Lectures on Physics? | |
| 635 How often does it happen that the oldest person alive dies? | |
| 636 Do mathematicians, in the end, always agree? | |
| 637 Can an infinite sum of irrational numbers be rational? | |
| 638 Unexpected examples of natural logarithm | |
| 639 What are the Axiom of Choice and Axiom of Determinacy? | |
| 640 Least prime of the form $38^n+31$ | |
| 641 Different ways to prove there are infinitely many primes? | |
| 642 Can you give an example of a complex math problem that is easy to solve? | |
| 643 Proof of Frullanis theorem | |
| 644 More than 99% of groups of order less than 2000 are of order 1024? | |
| 645 Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square | |
| 646 Does a four-variable analog of the Hall-Witt identity exist? | |
| 647 How do I get the square root of a complex number? | |
| 648 Prove that $||x|-|y||\le |x-y|$ | |
| 649 Prove that simultaneously diagonalizable matrices commute | |
| 650 Could someone explain conditional independence? | |
| 651 Good Book On Combinatorics | |
| 652 A good way to retain mathematical understanding? | |
| 653 Why is it important for a matrix to be square? | |
| 654 Are there real world applications of finite group theory? | |
| 655 Why cant calculus be done on the rational numbers? | |
| 656 Why is there no remainder in multiplication | |
| 657 What are the issues in modern set theory? | |
| 658 What makes a theorem fundamental? | |
| 659 Why is an average of an average usually incorrect? | |
| 660 Finding a primitive root of a prime number | |
| 661 Do factorials really grow faster than exponential functions? | |
| 662 What exactly is the difference between a derivative and a total derivative? | |
| 663 Nice proofs of $\zeta(4) = \frac{\pi^4}{90}$? | |
| 664 Why, historically, do we multiply matrices as we do? | |
| 665 Why do we still do symbolic math? | |
| 666 Fastest way to meet, without communication, on a sphere? | |
| 667 Grothendieck s question - any update? | |
| 668 How to sum this series for $\pi/2$ directly? | |
| 669 In a family with two children, what are the chances, if one of the children is a girl, that both children are girls? | |
| 670 Can someone clearly explain about the lim sup and lim inf? | |
| 671 How can I understand and prove the sum and difference formulas in trigonometry? | |
| 672 Is zero odd or even? | |
| 673 Continuity of the roots of a polynomial in terms of its coefficients | |
| 674 In calculus, which questions can the naive ask that the learned cannot answer? | |
| 675 Why are mathematical proofs that rely on computers controversial? | |
| 676 Getting Students to Not Fear Confusion | |
| 677 Topology: The Board Game | |
| 678 Fibonacci number that ends with 2014 zeros? | |
| 679 What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into? | |
| 680 Generalization of Liouvilles theorem | |
| 681 Complete course of self-study | |
| 682 Motivation for Ramanujans mysterious $\pi$ formula | |
| 683 What is the most unusual proof you know that $\sqrt{2}$ is irrational? | |
| 684 How do we know an $ \aleph_1 $ exists at all? | |
| 685 Connected metric spaces with disjoint open balls | |
| 686 Why is the volume of a sphere $\frac{4}{3}\pi r^3$? | |
| 687 Incremental averageing | |
| 688 How to show that a set of discontinuous points of an increasing function is at most countable | |
| 689 If I flip a coin 1000 times in a row and it lands on heads all 1000 times, what is the probability that its an unfair coin? | |
| 690 What made you choose your research field? | |
| 691 How Do You Actually Do Your Mathematics? | |
| 692 Is this continuous analogue to the AM–GM inequality true? | |
| 693 Open mathematical questions for which we really, really have no idea what the answer is | |
| 694 Is the derivative the natural logarithm of the left-shift? | |
| 695 Has Prof. Otelbaev shown existence of strong solutions for Navier-Stokes equations? | |
| 696 lim sup and lim inf of sequence of sets. | |
| 697 Why is it hard to prove whether $\pi+e$ is an irrational number? | |
| 698 How do you go about learning mathematics? | |
| 699 Is $[0,1]$ a countable disjoint union of closed sets? | |
| 700 Chatting about mathematics (with real-time LaTeX rendering) | |
| 701 Calculating the integral $\int_0^\infty \frac{\cos x}{1+x^2}\, \mathrm{d}x$ without using complex analysis | |
| 702 Finding the limit of $\frac {n}{\sqrt[n]{n!}}$ | |
| 703 What is the single most influential book every mathematician should read? | |
| 704 Logic puzzle: Which octopus is telling the truth? | |
| 705 Why is a geometric progression called so? | |
| 706 Why, intuitively, is the order reversed when taking the transpose of the product? | |
| 707 Prove the theorem on analytic geometry in the picture. | |
| 708 Good Physical Demonstrations of Abstract Mathematics | |
| 709 Can I think of Algebra like this? | |
| 710 Ways to evaluate $\int \sec \theta \, \mathrm d \theta$ | |
| 711 Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$ | |
| 712 Does this property characterize a space as Hausdorff? | |
| 713 All polynomials with no natural roots and integer coefficients such that $\phi(n)|\phi(P(n))$ | |
| 714 How to prove that eigenvectors from different eigenvalues are linearly independent | |
| 715 Lebesgue integral basics | |
| 716 Why rationalize the denominator? | |
| 717 Mathematicians ahead of their time? | |
| 718 Are all algebraic integers with absolute value 1 roots of unity? | |
| 719 Can we remove any prime number with this strange process? | |
| 720 Produce an explicit bijection between rationals and naturals? | |
| 721 Is math built on assumptions? | |
| 722 Riddles that can be solved by meta-assumptions | |
| 723 Why are vector spaces not isomorphic to their duals? | |
| 724 What are some examples of mathematics that had unintended useful applications much later? | |
| 725 Division by $0$ and its restrictions | |
| 726 Theorems with an extraordinary exception or a small number of sporadic exceptions | |
| 727 True or false? $x^2\ne x\implies x\ne 1$ | |
| 728 $\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis | |
| 729 An integral involving Airy functions $\int_0^\infty\frac{x^p}{\operatorname{Ai}^2 x + \operatorname{Bi}^2 x}\mathrm dx$ | |
| 730 Does notation ever become easier? | |
| 731 Mathematician vs. Computer: A Game | |
| 732 Non-textbook Math book recommendation to read to my kids | |
| 733 Cardioid in coffee mug? | |
| 734 Direct proof that the wedge product preserves integral cohomology classes? | |
| 735 How did Hermite calculate $e^{\pi\sqrt{163}}$ in 1859? | |
| 736 What does it mean to have a determinant equal to zero? | |
| 737 Why is the volume of a cone one third of the volume of a cylinder? | |
| 738 Dont see the point of the Fundamental Theorem of Calculus. | |
| 739 Comparing $\pi^e$ and $e^\pi$ without calculating them | |
| 740 Is Bayes Theorem really that interesting? | |
| 741 Unconventional mathematics books | |
| 742 Does LHôpitals work the other way? | |
| 743 Geometric interpretation of the Riemann-Roch for curves | |
| 744 Whats the difference between theorem, lemma and corollary? | |
| 745 Unusual mathematical terms | |
| 746 Is infinity an odd or even number? | |
| 747 How do you find the center of a circle with a pencil and a book? | |
| 748 Using we have in maths papers | |
| 749 How to learn from proofs? | |
| 750 What are Some Tricks to Remember Fatous Lemma? | |
| 751 Why dont analysts do category theory? | |
| 752 Defining a manifold without reference to the reals | |
| 753 Does a non-trivial solution exist for $f(x)=f(f(x))$? | |
| 754 A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent | |
| 755 A real number $x$ such that $x^n$ and $(x+1)^n$ are rational is itself rational | |
| 756 Expectation of the maximum of gaussian random variables | |
| 757 Simplest or nicest proof that $1+x \le e^x$ | |
| 758 What would base $1$ be? | |
| 759 Should I put number combinations like 1111111 onto my lottery ticket? | |
| 760 Continuous bijection from $(0,1)$ to $[0,1]$ | |
| 761 How is a system of axioms different from a system of beliefs? | |
| 762 Why cant you add apples and oranges, but you can multiply and divide them? | |
| 763 How can adding an infinite number of rationals yield an irrational number? | |
| 764 Example of a very simple math statement in old literature which is (verbatim) a pain to understand | |
| 765 Whats the largest possible volume of a taco, and how do I make one that big? | |
| 766 Limit of sequence in which each term is defined by the average of preceding two terms | |
| 767 Why are all the interesting constants so small? | |
| 768 Help me put these enormous numbers in order: googol, googol-plex-bang, googol-stack and so on | |
| 769 $4494410$ and friends | |
| 770 A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$ | |
| 771 Arithmetic-geometric mean of 3 numbers | |
| 772 Geometric way to view the truncated braid groups? | |
| 773 Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$ | |
| 774 How to find a general sum formula for the series: 5+55+555+5555+.....? | |
| 775 What is the difference between a class and a set? | |
| 776 Why is $\frac{987654321}{123456789} = 8.0000000729?!$ | |
| 777 The Langlands program for beginners | |
| 778 What makes elementary functions elementary? | |
| 779 Why would I want to multiply two polynomials? | |
| 780 If $x$, $y$, $x+y$, and $x-y$ are prime numbers, what is their sum? | |
| 781 Mathematicians Tensors vs. Physicists Tensors | |
| 782 Is the determinant that shows up accidental? | |
| 783 Given a die, what is the probability that the second roll of a die will be less than the first roll? | |
| 784 Why is the set of all sets a paradox, in Laymans terms? | |
| 785 Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$ | |
| 786 What seemingly innocuous results in mathematics require advanced proofs? | |
| 787 Prove $\left(\frac{2}{5}\right)^{\frac{2}{5}}<\ln{2}$ | |
| 788 How to convince a math teacher of this simple and obvious fact? | |
| 789 What kind of symmetry is the symmetric group about? | |
| 790 What are good math habits that have improved your mathematical practice?$ $ | |
| 791 math fallacy problem: $-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1$? | |
| 792 Cover of Gödel, Escher, Bach | |
| 793 Problems that become easier in a more general form | |
| 794 How prove this nice limit $\lim\limits_{n\to\infty}\frac{a_{n}}{n}=\frac{12}{\log{432}}$ | |
| 795 When does a sequence of rotated-and-circumscribed rectangles converge to a square? | |
| 796 Why is the area under a curve the integral? | |
| 797 Good 1st PDE book for self study | |
| 798 Importance of matrix rank | |
| 799 Much less than, what does that mean? | |
| 800 Simple beautiful math proof | |
| 801 Anecdotes about famous mathematicians or physicists | |
| 802 Why do bell curves appear everywhere? | |
| 803 What are the differences between class, set, family, and collection? | |
| 804 What is the solution to Nashs problem presented in A Beautiful Mind? | |
| 805 Factorial and exponential dual identities | |
| 806 The pepperoni pizza problem | |
| 807 How to evaluate $\int_{0}^{\infty} \frac{x^{-\mathfrak{i}a}}{x^2+bx+1} \,\mathrm{d}x$ using complex analysis? | |
| 808 A Case Against the Math Gene | |
| 809 Complexity class of comparison of power towers | |
| 810 Does $\lfloor \sqrt{p} \rfloor$ generate all natural numbers? | |
| 811 Pointwise vs. Uniform Convergence | |
| 812 What is the algebraic intuition behind Vieta jumping in IMO1988 Problem 6? | |
| 813 GRE Subject Test - Past Papers, Books, Advice | |
| 814 Can the golden ratio accurately be expressed in terms of $e$ and $\pi$ | |
| 815 How do you explain the concept of logarithm to a five year old? | |
| 816 If $f_k \to f$ a.e. and the $L^p$ norms converge, then $f_k \to f$ in $L^p$ | |
| 817 What is a real-world metaphor for irrational numbers? | |
| 818 Intuitive explanation of Cauchys Integral Formula in Complex Analysis | |
| 819 Why should I believe in weak solutions to PDEs? | |
| 820 Explain homotopy to me | |
| 821 Prove elementarily that $\sqrt[n+1] {(n+1)!} - \sqrt[n] {n!}$ is strictly decreasing | |
| 822 Root Calculation by Hand | |
| 823 What does the dot product of two vectors represent? | |
| 824 Whats the difference between simple induction and strong induction? | |
| 825 What is the most elegant proof of the Pythagorean theorem? | |
| 826 Is the vector cross product only defined for 3D? | |
| 827 Best Maths Books for Non-Mathematicians | |
| 828 Self-studying real analysis — Tao or Rudin? | |
| 829 What are differences between affine space and vector space? | |
| 830 If $(a_n)\subset[0,\infty)$ is non-increasing and $\sum a_n<\infty$, then $\lim{n a_n} = 0$ | |
| 831 Is arrow notation for vectors not mathematically mature? | |
| 832 I roll a die repeatedly until I get 6, and then count the number of 3s I got. Whats my expected number of 3s? | |
| 833 What is the difference between a Hamel basis and a Schauder basis? | |
| 834 Is there any conjecture that has been proved to be solvable/provable but whose direct solution/proof is not yet known? | |
| 835 Results that came out of nowhere. | |
| 836 Can the product of infinitely many elements from $\mathbb Q$ be irrational? | |
| 837 Divisibility by 7 rule, and Congruence Arithmetic Laws | |
| 838 Can you make a sphere out of a plane? | |
| 839 Cutting sticks puzzle | |
| 840 The Right Triangle Game | |
| 841 Geometric interpretation of $\det(A^T) = \det(A)$ | |
| 842 How to prove that exponential grows faster than polynomial? | |
| 843 Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when its an integer | |
| 844 Good book for self study of functional analysis | |
| 845 If $S$ is an infinite $\sigma$ algebra on $X$ then $S$ is not countable | |
| 846 $x^y = y^x$ for integers $x$ and $y$ | |
| 847 100 blue-eyed islanders puzzle: 3 questions | |
| 848 Surprise exam paradox? | |
| 849 Demystify integration of $\int \frac{1}{x} \mathrm dx$ | |
| 850 Your favourite maths puzzles | |
| 851 Number of simple edge-disjoint paths needed to cover a planar graph | |
| 852 Good abstract algebra books for self study | |
| 853 Does convergence in $L^p$ imply convergence almost everywhere? | |
| 854 Is there any difference between mapping and function? | |
| 855 Normal subgroup of prime index | |
| 856 Implies ($\Rightarrow$) vs. Entails ($\models$) vs. Provable ($\vdash$) | |
| 857 Learning mathematics as if an absolute beginner? | |
| 858 Why did no student correctly find a pair of $2\times 2$ matrices with the same determinant and trace that are not similar? | |
| 859 Will it become impossible to learn math? | |
| 860 Should an undergrad accept that some things dont make sense, or study the foundation of mathematics to resolve this? | |
| 861 Is $0! = 1$ because there is only one way to do nothing? | |
| 862 Conjecture $\int_0^1\frac{\mathrm dx}{\sqrt{1-x}\ \sqrt[4]x\ \sqrt[4]{2-x\,\sqrt3}}\stackrel?=\frac{2\,\sqrt2}{3\,\sqrt[8]3}\pi$ | |
| 863 Why are groups more important than semigroups? | |
| 864 Can someone explain these strange properties of $10, 11, 12$ and $13$? | |
| 865 What is the best book for studying discrete mathematics? | |
| 866 Why cant you square both sides of an equation? | |
| 867 For any prime $p > 3$, why is $p^2-1$ always divisible by 24? | |
| 868 Is the notorious $n^2 + n + 41$ prime generator the last of its type? | |
| 869 Construct a function which is continuous in $[1,5]$ but not differentiable at $2, 3, 4$ | |
| 870 Easy math proofs or visual examples to make high school students enthusiastic about math | |
| 871 Why do we define quotient groups for normal subgroups only? | |
| 872 Formal proof for $(-1) \times (-1) = 1$ | |
| 873 Mathematically, why was the Enigma machine so hard to crack? | |
| 874 Is it possible to represent every huge number in abbreviated form? | |
| 875 $1=2$ | Continued fraction fallacy | |
| 876 How is a group made up of simple groups? | |
| 877 Cute Determinant Question | |
| 878 Modelling the Moving Sofa | |
| 879 Graph theoretic proof: For six irrational numbers, there are three among them such that the sum of any two of them is irrational. | |
| 880 Contest problem: Show $\sum_{n = 1}^\infty \frac{n^2a_n}{(a_1+\cdots+a_n)^2}0$, $\sum_{n = 1}^\infty \frac{1}{a_n}<\infty$ | |
| 881 Proof of every convex function is continuous | |
| 882 Are calculus and real analysis the same thing? | |
| 883 A goat tied to a corner of a rectangle | |
| 884 Predicting Real Numbers | |
| 885 Why is abuse of notation tolerated? | |
| 886 Why are gauge integrals not more popular? | |
| 887 Do numbers get worse than transcendental? | |
| 888 Whats so special about standard deviation? | |
| 889 What concept does an open set axiomatise? | |
| 890 Would you ever stop rolling the die? | |
| 891 Geometric & Intuitive Meaning of $SL(2,R)$, $SU(2)$, etc... & Representation Theory of Special Functions | |
| 892 References for multivariable calculus | |
| 893 When is the closure of an open ball equal to the closed ball? | |
| 894 Can manholes be made in other shapes than circles, that prevent the cover from being able to fall down its own hole? | |
| 895 In what sense are math axioms true? | |
| 896 Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$ | |
| 897 Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$ | |
| 898 What are some conceptualizations that work in mathematics but are not strictly true? | |
| 899 Why do mathematicians sometimes assume famous conjectures in their research? | |
| 900 Where are the axioms? | |
| 901 How to prove that $\frac{\zeta(2) }{2}+\frac{\zeta (4)}{2^3}+\frac{\zeta (6)}{2^5}+\frac{\zeta (8)}{2^7}+\cdots=1$? | |
| 902 How do we know that Cantors diagonalization isnt creating a different decimal of the same number? | |
| 903 In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual? | |
| 904 Determining information in minimum trials (combinatorics problem) | |
| 905 What is the term for a factorial type operation, but with summation instead of products? | |
| 906 Difference between gradient and Jacobian | |
| 907 Why does Turn! Turn! Turn! equal 241217.524881? | |
| 908 Is there a size of rectangle that retains its ratio when its folded in half? | |
| 909 What is ultrafinitism and why do people believe it? | |
| 910 Decidability of the Riemann Hypothesis vs. the Goldbach Conjecture | |
| 911 Intuition in algebra? | |
| 912 A continuous, nowhere differentiable but invertible function? | |
| 913 Conjecture $\int_0^1\frac{dx}{\sqrt[3]x\,\sqrt[6]{1-x}\,\sqrt{1-x\left(\sqrt{6}\sqrt{12+7\sqrt3}-3\sqrt3-6\right)^2}}=\frac\pi9(3+\sqrt2\sqrt[4]{27})$ | |
| 914 Can someone explain this integration trick for log-sine integrals? | |
| 915 Polynomials such that roots=coefficients | |
| 916 Does $X\times S^1\cong Y\times S^1$ imply that $X\times\mathbb R\cong Y\times\mathbb R$? | |
| 917 Do groups, rings and fields have practical applications in CS? If so, what are some? | |
| 918 What is special about the numbers 9801, 998001, 99980001 ..? | |
| 919 How does Cantors diagonal argument work? | |
| 920 Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$ | |
| 921 Why is a circle in a plane surrounded by 6 other circles? | |
| 922 Expected number of unpecked chicks - NYT article | |
| 923 Whats the difference between $\mathbb{R}^2$ and the complex plane? | |
| 924 What is your favorite application of the Pigeonhole Principle? | |
| 925 Is mathematics just a bunch of nested empty sets? | |
| 926 Easy example why complex numbers are cool | |
| 927 Why is the construction of the real numbers important? | |
| 928 Any rectangular shape on a calculator numpad when divided by 11 gives an integer. Why? | |
| 929 Calculating the volume of a restaurant take-away box that is circular on the bottom and square on the top | |
| 930 Paul Erdoss Two-Line Functional Analysis Proof | |
| 931 Numbers $n$ such that the digit sum of $n^2$ is a square | |
| 932 How to solve these two simultaneous divisibilities : $n+1\mid m^2+1$ and $m+1\mid n^2+1$ | |
| 933 Do most numbers have exactly $3$ prime factors? | |
| 934 Can a row of five equilateral triangles tile a big equilateral triangle? | |
| 935 Variance of sample variance? | |
| 936 Union of two vector subspaces not a subspace? | |
| 937 Probability density function vs. probability mass function | |
| 938 Determinant of a non-square matrix | |
| 939 What is a simple example of an unprovable statement? | |
| 940 Mathematical precise definition of a PDE being elliptic, parabolic or hyperbolic | |
| 941 Does commutativity imply Associativity? | |
| 942 What is the Tor functor? | |
| 943 100 Soldiers riddle | |
| 944 Why does Friedberg say that the role of the determinant is less central than in former times? | |
| 945 Is Lagranges theorem the most basic result in finite group theory? | |
| 946 Is $\sqrt {2 \sqrt {3 \sqrt {4 \ldots}}}$ algebraic or transcendental? | |
| 947 $6!\cdot 7!=10!$. Is there a natural bijection between $S_6\times S_7$ and $S_{10}$? | |
| 948 Show that the set of all finite subsets of $\mathbb{N}$ is countable. | |
| 949 $X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed | |
| 950 Why are rotational matrices not commutative? | |
| 951 How to use the Extended Euclidean Algorithm manually? | |
| 952 How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$? | |
| 953 What are some interpretations of Von Neumanns quote? | |
| 954 Why does the Mandelbrot set contain (slightly deformed) copies of itself? | |
| 955 If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$ | |
| 956 General request for a book on mathematical history, for a VERY advanced reader. | |
| 957 Terence Tao–type books in other fields? | |
| 958 Alice and Bob play the determinant game | |
| 959 Is there a definitive guide to speaking mathematics? | |
| 960 $\frac{1}{n}$ as a difference of Egyptian fractions with all denominators $<n$ | |
| 961 What are the practical applications of the Taylor Series? | |
| 962 Expected Number of Coin Tosses to Get Five Consecutive Heads | |
| 963 Understanding of the theorem that all norms are equivalent in finite dimensional vector spaces | |
| 964 Why is $e^{\pi \sqrt{163}}$ almost an integer? | |
| 965 $\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$ | |
| 966 Does mathematics require axioms? | |
| 967 The myth of no prime formula? | |
| 968 What is Bra and Ket notation and how does it relate to Hilbert spaces? | |
| 969 Intuitive meaning of Exact Sequence | |
| 970 Whats so natural about the base of natural logarithms? | |
| 971 What does surface area of a sphere actually mean (in terms of elementary school mathematics)? | |
| 972 The closed form of $\int_0^{\pi/4}\frac{\log(1-x) \tan^2(x)}{1-x\tan^2(x)} \ dx$ | |
| 973 Can one deduce Liouvilles theorem (in complex analysis) from the non-emptiness of spectra in complex Banach algebras? | |
| 974 How to get a reflection vector? | |
| 975 Prove that $i^i$ is a real number | |
| 976 Is there a bijective map from $(0,1)$ to $\mathbb{R}$? | |
| 977 Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$? | |
| 978 Cardinality of set of real continuous functions | |
| 979 A and B disjoint, A compact, and B closed implies there is positive distance between both sets | |
| 980 Why is a full turn of the circle 360°? Why not any other number? | |
| 981 Is there any easy way to understand the definition of Gaussian Curvature? | |
| 982 Are all infinities equal? | |
| 983 How to generate a random number between 1 and 10 with a six-sided die? | |
| 984 What is $\gcd(0,0)$? | |
| 985 In Linear Algebra, what is a vector? | |
| 986 Why isnt reflexivity redundant in the definition of equivalence relation? | |
| 987 Do you prove all theorems whilst studying? | |
| 988 Are all mathematicians human calculators? | |
| 989 Compute $ \lim\limits_{n \to \infty }\sin \sin \dots\sin n$ | |
| 990 Does mathematics become circular at the bottom? What is at the bottom of mathematics? | |
| 991 linear algebra over a division ring vs. over a field | |
| 992 Why is compactness in logic called compactness? | |
| 993 20 circles in the plane, all passing through the origin | |
| 994 How to find this limit: $A=\lim_{n\to \infty}\sqrt{1+\sqrt{\frac{1}{2}+\sqrt{\frac{1}{3}+\cdots+\sqrt{\frac{1}{n}}}}}$ | |
| 995 Visual proof of $\sum_{n=1}^\infty \frac{1}{n^4} = \frac{\pi^4}{90}$? | |
| 996 In $n>5$, topology = algebra | |
| 997 Conjectured formula for the Fabius function | |
| 998 Element-wise (or pointwise) operations notation? | |
| 999 Where exactly are complex numbers used in the real world? | |
| 1000 Is zero positive or negative? | |
| 1001 Prove that $\lim \limits_{n \to \infty} \frac{x^n}{n!} = 0$, $x \in \Bbb R$. | |
| 1002 Finding the Transform matrix from 4 projected points (with Javascript) | |
| 1003 Reference book on measure theory | |
| 1004 How to effectively and efficiently learn mathematics | |
| 1005 Logic problem: Identifying poisoned wines out of a sample, minimizing test subjects with constraints | |
| 1006 What is a universal property? | |
| 1007 Why are differentiable complex functions infinitely differentiable? | |
| 1008 Sheaf cohomology: what is it and where can I learn it? | |
| 1009 Koch snowflake paradox: finite area, but infinite perimeter | |
| 1010 I lost my love of math; Im getting it back. How can I determine if math is actually right for me? | |
| 1011 Is there a function with a removable discontinuity at every point? | |
| 1012 Direct proof that $\pi$ is not constructible | |
| 1013 Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$ | |
| 1014 Rigorous nature of combinatorics | |
| 1015 Integrals of $\sqrt{x+\sqrt{\phantom|\dots+\sqrt{x+1}}}$ in elementary functions | |
| 1016 Escaping infinitely many pursuers | |
| 1017 Relations between p norms | |
| 1018 Projection map being a closed map | |
| 1019 Math behind rotation in MS Paint | |
| 1020 The Monty Hall problem | |
| 1021 Why is the Möbius strip not orientable? | |
| 1022 Help me solve my fathers riddle and get my book back | |
| 1023 Why did my friend lose all his money? | |
| 1024 What is lost when we move from reals to complex numbers? | |
| 1025 Is linear algebra more “fully understood” than other maths disciplines? | |
| 1026 Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct? | |
| 1027 How deep is the liquid in a half-full hemisphere? | |
| 1028 Why do books titled Abstract Algebra mostly deal with groups/rings/fields? | |
| 1029 What exactly are eigen-things? | |
| 1030 What is an example of a sequence which thins out and is finite? | |
| 1031 Why is $\omega$ the smallest $\infty$? | |
| 1032 Besides proving new theorems, how can a person contribute to mathematics? | |
| 1033 The Intuition behind lHopitals Rule | |
| 1034 Motivation for spectral graph theory. | |
| 1035 Mathematicians shocked(?) to find pattern in prime numbers | |
| 1036 Closed form for $\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx$ | |
| 1037 Why cant the Polynomial Ring be a Field? | |
| 1038 A path to truly understanding probability and statistics | |
| 1039 Is there a shape with infinite area but finite perimeter? | |
| 1040 Infinite sets dont exist!? | |
| 1041 Fastest way to check if $x^y > y^x$? | |
| 1042 What is integration by parts, really? | |
| 1043 Conjectures (or intuitions) that turned out wrong in an interesting or useful way | |
| 1044 What is the intuition behind uniform continuity? | |
| 1045 Dividing 100% by 3 without any left | |
| 1046 Inscribing square in circle in just seven compass-and-straightedge steps | |
| 1047 List of interesting integrals for early calculus students | |
| 1048 The Duals of $l^\infty$ and $L^{\infty}$ | |
| 1049 Finite subgroups of the multiplicative group of a field are cyclic | |
| 1050 Whats a proof that the angles of a triangle add up to 180°? | |
| 1051 Stirlings formula: proof? | |
| 1052 Is learning (theoretical) physics useful/important for a mathematician? | |
| 1053 An example of a problem which is difficult but is made easier when a diagram is drawn | |
| 1054 Multiple-choice: sum of primes below $1000$ | |
| 1055 Fake induction proofs | |
| 1056 Theorem that von Neumann proved in five minutes. | |
| 1057 Why did mathematicians introduce the concept of uniform continuity? | |
| 1058 Why is $i! = 0.498015668 - 0.154949828i$? | |
| 1059 Gerrymandering on a high-genus surface/can I use my powers for evil? | |
| 1060 A strange integral: $\int_{-\infty}^{+\infty} {dx \over 1 + \left(x + \tan x\right)^2} = \pi.$ | |
| 1061 Denesting radicals like $\sqrt[3]{\sqrt[3]{2} - 1}$ | |
| 1062 How are mathematicians taught to write with such an expository style? | |
| 1063 Number of ways to write n as a sum of k nonnegative integers | |
| 1064 What is $\sqrt{i}$? | |
| 1065 Teenager solves Newton dynamics problem - where is the paper? | |
| 1066 Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$ | |
| 1067 What is the meaning of the third derivative of a function at a point | |
| 1068 Continuous mapping on a compact metric space is uniformly continuous | |
| 1069 Prove that the set of all algebraic numbers is countable | |
| 1070 Difference between metric and norm made concrete: The case of Euclid | |
| 1071 (Theoretical) Multivariable Calculus Textbooks | |
| 1072 Quotient ring of Gaussian integers | |
| 1073 String Theory: What to do? | |
| 1074 What is the chance to get a parking ticket in half an hour if the chance to get a ticket is 80% in 1 hour? | |
| 1075 Why there is no sign of logic symbols in mathematical texts? | |
| 1076 Connections between metrics, norms and scalar products (for understanding e.g. Banach and Hilbert spaces) | |
| 1077 Interesting and unexpected applications of $\pi$ | |
| 1078 How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$? | |
| 1079 Thurstons 37th way of thinking about the derivative | |
| 1080 Volumes of n-balls: what is so special about n=5? | |
| 1081 Ramanujan log-trigonometric integrals | |
| 1082 Finding out the area of a triangle if the coordinates of the three vertices are given | |
| 1083 Factorial, but with addition | |
| 1084 A simple explanation of eigenvectors and eigenvalues with big picture ideas of why on earth they matter | |
| 1085 Zero probability and impossibility | |
| 1086 Whats the difference between stochastic and random? | |
| 1087 How many connected components does $\mathrm{GL}_n(\mathbb R)$ have? | |
| 1088 Mathematical subjects you wish you learned earlier | |
| 1089 Closed form for $\sum \frac{1}{n^n}$ | |
| 1090 Why cant you pick socks using coin flips? | |
| 1091 Is it bad form to write mysterious proofs without explaining what one intends to do? | |
| 1092 Does $G\cong G/H$ imply that $H$ is trivial? | |
| 1093 What does the mysterious constant marked by C on a slide rule indicate? | |
| 1094 Two curious identities on $x^x$,$e$,and $\pi$ | |
| 1095 How to find perpendicular vector to another vector? | |
| 1096 How to calculate $\,(a-b)\bmod n\,$ and $ {-}b \bmod n$ | |
| 1097 How was the normal distribution derived? | |
| 1098 What is the proper way to study (more advanced) math? | |
| 1099 What are the applications of functional analysis? | |
| 1100 Very *mathematical* general physics book | |
| 1101 Why not include as a requirement that all functions must be continuous to be differentiable? | |
| 1102 Bag of tricks in Advanced Calculus/ Real Analysis/Complex Analysis | |
| 1103 What would have been our number system if humans had more than 10 fingers? Try to solve this puzzle. | |
| 1104 Does associativity imply commutativity? | |
| 1105 Algebraic Intuition for Homological Algebra and Applications to More Elementary Algebra | |
| 1106 A new imaginary number? $x^c = -x$ | |
| 1107 About Euclids Elements and modern video games | |
| 1108 A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum | |
| 1109 What is the math behind the game Spot It? | |
| 1110 Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!) | |
| 1111 Why determinant of a 2 by 2 matrix is the area of a parallelogram? | |
| 1112 Intuition behind using complementary CDF to compute expectation for nonnegative random variables | |
| 1113 Proof that a Combination is an integer | |
| 1114 A map is continuous if and only if for every set, the image of closure is contained in the closure of image | |
| 1115 Examples of finite nonabelian groups. | |
| 1116 Whats going on with compact implies sequentially compact? | |
| 1117 Best Algebraic Geometry text book? (other than Hartshorne) | |
| 1118 Why does the symbol for the multiplication operation change shape? | |
| 1119 Hanging a picture on the wall using two nails in such a way that removing any nail makes the picture fall down | |
| 1120 Why does the google calculator give $\tan 90^{\circ} = 1.6331779e^{+16}$? | |
| 1121 Reference request: introduction to commutative algebra | |
| 1122 When writing in math, do you use a comma or colon preceding an equation? | |
| 1123 Is linear algebra laying the foundation for something important? | |
| 1124 How come $32.5 = 31.5$? (The Missing Square puzzle.) | |
| 1125 Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods? | |
| 1126 Is there an easy way to show which spheres can be Lie groups? | |
| 1127 How to solve fifth-degree equations by elliptic functions? | |
| 1128 Intuition behind conjugation in group theory | |
| 1129 How to stop forgetting proofs - for a first course in Real Analysis? | |
| 1130 Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$ | |
| 1131 How to find the inverse modulo $m$? | |
| 1132 Finding a point along a line a certain distance away from another point! | |
| 1133 Graph theory: adjacency vs incident | |
| 1134 Space of bounded continuous functions is complete | |
| 1135 Why is $\Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}$? | |
| 1136 Simplest proof of Taylors theorem | |
| 1137 What algorithm is used by computers to calculate logarithms? | |
| 1138 Why do we need to learn integration techniques? | |
| 1139 Solving $DEF+FEF=GHH$, $KLM+KLM=NKL$, $ABC+ABC+ABC=BBB$ | |
| 1140 Why can a real number be defined as a Dedekind cut, that is, as a set of rational numbers? | |
| 1141 Mathematical research of Pokémon | |
| 1142 Why Zariski topology? | |
| 1143 Why should we prove obvious things? | |
| 1144 Drunk man with a set of keys. | |
| 1145 Will assuming the existence of a solution ever lead to a contradiction? | |
| 1146 What is $x^y$? How to understand it? | |
| 1147 Lebesgue measure theory vs differential forms? | |
| 1148 Naturally occurring non-Hausdorff spaces? | |
| 1149 What are some mathematical topics that involve adding and multiplying pictures? | |
| 1150 How to cut a cube out of a tree stump, such that a pair of opposing vertices are in the center? | |
| 1151 Why are the last two numbers of this sequence never prime? | |
| 1152 Is $ 0.112123123412345123456\dots $ algebraic or transcendental? | |
| 1153 Integral $\int_1^\infty\frac{\operatorname{arccot}\left(1+\frac{2\pi}{\operatorname{arcoth}x-\operatorname{arccsc}x}\right)}{\sqrt{x^2-1}}\mathrm dx$ | |
| 1154 Representing every positive rational number in the form of $(a^n+b^n)/(c^n+d^n)$ | |
| 1155 Difference between Fourier transform and Wavelets | |
| 1156 Is there a known mathematical equation to find the nth prime? | |
| 1157 Understanding Borel sets | |
| 1158 $\infty = -1 $ paradox | |
| 1159 What do $\pi$ and $e$ stand for in the normal distribution formula? | |
| 1160 Completion of rational numbers via Cauchy sequences | |
| 1161 Convergence of $\sqrt{n}x_{n}$ where $x_{n+1} = \sin(x_{n})$ | |
| 1162 Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even | |
| 1163 Why does being holomorphic imply so much about a function? | |
| 1164 Why should I care about adjoint functors | |
| 1165 How did Euler prove the Mersenne number $2^{31}-1$ is a prime so early in history? | |
| 1166 Pseudo Proofs that are intuitively reasonable | |
| 1167 Is $\sqrt1+\sqrt2+\dots+\sqrt n$ ever an integer? | |
| 1168 Is this determinant identity known? | |
| 1169 How was the Monsters existence originally suspected? | |
| 1170 How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$ | |
| 1171 Conjecture $_2F_1\left(\frac14,\frac34;\,\frac23;\,\frac13\right)=\frac1{\sqrt{\sqrt{\frac4{\sqrt{2-\sqrt[3]4}}+\sqrt[3]{4}+4}-\sqrt{2-\sqrt[3]4}-2}}$ | |
| 1172 What exactly is Laplace transform? | |
| 1173 $\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this? | |
| 1174 Can a limit of an integral be moved inside the integral? | |
| 1175 If $G/Z(G)$ is cyclic, then $G$ is abelian | |
| 1176 Prove if $n^2$ is even, then $n$ is even. | |
| 1177 An Explanation of the Kalman Filter | |
| 1178 Geometric interpretation for complex eigenvectors of a 2×2 rotation matrix | |
| 1179 Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$ | |
| 1180 incremental computation of standard deviation | |
| 1181 Intuitive explanation of a definition of the Fisher information | |
| 1182 Not every metric is induced from a norm | |
| 1183 Why does multiplying a number on a clock face by 10 and then halving, give the minutes? ${}{}$ | |
| 1184 Equivalent Definitions of the Operator Norm | |
| 1185 Is it morally right and pedagogically right to google answers to homework? | |
| 1186 Why is the complex plane shaped like it is? | |
| 1187 What are some applications of elementary linear algebra outside of math? | |
| 1188 How can one prove that $e<\pi$? | |
| 1189 Why does this miracle method for matrix inversion work? | |
| 1190 Is there an intuitive reason for a certain operation to be associative? | |
| 1191 Laplace, Legendre, Fourier, Hankel, Mellin, Hilbert, Borel, Z...: unified treatment of transforms? | |
| 1192 Are there infinitely many super-palindromes? | |
| 1193 Let, $A\subset\mathbb{R}^2$. Show that $A$ can contain at most one point $p$ such that $A$ is isometric to $A \setminus \{p\}$. | |
| 1194 Numerical phenomenon. Who can explain? | |
| 1195 Probability of 3 people in a room of 30 having the same birthday | |
| 1196 Difference between continuity and uniform continuity | |
| 1197 Compact sets are closed? | |
| 1198 What is mathematical research like? | |
| 1199 Difference between complete and closed set | |
| 1200 When does L Hopitals rule fail? | |
| 1201 In classical logic, why is $(p\Rightarrow q)$ True if $p$ is False and $q$ is True? | |
| 1202 Whats a good place to learn Lie groups? | |
| 1203 Why do we use a Least Squares fit? | |
| 1204 Chance of meeting in a bar | |
| 1205 What is the most expensive item I could buy with £50? | |
| 1206 Can someone please explain the Riemann Hypothesis to me... in English? | |
| 1207 Prove $0! = 1$ from first principles | |
| 1208 Why cant the second fundamental theorem of calculus be proved in just two lines? | |
| 1209 What is so interesting about the zeroes of the Riemann $\zeta$ function? | |
| 1210 Does every Abelian group admit a ring structure? | |
| 1211 Are there an infinite number of prime numbers where removing any number of digits leaves a prime? | |
| 1212 Japanese Temple Problem From 1844 | |
| 1213 The limit of truncated sums of harmonic series, $\lim\limits_{k\to\infty}\sum_{n=k+1}^{2k}{\frac{1}{n}}$ | |
| 1214 Understandable questions which are hard for non-mathematicians but easy for mathematicians | |
| 1215 Do there exist pairs of distinct real numbers whose arithmetic, geometric and harmonic means are all integers? | |
| 1216 Fractal behavior along the boundary of convergence? | |
| 1217 Are there any valid continuous Sudoku grids? | |
| 1218 A nasty integral of a rational function | |
| 1219 Show that $\int_{0}^{\pi/2}\frac {\log^2\sin x\log^2\cos x}{\cos x\sin x}\mathrm{d}x=\frac14\left( 2\zeta (5)-\zeta(2)\zeta (3)\right)$ | |
| 1220 How much does symbolic integration mean to mathematics? | |
| 1221 Evaluating sums and integrals using Taylors Theorem | |
| 1222 How to show that $\det(AB) =\det(A) \det(B)$? | |
| 1223 What is the equation for a 3D line? | |
| 1224 Density of sum of two independent uniform random variables on $[0,1]$ | |
| 1225 Use of without loss of generality | |
| 1226 Why is $\pi $ equal to $3.14159...$? | |
| 1227 $\sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt{7\cdots}}}}}$ approximation | |
| 1228 Limit $\frac{x^2y}{x^4+y^2}$ is found using polar coordinates but it is not supposed to exist. | |
| 1229 What is the largest eigenvalue of the following matrix? | |
| 1230 Good books on Math History | |
| 1231 Why is a circle 1-dimensional? | |
| 1232 Overview of basic results on cardinal arithmetic | |
| 1233 Is The empty set is a subset of any set a convention? | |
| 1234 How do people apply the Lebesgue integration theory? | |
| 1235 Why is radian so common in maths? | |
| 1236 Why do engineers use derivatives in discontinuous functions? Is it correct? | |
| 1237 Why are addition and multiplication commutative, but not exponentiation? | |
| 1238 $100$-th derivative of the function $f(x)=e^{x}\cos(x)$ | |
| 1239 Is it generally accepted that if you throw a dart at a number line you will NEVER hit a rational number? | |
| 1240 Is memory unimportant in doing mathematics? | |
| 1241 Theorems names that dont credit the right people | |
| 1242 What is the oldest open problem in geometry? | |
| 1243 Why the emphasis on Projective Space in Algebraic Geometry? | |
| 1244 Is there a great mathematical example for a 12-year-old? | |
| 1245 Am I too young to learn more advanced math and get a teacher? | |
| 1246 How to straighten a parabola? | |
| 1247 Geometric intuition for the tensor product of vector spaces | |
| 1248 How likely is it not to be anyones best friend? | |
| 1249 What is a real world application of polynomial factoring? | |
| 1250 What is the proof that the total number of subsets of a set is $2^n$? | |
| 1251 How to explain for my daughter that $\frac {2}{3}$ is greater than $\frac {3}{5}$? | |
| 1252 Where is the flaw in this proof that 1=2? (Derivative of repeated addition) | |
| 1253 How to write a good mathematical paper? | |
| 1254 What are the names of numbers in the binary system? | |
| 1255 Why $9$ & $11$ are special in divisibility tests using decimal digit sums? (casting out nines & elevens) | |
| 1256 Is it technically incorrect to write proofs forward? | |
| 1257 What Is Exponentiation? | |
| 1258 Why do I get one extra wrong solution when solving $2-x=-\sqrt{x}$? | |
| 1259 Mathematicians dont quit, they fade away | |
| 1260 If I know the order of every element in a group, do I know the group? | |
| 1261 Is it possible to find an infinite set of points in the plane where the distance between any pair is rational? | |
| 1262 Have there been efforts to introduce non Greek or Latin alphabets into mathematics? | |
| 1263 Algebra: Best mental images | |
| 1264 What is the average rational number? | |
| 1265 Is this similarity to the Fourier transform of the von Mangoldt function real? | |
| 1266 Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$ | |
| 1267 Topological spaces admitting an averaging function | |
| 1268 How do I tell if matrices are similar? | |
| 1269 What isnt a vector space? | |
| 1270 Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$ | |
| 1271 Why is Euclids proof on the infinitude of primes considered a proof? | |
| 1272 When not to treat dy/dx as a fraction in single-variable calculus? | |
| 1273 how to read a mathematical paper? | |
| 1274 Why do people lose in chess? | |
| 1275 Is it mathematically valid to separate variables in a differential equation? | |
| 1276 How much Math do you REALLY do in your job? | |
| 1277 What is the importance of the infinitesimal generator of Brownian motion? | |
| 1278 Do Parabolic Trigonometric Functions exist? | |
| 1279 Why is the tensor product important when we already have direct and semidirect products? | |
| 1280 Nuking the Mosquito — ridiculously complicated ways to achieve very simple results | |
| 1281 Are proofs by contradiction really logical? | |
| 1282 Is it possible to formulate category theory without set theory? | |
| 1283 What is the logic/rationale behind the vector cross product? | |
| 1284 Is there a simple function that generates the series; $1,1,2,1,1,2,1,1,2...$ or $-1,-1,1,-1,-1,1...$ | |
| 1285 Integral $\int_0^1\frac{\ln\left(x+\sqrt2\right)}{\sqrt{2-x}\,\sqrt{1-x}\,\sqrt{\vphantom{1}x}}\mathrm dx$ | |
| 1286 Can $18$ consecutive integers be separated into two groups,such that their product is equal? | |
| 1287 Integration of forms and integration on a measure space | |
| 1288 Simplicial homology of real projective space by Mayer-Vietoris | |
| 1289 Evaluating the log gamma integral $\int_{0}^{z} \log \Gamma (x) \, \mathrm dx$ in terms of the Hurwitz zeta function | |
| 1290 Does the string of prime numbers contain all natural numbers? | |
| 1291 Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even | |
| 1292 Differential forms on fuzzy manifolds | |
| 1293 Difference between NFA and DFA | |
| 1294 Given this transformation matrix, how do I decompose it into translation, rotation and scale matrices? | |
| 1295 How can a probability density be greater than one and integrate to one | |
| 1296 Good books on mathematical logic? | |
| 1297 There are 4 cups of liquid. Three are water and one is poison. If you were to drink 3 of the 4 cups, what is the probability of being poisoned? | |
| 1298 How to convince a layperson that the $\pi = 4$ proof is wrong? | |
| 1299 Every subsequence of $x_n$ has a further subsequence which converges to $x$. Then the sequence $x_n$ converges to $x$. | |
| 1300 Intuitive explanation of a positive semidefinite matrix | |
| 1301 Proving that the tensor product is right exact | |
| 1302 Integrals of the form ${\large\int}_0^\infty\operatorname{arccot}(x)\cdot\operatorname{arccot}(a\,x)\cdot\operatorname{arccot}(b\,x)\ dx$ | |
| 1303 Express 99 2/3% as a fraction? No calculator | |
| 1304 What exactly is calculus? | |
| 1305 Does it ever make sense NOT to go to the most prestigious graduate school you can get into? | |
| 1306 Set of continuity points of a real function | |
| 1307 Does every prime divide some Fibonacci number? | |
| 1308 Does $\sum _{n=1}^{\infty } \frac{\sin(\text{ln}(n))}{n}$ converge? | |
| 1309 Understanding the Laplace operator conceptually | |
| 1310 What is Cauchy Schwarz in 8th grade terms? | |
| 1311 Proving the existence of a proof without actually giving a proof | |
| 1312 How and why does Grothendiecks work provide tools to attack problems in number theory? | |
| 1313 Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$ | |
| 1314 Does multiplying all a numbers roots together give a product of infinity? | |
| 1315 What are some good ways to get children excited about math? | |
| 1316 Why does $\cos(x) + \cos(y) - \cos(x + y) = 0$ look like an ellipse? | |
| 1317 When is an infinite product of natural numbers regularizable? | |
| 1318 Why is it not true that $\int_0^{\pi} \sin(x)\; dx = 0$? | |
| 1319 Evaluating $\int_{0}^{1}\cdots\int_{0}^{1}\bigl\{\frac{1}{x_{1}\cdots x_{n}}\bigr\}^{2}\:\mathrm{d}x_{1}\cdots\mathrm{d}x_{n}$ | |
| 1320 Are the sums $\sum_{n=1}^{\infty} \frac{1}{(n!)^k}$ transcendental? | |
| 1321 Does $\Bbb{CP}^{2n} \mathbin{\#} \Bbb{CP}^{2n}$ ever support an almost complex structure? | |
| 1322 Closed form solution for $\sum_{n=1}^\infty\frac{1}{1+\frac{n^2}{1+\frac{1}{\stackrel{\ddots}{1+\frac{1}{1+n^2}}}}}$. | |
| 1323 What is a good book for learning math, from middle school level? | |
| 1324 difference between dot product and inner product | |
| 1325 Check if a point is within an ellipse | |
| 1326 What does proving the Riemann Hypothesis accomplish? | |
| 1327 Is Serge Langs Algebra still worth reading? | |
| 1328 Highest power of a prime $p$ dividing $N!$ | |
| 1329 Proof that Pi is constant (the same for all circles), without using limits | |
| 1330 Interesting real life applications of serious theorems | |
| 1331 How do I motivate myself to do math again? | |
| 1332 Under what conditions the quotient space of a manifold is a manifold? | |
| 1333 How to effectively study math? | |
| 1334 Is there any branch of Mathematics which has no applications in any other field or in real world? | |
| 1335 Nice expression for minimum of three variables? | |
| 1336 What exactly is a number? | |
| 1337 Dominoes and induction, or how does induction work? | |
| 1338 Riemann hypothesis: is Bender-Brody-Müller Hamiltonian a new line of attack? | |
| 1339 Why do we not have to prove definitions? | |
| 1340 Optimal strategy for cutting a sausage? | |
| 1341 Symbol for probably equal to (barring pathology)? | |
| 1342 Is it not effective to learn math top-down? | |
| 1343 If we randomly select 25 integers between 1 and 100, how many consecutive integers should we expect? | |
| 1344 A new general formula for the quadratic equation? | |
| 1345 Conways Murder Weapon | |
| 1346 How to explain to the layperson what mathematics is, why its important, and why its interesting | |
| 1347 Is the box topology good for anything? | |
| 1348 Does the series $ \sum\limits_{n=1}^{\infty} \frac{1}{n^{1 + |\sin(n)|}} $ converge or diverge? | |
| 1349 Does Fermats Last Theorem hold for cyclotomic integers in $\mathbb{Q(\zeta_{37})}$? | |
| 1350 In combinatorics, how can one verify that one has counted correctly? | |
| 1351 Algebraic Topology Challenge: Homology of an Infinite Wedge of Spheres | |
| 1352 Fourier Transform of Derivative | |
| 1353 What is the relation between rank of a matrix, its eigenvalues and eigenvectors | |
| 1354 What is the standard basis for fields of complex numbers? | |
| 1355 Good books for a high schooler self-studying Abstract Algebra? | |
| 1356 Why do the French count so strangely? | |
| 1357 A comprehensive list of binomial identities? | |
| 1358 What is a covector and what is it used for? | |
| 1359 First-Order Logic vs. Second-Order Logic | |
| 1360 Why is the determinant the volume of a parallelepiped in any dimensions? | |
| 1361 Introductory texts on manifolds | |
| 1362 Functions that are their own inverse. | |
| 1363 How do I convince my students that the choice of variable of integration is irrelevant? | |
| 1364 If a coin toss is observed to come up as heads many times, does that affect the probability of the next toss? | |
| 1365 A way to find this shaded area without calculus? | |
| 1366 Learning Roadmap for Algebraic Topology | |
| 1367 What is the limit of $n \sin (2 \pi \cdot e \cdot n!)$ as $n$ goes to infinity? | |
| 1368 How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical communitys standards? | |
| 1369 When to give up on a hard math problem? | |
| 1370 Simplicial Complex vs Delta Complex vs CW Complex | |
| 1371 Why are primes considered to be the building blocks of the integers? | |
| 1372 What are some mathematically interesting computations involving matrices? | |
| 1373 Arranging numbers from $1$ to $n$ such that the sum of every two adjacent numbers is a perfect power | |
| 1374 Given real numbers: define integers? | |
| 1375 Arc length contest! Minimize the arc length of $f(x)$ when given three conditions. | |
| 1376 Is $ \sum\limits_{n=1}^\infty \frac{|\sin n|^n}n$ convergent？ | |
| 1377 What does strength refer to in mathematics? | |
| 1378 Is there a reason it is so rare we can solve differential equations? | |
| 1379 Why it is important to write a function as sum of even and odd functions? | |
| 1380 What is a proof? | |
| 1381 Area covered by a constant length segment rotating around the center of a square. | |
| 1382 Is it normal to treat Math Theorems as Black Boxes | |
| 1383 Good history of mathematical ideas book? | |
| 1384 Abstract nonsense proof of snake lemma | |
| 1385 How to find a total order with constrained comparisons | |
| 1386 Integers $n$ such that $i(i+1)(i+2) \cdots (i+n)$ is real or pure imaginary | |
| 1387 Which Algebraic Properties Distinguish Lie Groups from Abstract Groups? | |
| 1388 I have learned that 1/0 is infinity, why isnt it minus infinity? | |
| 1389 Difference between axioms, theorems, postulates, corollaries, and hypotheses | |
| 1390 Is the sum and difference of two irrationals always irrational? | |
| 1391 What is the difference between the Frobenius norm and the 2-norm of a matrix? | |
| 1392 How does a calculator calculate the sine, cosine, tangent using just a number? | |
| 1393 How do you compute negative numbers to fractional powers? | |
| 1394 Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction | |
| 1395 Probability that random moves in the game 2048 will win | |
| 1396 Why does $\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3)=\pi$? | |
| 1397 Proof of the Hockey-Stick Identity: $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$ | |
| 1398 How can you prove that the square root of two is irrational? | |
| 1399 Is the Law of Large Numbers empirically proven? | |
| 1400 Cardinality of Borel sigma algebra | |
| 1401 Motivation and methods for self-study | |
| 1402 Intuition on group homomorphisms | |
| 1403 Can someone explain the Yoneda Lemma to an applied mathematician? | |
| 1404 Polynomial division: an obvious trick? [reducing mod $\textit{simpler}$ multiples] | |
| 1405 How can I introduce complex numbers to precalculus students? | |
| 1406 $n$th derivative of $e^{1/x}$ | |
| 1407 What should an amateur do with a proof of an open problem? | |
| 1408 Why does an exponential function eventually get bigger than a quadratic | |
| 1409 Big List of Erdős elementary proofs | |
| 1410 Continuity and the Axiom of Choice | |
| 1411 Graphs for which a calculus student can reasonably compute the arclength | |
| 1412 Conjugate subgroup strictly contained in the initial subgroup? | |
| 1413 Rigour in mathematics | |
| 1414 Where does the word torsion in algebra come from? | |
| 1415 Computation with a memory wiped computer | |
| 1416 Let $k$ be a natural number . Then $3k+1$ , $4k+1$ and $6k+1$ cannot all be square numbers. | |
| 1417 Unexpected approximations which have led to important mathematical discoveries | |
| 1418 On Ramanujans curious equality for $\sqrt{2\,(1-3^{-2})(1-7^{-2})(1-11^{-2})\cdots} $ | |
| 1419 Is $\lfloor n!/e\rfloor$ always even for $n\in\mathbb N$? | |
| 1420 How do I prove that a function is well defined? | |
| 1421 Is the rank of a matrix the same of its transpose? If yes, how can I prove it? | |
| 1422 Evaluating the indefinite integral $ \int \sqrt{\tan x} ~ \mathrm{d}{x}. $ | |
| 1423 Proof that the irrational numbers are uncountable | |
| 1424 Can a complex number ever be considered bigger or smaller than a real number, or vice versa? | |
| 1425 Prove every odd integer is the difference of two squares | |
| 1426 how to be good at proving? | |
| 1427 Are there any examples of non-computable real numbers? | |
| 1428 What is a good book to study linear algebra? | |
| 1429 Why is empty set an open set? | |
| 1430 How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$? | |
| 1431 Probability for the length of the longest run in $n$ Bernoulli trials | |
| 1432 Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$ | |
| 1433 What do prime ideals in $k[x,y]$ look like? | |
| 1434 Characterizing units in polynomial rings | |
| 1435 Entire one-to-one functions are linear | |
| 1436 Let $X$ be an infinite dimensional Banach space. Prove that every Hamel basis of X is uncountable. | |
| 1437 How do you show monotonicity of the $\ell^p$ norms? | |
| 1438 Strategies to denest nested radicals $\sqrt{a+b\sqrt{c}}$ | |
| 1439 How would you explain to a 9th grader the negative exponent rule? | |
| 1440 Why learn to solve differential equations when computers can do it? | |
| 1441 Big List of Fun Math Books | |
| 1442 What is the definition of a set? | |
| 1443 Is there such a thing as proof by example (not counter example) | |
| 1444 Can there be two distinct, continuous functions that are equal at all rationals? | |
| 1445 Whats the goal of mathematics? | |
| 1446 How to debug math? | |
| 1447 What does communicated by mean in math papers? | |
| 1448 Using Gröbner bases for solving polynomial equations | |
| 1449 Which is larger? $20!$ or $2^{40}$? | |
| 1450 Unsolved Problems due to Lack of Computational Power | |
| 1451 Whats wrong with this reasoning that $\frac{\infty}{\infty}=0$? | |
| 1452 Are there theoretical applications of trigonometry? | |
| 1453 The last digit of $2^{2006}$ | |
| 1454 Intuition for the Importance of Modular Forms | |
| 1455 Linear Algebra Versus Functional Analysis | |
| 1456 Whats the point of studying topological (as opposed to smooth, PL, or PDiff) manifolds? | |
| 1457 Find three non-constant, pairwise unequal functions $f,g,h:\mathbb R\to \mathbb R$... | |
| 1458 Surprisingly elementary and direct proofs | |
| 1459 Closed Form for $~\int_0^1\frac{\text{arctanh }x}{\tan\left(\frac\pi2~x\right)}~dx$ | |
| 1460 Is $n \sin n$ dense on the real line? | |
| 1461 When are nonintersecting finite degree field extensions linearly disjoint? | |
| 1462 The relation between trace and determinant of a matrix | |
| 1463 How to prove every closed interval in R is compact? | |
| 1464 Is there a step by step checklist to check if a multivariable limit exists and find its value? | |
| 1465 Is an automorphism of the field of real numbers the identity map? | |
| 1466 What do eigenvalues have to do with pictures? | |
| 1467 Why cant you flatten a sphere? | |
| 1468 List of problem books in undergraduate and graduate mathematics | |
| 1469 What is the importance of Calculus in todays Mathematics? | |
| 1470 Why does $\frac{1}{x} < 4$ have two answers? | |
| 1471 Explain this mathematical meme (Geometers bird interrupting Topologists bird) | |
| 1472 Coin flipping probability game ; 7 flips vs 8 flips | |
| 1473 Finite Groups with exactly $n$ conjugacy classes $(n=2,3,...)$ | |
| 1474 Help understanding Algebraic Geometry | |
| 1475 7 fishermen caught exactly 100 fish and no two had caught the same number of fish. Then there are three who have together captured at least 50 fish. | |
| 1476 Can a number have infinitely many digits before the decimal point? | |
| 1477 How can I show that $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt\ldots}}}$ exists? | |
| 1478 Whats the intuition with partitions of unity? | |
| 1479 Center-commutator duality | |
| 1480 In how many different ways can a 9-panel comic grid be used? | |
| 1481 I need mathematical proof that the distance from zero to 1 is the equal to the distance from 1 to 2 | |
| 1482 I almost quit self-studying mathematics, but should I continue? | |
| 1483 What is Trinity Hall Prime number? | |
| 1484 Examples of morphisms of schemes to keep in mind? | |
| 1485 Review of my T-shirt design | |
| 1486 Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix | |
| 1487 Is A New Kind of Science a new kind of science? | |
| 1488 What am I doing when I separate the variables of a differential equation? | |
| 1489 Does every set have a group structure? | |
| 1490 Why do we use trig functions in Fourier transforms, and not other periodic functions? | |
| 1491 How to evaluate $I=\int_0^{\pi/2}x^2\ln(\sin x)\ln(\cos x)\ \mathrm dx$ | |
| 1492 Is it possible to simplify $\frac{\Gamma\left(\frac{1}{10}\right)}{\Gamma\left(\frac{2}{15}\right)\ \Gamma\left(\frac{7}{15}\right)}$? | |
| 1493 Can squares of infinite area always cover a unit square? | |
| 1494 Whats the probability that a sequence of coin flips never has twice as many heads as tails? | |
| 1495 $5^n+n$ is never prime? | |
| 1496 What does it take to divide by $2$? | |
| 1497 If a two variable smooth function has two global minima, will it necessarily have a third critical point? | |
| 1498 Subgroups as isotropy subgroups and regular orbits on tuples | |
| 1499 A question about Sylow subgroups and $C_G(x)$ | |
| 1500 How to know if a point is inside a circle? | |
| 1501 Poisson Distribution of sum of two random independent variables $X$, $Y$ | |
| 1502 Explanation on arg min | |
| 1503 Product of two Gaussian PDFs is a Gaussian PDF, but Product of two Gaussian Variables is not Gaussian | |
| 1504 Is the product of symmetric positive semidefinite matrices positive definite? | |
| 1505 Matrices commute if and only if they share a common basis of eigenvectors? | |
| 1506 What are the formal names of operands and results for basic operations? | |
| 1507 Differentiating an Inner Product | |
| 1508 How to show that the commutator subgroup is a normal subgroup | |
| 1509 Nobody told me that self teaching could be so damaging... | |
| 1510 (undergraduate) Algebraic Geometry Textbook Recommendations | |
| 1511 Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD? | |
| 1512 Dot Product Intuition | |
| 1513 Divisor -- line bundle correspondence in algebraic geometry | |
| 1514 How to tell if Im good enough for graduate school? | |
| 1515 How is the derivative truly, literally the best linear approximation near a point? | |
| 1516 Why is the Continuum Hypothesis (not) true? | |
| 1517 Good examples of double induction | |
| 1518 A very general method for proving inequalities. Too good to be true? | |
| 1519 Is it possible to have three real numbers that have both their sum and product equal to $1$? | |
| 1520 What was the book that opened your mind to the beauty of mathematics? | |
| 1521 Research done by high-school students | |
| 1522 Why does the discriminant in the Quadratic Formula reveal the number of real solutions? | |
| 1523 Understanding the intuition behind math | |
| 1524 A circle rolls along a parabola | |
| 1525 Why is $\varphi$ called the most irrational number? | |
| 1526 How can I intuitively understand complex exponents? | |
| 1527 It looks straightforward, but actually it isnt | |
| 1528 Refuting the Anti-Cantor Cranks | |
| 1529 Could I be using proof by contradiction too much? | |
| 1530 Is there any geometric intuition for the factorials in Taylor expansions? | |
| 1531 Why do differential forms have a much richer structure than vector fields? | |
| 1532 A Challenging Logarithmic Integral $\int_0^1 \frac{\log(x)\log(1-x)\log^2(1+x)}{x}dx$ | |
| 1533 Quadratic reciprocity via generalized Fibonacci numbers? | |
| 1534 Penroses remark on impossible figures | |
| 1535 Why are asymptotically one half of the integer compositions gap-free? | |
| 1536 Mirror algorithm for computing $\pi$ and $e$ - does it hint on some connection between them? | |
| 1537 Difference between ≈, ≃, and ≅ | |
| 1538 What is the difference between only if and iff? | |
| 1539 Gradient of squared $2$-norm | |
| 1540 Distance/Similarity between two matrices | |
| 1541 Are all eigenvectors, of any matrix, always orthogonal? | |
| 1542 Area of a square inside a square created by connecting point-opposite midpoint | |
| 1543 How to generate random points on a sphere? | |
| 1544 Number of monic irreducible polynomials of prime degree $p$ over finite fields | |
| 1545 Should I be worried that I am doing well in analysis and not well in algebra? | |
| 1546 Negative versus Minus | |
| 1547 Discontinuous linear functional | |
| 1548 Geometric interpretation for sum of fourth powers | |
| 1549 The two-daughter-problem | |
| 1550 Has there ever been an application of dividing by $0$? | |
| 1551 Why do we miss 8 in the decimal expansion of 1/81, and 98 in the decimal expansion of 1/9801? | |
| 1552 Why does the Cauchy-Schwarz Inequality even have a name? | |
| 1553 What use is the Yoneda lemma? | |
| 1554 Is there a function whose antiderivative can be found but whose derivative cannot? | |
| 1555 Similar matrices and field extensions | |
| 1556 Are there mathematical concepts that exist in dimension $4$, but not in dimension $3$? | |
| 1557 Is there a definition of determinants that does not rely on how they are calculated? | |
| 1558 Unexpected use of topology in proofs | |
| 1559 Does this Fractal Have a Name? | |
| 1560 How is the Gödels Completeness Theorem not a tautology? | |
| 1561 How many 7-note musical scales are possible within the 12-note system? | |
| 1562 Approximating a $\sigma$-algebra by a generating algebra | |
| 1563 How do different definitions of degree coincide? | |
| 1564 What is the size of each side of the square? | |
| 1565 A non-losing strategy for tic-tac-toe $\times$ tic-tac-toe | |
| 1566 Can there be an injective function whose derivative is equivalent to its inverse function? | |
| 1567 Evaluating $\int_0^\infty \frac{dx}{\sqrt{x}[x^2+(1+2\sqrt{2})x+1][1-x+x^2-x^3+...+x^{50}]}$ | |
| 1568 Trigonometric sums related to the Verlinde formula | |
| 1569 A bestiary about adjunctions | |
| 1570 Is OEIS A248049 an integer sequence? | |
| 1571 Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $ | |
| 1572 Golden Number Theory | |
| 1573 Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$ | |
| 1574 An illusionist and their assistant are about to perform the following magic trick | |
| 1575 The most effective windshield-wiper setup. (Packing a square with sectors) | |
| 1576 How prove this inequality $\sin{\sin{\sin{\sin{x}}}}\le\frac{4}{5}\cos{\cos{\cos{\cos{x}}}}$ | |
| 1577 Period of the sum/product of two functions | |
| 1578 Example of Partial Order thats not a Total Order and why? | |
| 1579 What does curly (curved) less than sign $\succcurlyeq$ mean? | |
| 1580 Why we consider log likelihood instead of Likelihood in Gaussian Distribution | |
| 1581 Is there an equation to describe regular polygons? | |
| 1582 Eigenvalues of the rank one matrix $uv^T$ | |
| 1583 Under what condition we can interchange order of a limit and a summation? | |
| 1584 Calculating pi manually | |
| 1585 Difference between basis and subbasis in a topology? | |
| 1586 Visualizing the 4th dimension. | |
| 1587 Why does the derivative of sine only work for radians? | |
| 1588 Origin of the dot and cross product? | |
| 1589 What is the arithmetic mean of no numbers? | |
| 1590 The $\sigma$-algebra of subsets of $X$ generated by a set $\mathcal{A}$ is the smallest sigma algebra including $\mathcal{A}$ | |
| 1591 Would a proof to the Riemann Hypothesis affect security? | |
| 1592 What lies beyond the Sedenions | |
| 1593 Is it possible to determine if you were on a Möbius strip? | |
| 1594 Big O Notation is element of or is equal | |
| 1595 Is there a slowest rate of divergence of a series? | |
| 1596 Any smart ideas on finding the area of this shaded region? | |
| 1597 Can we calculate $ i\sqrt { i\sqrt { i\sqrt { \cdots } } }$? | |
| 1598 Is it possible that A counter-example exists but it cannot be found | |
| 1599 Applications of complex numbers to solve non-complex problems | |
| 1600 Is it an abuse of language to say *the* integers, *the* rational numbers, or *the* real numbers, etc.? | |
| 1601 Paradox: increasing sequence that goes to $0$? | |
| 1602 Is it possible to prove a mathematical statement by proving that a proof exists? | |
| 1603 Is $6.12345678910111213141516171819202122\ldots$ transcendental? | |
| 1604 Big list of guided discovery books | |
| 1605 Are there any Turing-undecidable problems whose undecidability is independent of the Halting problem? | |
| 1606 Funny double infinite sum | |
| 1607 Geometry problem involving infinite number of circles | |
| 1608 What proportion of positive integers have two factors that differ by 1? | |
| 1609 What are Different Approaches to Introduce the Elementary Functions? | |
| 1610 Finding triplets $(a,b,c)$ such that $\sqrt{abc}\in\mathbb N$ divides $(a-1)(b-1)(c-1)$ | |
| 1611 How to think of the group ring as a Hopf algebra? | |
| 1612 Whats the value of this Viète-style product involving the golden ratio? | |
| 1613 Is $1+x+\frac{x^2}2+\dots+\frac{x^n}{n!}$ irreducible? | |
| 1614 How many values of $2^{2^{2^{.^{.^{.^{2}}}}}}$ depending on parenthesis? | |
| 1615 Looking for a definitive source about Dirichlet finally proving the Unit Theorem in the Sistine Chapel | |
| 1616 Whats the sign of $\det\left(\sqrt{i^2+j^2}\right)_{1\le i,j\le n}$? | |
| 1617 Is there a good reason why $\left\lfloor \frac{n!}{11e}\right\rfloor$ is always even? | |
| 1618 What does E mean in 9.0122222900391E-5? | |
| 1619 What’s the difference between analytical and numerical approaches to problems? | |
| 1620 How to find the multiplicity of eigenvalues? | |
| 1621 Is the power set of the natural numbers countable? | |
| 1622 Finding $\int x^xdx$ | |
| 1623 Calculate on which side of a straight line is a given point located? | |
| 1624 Generating correlated random numbers: Why does Cholesky decomposition work? | |
| 1625 product distribution of two uniform distribution, what about 3 or more | |
| 1626 Dantzigs unsolved homework problems | |
| 1627 Interesting math-facts that are visually attractive | |
| 1628 How does TREE(3) grow to get so big? (Laymen explanation) | |
| 1629 Order of general- and special linear groups over finite fields. | |
| 1630 Why are two permutations conjugate iff they have the same cycle structure? | |
| 1631 What is an operator in mathematics? | |
| 1632 Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral? | |
| 1633 Are there any differences between tensors and multidimensional arrays? | |
| 1634 Is it possible to write a sum as an integral to solve it? | |
| 1635 Why divide by $2m$ | |
| 1636 Can math be subjective? | |
| 1637 Is there an easy way to see associativity or non-associativity from an operations table? | |
| 1638 Matrix is conjugate to its own transpose | |
| 1639 Is there a third dimension of numbers? | |
| 1640 Proving that $m+n\sqrt{2}$ is dense in $\mathbb R$ | |
| 1641 What is the antiderivative of $e^{-x^2}$ | |
| 1642 Is there a math expression equivalent to the conditional ternary operator? | |
| 1643 Understanding Gödels Incompleteness Theorem | |
| 1644 Do harmonic numbers have a “closed-form” expression? | |
| 1645 Is $\{0\}$ a field? | |
| 1646 How hard is the proof of $\pi$ or $e$ being transcendental? | |
| 1647 Interesting results easily achieved using complex numbers | |
| 1648 All natural numbers are equal. | |
| 1649 Geometrical interpretation of Ricci curvature | |
| 1650 Why are real numbers useful? | |
| 1651 $x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible? | |
| 1652 What kind of work do modern day algebraists do? | |
| 1653 Choice of $q$ in Baby Rudins Example 1.1 | |
| 1654 Why is there never a proof that extending the reals to the complex numbers will not cause contradictions? | |
| 1655 Is there any conjecture that we know is provable/disprovable but we havent found a proof of yet? | |
| 1656 Gaps or holes in rational number system | |
| 1657 What is $-i$ exactly? | |
| 1658 What knot is this? | |
| 1659 Doesnt the unprovability of the continuum hypothesis prove the continuum hypothesis? | |
| 1660 What is the fastest/most efficient algorithm for estimating Eulers Constant $\gamma$? | |
| 1661 What is the crime of lèse-Bourbaki? | |
| 1662 Natural example of cosets | |
| 1663 Is Complex Analysis equivalent Real Analysis with $f:\mathbb R^2 \to \mathbb R^2$? | |
| 1664 If $e^A$ and $e^B$ commute, do $A$ and $B$ commute? | |
| 1665 A discrete math riddle | |
| 1666 How does one give a mathematical talk? | |
| 1667 Probability that a quadratic equation has real roots | |
| 1668 How to identify surfaces of revolution | |
| 1669 Is there an abstract definition of a matrix being upper triangular? | |
| 1670 Self-learning mathematics - help needed! | |
| 1671 What is this pattern called? | |
| 1672 The $100$th derivative of $(x^2 + 1)/(x^3 - x)$ | |
| 1673 Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$ | |
| 1674 Infinite Series $\sum\limits_{n=1}^\infty\frac{(H_n)^2}{n^3}$ | |
| 1675 In which ordered fields does absolute convergence imply convergence? | |
| 1676 Crazy pattern in the simple continued fraction for $\sum_{k=1}^\infty \frac{1}{(2^k)!}$ | |
| 1677 A sequence that avoids both arithmetic and geometric progressions | |
| 1678 Proof of triangle inequality | |
| 1679 How to find the factorial of a fraction? | |
| 1680 What is the general equation of the ellipse that is not in the origin and rotated by an angle? | |
| 1681 Prove that the union of countably many countable sets is countable. | |
| 1682 Symbol for elementwise multiplication of vectors | |
| 1683 Difference between supremum and maximum | |
| 1684 What is difference between a ring and a field? | |
| 1685 Picking random points in the volume of sphere with uniform probability | |
| 1686 Necessity/Advantage of LU Decomposition over Gaussian Elimination | |
| 1687 Introductory Group theory textbook | |
| 1688 Does non-symmetric positive definite matrix have positive eigenvalues? | |
| 1689 Difference between Analytic and Holomorphic function | |
| 1690 Evaluating the nested radical $ \sqrt{1 + 2 \sqrt{1 + 3 \sqrt{1 + \cdots}}} $. | |
| 1691 Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials? | |
| 1692 What does it take to get a job at a top 50 math program in the U.S.? | |
| 1693 Is an irrational number odd or even? | |
| 1694 Definitions of Hessian in Riemannian Geometry | |
| 1695 How to calculate the pullback of a $k$-form explicitly | |
| 1696 How to prove that $\log(x)1$? | |
| 1697 Exam with $12$ yes/no questions (half yes, half no) and $8$ correct needed to pass, is it better to answer randomly or answer exactly 6 times yes? | |
| 1698 Distinguishing probability measure, function and distribution | |
| 1699 False proof: $\pi = 4$, but why? | |
| 1700 Books about the Riemann Hypothesis | |
| 1701 Why is $\text{Hom}(V,W)$ the same thing as $V^* \otimes W$? | |
| 1702 What is exactly the difference between a definition and an axiom? | |
| 1703 Non-associative operations | |
| 1704 Is $\sqrt{64}$ considered $8$? or is it $8,-8$? | |
| 1705 What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$? | |
| 1706 Mathematical explanation behind a picture posted (lifted from facebook) | |
| 1707 Path-connected and locally connected space that is not locally path-connected | |
| 1708 Can I search for factors of $\ (11!)!+11!+1\ $ efficiently? | |
| 1709 Solutions to the matrix equation $\mathbf{AB-BA=I}$ over general fields | |
| 1710 Square root confusion: Why am I getting an answer if it doesnt work? | |
| 1711 Geometric understanding of differential forms. | |
| 1712 Why are the only division algebras over the real numbers the real numbers, the complex numbers, and the quaternions? | |
| 1713 What is the formula for pi used in the Python decimal library? | |
| 1714 Intuition for why the difference between $\frac{2x^2-x}{x^2-x+1}$ and $\frac{x-2}{x^2-x+1}$ is a constant? | |
| 1715 Axiom of choice and automorphisms of vector spaces | |
| 1716 Show that floating point $\sqrt{x \cdot x} \geq x$ for all long $x$. | |
| 1717 How to entertain a crowd with mathematics? | |
| 1718 Colliding Bullets | |
| 1719 False beliefs about Lebesgue measure on $\mathbb{R}$ | |
| 1720 Evaluating $\int P(\sin x, \cos x) \text{d}x$ | |
| 1721 Is there a geometric idea behind Sylows theorems? | |
| 1722 Is $29$ the only prime of the form $p^p+2$? | |
| 1723 Is Stokes Theorem natural in the sense of category theory? | |
| 1724 Trying to define $\mathbb{R}^{0.5}$ topologically | |
| 1725 Conjectured value of a harmonic sum $\sum_{n=1}^\infty\left(H_n-\,2H_{2n}+H_{4n}\right)^2$ | |
| 1726 Elementary proof that the derivative of a real function is continuous somewhere | |
| 1727 Can $\sqrt{p}^{\sqrt{p}^{\sqrt{p}}}$ be an integer, if $p$ is a non-square positive integer? | |
| 1728 How to tell if a set of vectors spans a space? | |
| 1729 Easy way of memorizing values of sine, cosine, and tangent | |
| 1730 What does ∈ mean? | |
| 1731 Recognizable vs Decidable | |
| 1732 Why have we chosen our number system to be decimal (base 10)? | |
| 1733 How the product of two integrals is iterated integral? $\int\cdot \int = \iint$ | |
| 1734 How to take the gradient of the quadratic form? | |
| 1735 Why cant a set have two elements of the same value? | |
| 1736 Order of finite fields is $p^n$ | |
| 1737 Why is $A^TA$ invertible if $A$ has independent columns? | |
| 1738 Proof that the largest eigenvalue of a stochastic matrix is $1$ | |
| 1739 how does expectation maximization work? | |
| 1740 Are functions of independent variables also independent? | |
| 1741 What is an intuitive explanation for $\operatorname{div} \operatorname{curl} F = 0$? | |
| 1742 What is the difference between projected gradient descent and ordinary gradient descent? | |
| 1743 Functions which are Continuous, but not Bicontinuous | |
| 1744 Choose a random number between $0$ and $1$ and record its value. Keep doing it until the sum of the numbers exceeds $1$. How many tries do we need? | |
| 1745 How I can prove that the sequence $\sqrt{2} , \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}$ converges to 2? | |
| 1746 Difference between bijection and isomorphism? | |
| 1747 $\lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite | |
| 1748 An easy example of a non-constructive proof without an obvious fix? | |
| 1749 Why doesnt induction extend to infinity? (re: Fourier series) | |
| 1750 A really complicated calculus book | |
| 1751 Why isnt several complex variables as fundamental as multivariable calculus? | |
| 1752 Parabola is an ellipse, but with one focal point at infinity | |
| 1753 Formal definition of conditional probability | |
| 1754 Why is it worth spending time on type theory? | |
| 1755 Why is cross product defined in the way that it is? | |
| 1756 What are the rules for equals signs with big-O and little-o? | |
| 1757 What book can bridge high school math and the more advanced topics? | |
| 1758 Foundation for analysis without axiom of choice? | |
| 1759 Intuition behind ideal | |
| 1760 How far is the list of known primes known to be complete? | |
| 1761 Why the real and imaginary parts of a complex analytic function are not independent? | |
| 1762 Do circles divide the plane into more regions than lines? | |
| 1763 On the functional square root of $x^2+1$ | |
| 1764 $n!+1$ being a perfect square | |
| 1765 Does $\zeta(3)$ have a connection with $\pi$? | |
| 1766 Why do we need so many trigonometric definitions? | |
| 1767 Prove that the sum of pythagorean triples is always even | |
| 1768 What is the explanation for this visual proof of the sum of squares? | |
| 1769 Why are topological spaces interesting to study? | |
| 1770 Good math books to discover stuff by yourself | |
| 1771 Integral $\int_{-1}^{1} \frac{1}{x}\sqrt{\frac{1+x}{1-x}} \log \left( \frac{(r-1)x^{2} + sx + 1}{(r-1)x^{2} - sx + 1} \right) \, \mathrm dx$ | |
| 1772 Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space? | |
| 1773 Why is the Laplacian important in Riemannian geometry? | |
| 1774 MIT 2015 Integration Question | |
| 1775 Is there a name for this type of polygon? | |
| 1776 Intuition behind Snake Lemma | |
| 1777 Is it possible for a function to be smooth everywhere, analytic nowhere, yet Taylor series at any point converges in a nonzero radius? | |
| 1778 Proof that a trigonometric function of a rational angle must be non-transcendental | |
| 1779 Does $|n^2 \cos n|$ diverge to $+\infty$? | |
| 1780 What are exact sequences, metaphysically speaking? | |
| 1781 What structure does the alternating group preserve? | |
| 1782 About the integral $\int_{0}^{+\infty}\sin(x\,\log x)\,dx$ | |
| 1783 Effective Research Notes | |
| 1784 A new continued fraction for Apérys constant, $\zeta(3)$? | |
| 1785 Two questions about weakly convergent series related to $\sin(n^2)$ and Weyls inequality | |
| 1786 What is the integral of 1/x? | |
| 1787 How does one denote the set of all positive real numbers? | |
| 1788 Prove: If a sequence converges, then every subsequence converges to the same limit. | |
| 1789 How many prime numbers are known? | |
| 1790 What books are prerequisites for Spivaks Calculus? | |
| 1791 Create unique number from 2 numbers | |
| 1792 What is the main difference between a vector space and a field? | |
| 1793 If eigenvalues are positive, is the matrix positive definite? | |
| 1794 $\epsilon$-$\delta$ proof that $\lim\limits_{x \to 1} \frac{1}{x} = 1$. | |
| 1795 Finding Value of the Infinite Product $\prod \Bigl(1-\frac{1}{n^{2}}\Bigr)$ | |
| 1796 Pen, pencils and paper to write math | |
| 1797 Video lectures on Real Analysis? | |
| 1798 If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative. | |
| 1799 Which of the numbers $1, 2^{1/2}, 3^{1/3}, 4^{1/4}, 5^{1/5}, 6^{1/6} , 7^{1/7}$ is largest, and how to find out without calculator? | |
| 1800 Zero divided by zero must be equal to zero | |
| 1801 Proof that every number ≥ $8$ can be represented by a sum of fives and threes. | |
| 1802 What is the difference between a Ring and an Algebra? | |
| 1803 Intuitive understanding of the derivatives of $\sin x$ and $\cos x$ | |
| 1804 A linear operator commuting with all such operators is a scalar multiple of the identity. | |
| 1805 Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian | |
| 1806 Is $\pi$ equal to $180^\circ$? | |
| 1807 Is every Lebesgue measurable function on $\mathbb{R}$ the pointwise limit of continuous functions? | |
| 1808 Seeking a laymans guide to Measure Theory | |
| 1809 What are the Laws of Rational Exponents? | |
| 1810 An intuitive approach to the Jordan Normal form | |
| 1811 Intuitive Understanding of the constant $e$ | |
| 1812 How far can one see over the ocean? | |
| 1813 Every power series is the Taylor series of some $C^{\infty}$ function | |
| 1814 Is the axiom of choice really all that important? | |
| 1815 On average, how many friends would I need to have to have at least one friends birthday every day? | |
| 1816 Is there a purely algebraic proof of the Fundamental Theorem of Algebra? | |
| 1817 What books should I get to self study beyond Calculus for someone about to start undergrad mathematics? | |
| 1818 Are there any objects which arent sets? | |
| 1819 What is the theme of analysis? | |
| 1820 Is there any geometric way to characterize $e$? | |
| 1821 Why and How do certain manipulations in indefinite integrations just work? | |
| 1822 History of the Concept of a Ring | |
| 1823 Simplest way to get the lower bound $\pi > 3.14$ | |
| 1824 What to answer when people ask what I do in mathematics | |
| 1825 How many super imaginary numbers are there? | |
| 1826 Fibonacci infinite sum resulting in $\pi$ | |
| 1827 Is $i = \sqrt{e^{\pi\sqrt{e^{\pi\sqrt\ldots}}}}$? | |
| 1828 Example of a compact set that isnt the spectrum of an operator | |
| 1829 Why is one $\infty$ number enough for complex numbers? | |
| 1830 How do the Catalan numbers turn up here? | |
| 1831 What is so special about $\alpha=-1$ in the integral of $x^\alpha$? | |
| 1832 To evaluate $\int_0^{+\infty} \frac{\;\mathrm dx}{\sqrt[3]{x^3+a^3}\sqrt[3]{x^3+b^3}\sqrt[3]{x^3+c^3}}$ | |
| 1833 On a long proof | |
| 1834 Why do all the Platonic Solids exist? | |
| 1835 Bijection $f\colon\mathbb{N}\to\mathbb{N}$ with $f(0)=0$ and $|f(n)-f(n-1)|=n$ | |
| 1836 How to solve an nth degree polynomial equation | |
| 1837 Number of onto functions | |
| 1838 What does := mean? | |
| 1839 Adding two polar vectors | |
| 1840 Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $ | |
| 1841 Average Distance Between Random Points on a Line Segment | |
| 1842 Understanding Dot and Cross Product | |
| 1843 What are good books/other readings for elementary set theory? | |
| 1844 Best Algebraic Topology book/Alternative to Allen Hatcher free book? | |
| 1845 What is the implicit function theorem? | |
| 1846 What does it mean to integrate with respect to the distribution function? | |
| 1847 Very good linear algebra book. | |
| 1848 Can a piece of A4 paper be folded so that its thick enough to reach the moon? | |
| 1849 Every nonzero element in a finite ring is either a unit or a zero divisor | |
| 1850 Projection is an open map | |
| 1851 Can someone explain Cayleys Theorem step by step? | |
| 1852 Lemma/Proposition/Theorem, which one should we pick? | |
| 1853 Game theory - self study | |
| 1854 What are the required backgrounds of Robin Hartshornes Algebraic Geometry book? | |
| 1855 Semi-direct v.s. Direct products | |
| 1856 Why is it that if I count years from 2011 to 2014 as intervals I get 3 years, but if I count each year separately I get 4 years? | |
| 1857 What exactly is infinity? | |
| 1858 How do we know the ratio between circumference and diameter is the same for all circles? | |
| 1859 Good introductory book on geometric algebra | |
| 1860 Jacobi identity - intuitive explanation | |
| 1861 Why does the volume of the unit sphere go to zero? | |
| 1862 Is it possible to place 26 points inside a rectangle that is 20 cm by 15 cm so that the distance between every pair of points is greater than 5 cm? | |
| 1863 What does it mean to solve an equation? | |
| 1864 Isomorphic quotients by isomorphic normal subgroups | |
| 1865 How can this function have two different antiderivatives? | |
| 1866 Why arent integration and differentiation inverses of each other? | |
| 1867 Is 128 the only multi-digit power of 2 such that each of its digits is also a power of 2? | |
| 1868 Do we really need reals? | |
| 1869 How can someone reject a math result if everything has to be proved? | |
| 1870 What are some things we can prove they must exist, but have no idea what they are? | |
| 1871 I dont understand Gödels incompleteness theorem anymore | |
| 1872 Where to begin with foundations of mathematics | |
| 1873 Development of the Idea of the Determinant | |
| 1874 Do we need to formally teach the Greek Alphabet? | |
| 1875 The Meaning of the Fundamental Theorem of Calculus | |
| 1876 A conjecture involving prime numbers and circles | |
| 1877 Is the percentage symbol a constant? | |
| 1878 Is a proof still valid if only the writer understands it? | |
| 1879 Set Theoretic Definition of Numbers | |
| 1880 Why cant Antoines necklace fall apart? | |
| 1881 Areas versus volumes of revolution: why does the area require approximation by a cone? | |
| 1882 Designing an Irrational Numbers Wall Clock | |
| 1883 Must eigenvalues be numbers? | |
| 1884 How does the divisibility graphs work? | |
| 1885 Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem. | |
| 1886 The identity cannot be a commutator in a Banach algebra? | |
| 1887 If the field of a vector space werent characteristic zero, then what would change in the theory? | |
| 1888 What are some math books written in dialogue or story form, e.g., a teacher explaining to a student? | |
| 1889 A zero sum subset of a sum-full set | |
| 1890 Why cant we define more elementary functions? | |
| 1891 A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$ | |
| 1892 Sheldon Cooper Primes | |
| 1893 Notations that are mnemonic outside of English | |
| 1894 Hidden patterns in $\sin(a x^2)$ | |
| 1895 AM-GM-HM Triplets | |
| 1896 Why is the Galois Correspondence intuitively plausible? | |
| 1897 Generalizing the sum of consecutive cubes $\sum_{k=1}^n k^3 = \Big(\sum_{k=1}^n k\Big)^2$ to other odd powers | |
| 1898 A curious equality of integrals involving the prime counting function? | |
| 1899 Xmas Maths 2015 | |
| 1900 How to evaluate $\int_0^\infty\operatorname{erfc}^n x\ \mathrm dx$? | |
| 1901 Time to reach a final state in a random dynamical system (answer known, proof unknown) | |
| 1902 What numbers can be created by $1-x^2$ and $x/2$? | |
| 1903 Is there a way to get trig functions without a calculator? | |
| 1904 Sample Standard Deviation vs. Population Standard Deviation | |
| 1905 Why does an integral change signs when flipping the boundaries? | |
| 1906 Why is the absolute value function not differentiable at $x=0$? | |
| 1907 Effect of elementary row operations on determinant? | |
| 1908 Do all square matrices have eigenvectors? | |
| 1909 Is zero a prime number? | |
| 1910 How to find a basis for the intersection of two vector spaces in $\mathbb{R}^n$? | |
| 1911 Subgroup of index $2$ is Normal | |
| 1912 The generating function for the Fibonacci numbers | |
| 1913 Examples of infinite groups such that all their respective elements are of finite order. | |
| 1914 Why are $3D$ transformation matrices $4 \times 4$ instead of $3 \times 3$? | |
| 1915 Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$ | |
| 1916 Every linear mapping on a finite dimensional space is continuous | |
| 1917 difference between maximal element and greatest element | |
| 1918 How can a set contain itself? | |
| 1919 Sum of two closed sets in $\mathbb R$ is closed? | |
| 1920 How unique are $U$ and $V$ in the Singular Value Decomposition? | |
| 1921 Are normal subgroups transitive? | |
| 1922 Why is the ring of matrices over a field simple? | |
| 1923 In set theory, how are real numbers represented as sets? | |
| 1924 Is it possible to plot a graph of any shape? | |
| 1925 Proving $\frac{\sin x}{x} =\left(1-\frac{x^2}{\pi^2}\right)\left(1-\frac{x^2}{2^2\pi^2}\right) \left(1-\frac{x^2}{3^2\pi^2}\right)\cdots$ | |
| 1926 Subgroups of finitely generated groups are not necessarily finitely generated | |
| 1927 $|G|>2$ implies $G$ has non trivial automorphism | |
| 1928 There exists a power of 2 such that the last five digits are all 3s or 6s. Find the last 5 digits of this number | |
| 1929 Does a Fourier transformation on a (pseudo-)Riemannian manifold make sense? | |
| 1930 $\sin 1^\circ$ is irrational but how do I prove it in a slick way? And $\tan(1^\circ)$ is ..... | |
| 1931 How many fair dice exist? | |
| 1932 How to start a math blog? | |
| 1933 Modus moron rule of inference? | |
| 1934 precise official definition of a cell complex and CW-complex | |
| 1935 Alternative proofs that $A_5$ is simple | |
| 1936 Can you give me some concrete examples of magmas? | |
| 1937 Does Monty Hall logic apply to this real world situation? | |
| 1938 Are there dictionaries in math? | |
| 1939 How did early mathematicians make it without Set theory? | |
| 1940 Sharing a pepperoni pizza with your worst enemy | |
| 1941 Is it wrong to tell children that $1/0 =$ NaN is incorrect, and should be $∞$? | |
| 1942 Why is the Daniell integral not so popular? | |
| 1943 Say $a=b$. Is Do the same thing to both sides of an equation, and it still holds an axiom? | |
| 1944 Why is there antagonism towards extended real numbers? | |
| 1945 What is a topological space good for? | |
| 1946 Are rational points dense on every circle in the coordinate plane? | |
| 1947 What do mathematicians mean by equipped? | |
| 1948 Category-theoretic limit related to topological limit? | |
| 1949 Notation for an interval when you dont know which bound is greater | |
| 1950 Why can we use induction when studying metamathematics? | |
| 1951 Finding the value of $\sqrt{1+2\sqrt{2+3\sqrt{3+4\sqrt{4+5\sqrt{5+\dots}}}}}$ | |
| 1952 What if $\pi$ was an algebraic number? (significance of algebraic numbers) | |
| 1953 Solution to the equation of a polynomial raised to the power of a polynomial. | |
| 1954 Are commutative C*-algebras really dual to locally compact Hausdorff spaces? | |
| 1955 Is $dx\,dy$ really a multiplication of $dx$ and $dy$? | |
| 1956 Proving $\sum_{n=-\infty}^\infty e^{-\pi n^2} = \frac{\sqrt[4] \pi}{\Gamma\left(\frac 3 4\right)}$ | |
| 1957 How do you prove Gautschis inequality for the gamma function? | |
| 1958 Function that is the sum of all of its derivatives | |
| 1959 Identity for simple 1D random walk | |
| 1960 Prove $\int\limits_{0}^{\pi/2}\frac{dx}{1+\sin^2{(\tan{x})}}=\frac{\pi}{2\sqrt{2}}\bigl(\frac{e^2+3-2\sqrt{2}}{e^2-3+2\sqrt{2}}\bigr)$ | |
| 1961 How to maintain enthusiasm and joy in teaching when the material grows stale | |
| 1962 An exotic sequence | |
| 1963 Making trigonometric substitutions rigorous | |
| 1964 A new kind of fractal? | |
| 1965 How do you go about doing mathematics on a day to day basis? | |
| 1966 $C^{k}$-manifolds: how and why? | |
| 1967 Why do I only breathe out of one nostril? | |
| 1968 Why are so few foods blue? | |
| 1969 Does DNA have the equivalent of IF-statements, WHILE loops, or function calls? How about GOTO? | |
| 1970 How many times did terrestrial life emerge from the ocean? | |
| 1971 Do bacteria die of old age? | |
| 1972 Is there a reason why human eyesight and plants make use of the same wavelength of light? | |
| 1973 Why is thymine rather than uracil used in DNA? | |
| 1974 Are male and female brains physically different from birth? | |
| 1975 What is the effect of non-vaccinated people on vaccinated people? | |
| 1976 Why do plants have green leaves and not red? | |
| 1977 Can HIV be transmitted via mosquitos? | |
| 1978 Whats the evidence against SARS-CoV-2 being engineered by humans? | |
| 1979 Do beneficial viruses exist? If so, what examples are there? | |
| 1980 Does the string ...CATCAT... appear in the DNA of Felis catus? | |
| 1981 Why did the process of sleep evolve in many animals? What is its evolutionary advantage? | |
| 1982 Are humans the only species who drink milk as adults? | |
| 1983 How could humans have interbred with Neanderthals if were a different species? | |
| 1984 Why do some bad traits evolve, and good ones dont? | |
| 1985 Death because of distilled water consumption | |
| 1986 Why is the heart not in the middle of the body? | |
| 1987 Why 20 amino acids instead of 64? | |
| 1988 Is there an RGB equivalent for smells? | |
| 1989 Whats up with this leaf? | |
| 1990 How does the brains energy consumption depend on mental activity? | |
| 1991 Do animals exhibit handedness (paw-ness?) preference? | |
| 1992 Why do Humans not produce Vitamin C like other mammals? | |
| 1993 Why shouldnt dogs eat chocolate? | |
| 1994 Why are there no wheeled animals? | |
| 1995 What is the evolutionary advantage of red-green color blindness? | |
| 1996 Do ants or other insects sleep, and if so why? | |
| 1997 What could cause a forest of bent trees? | |
| 1998 Is there any evidence that sexual selection may lead to extinction of species? | |
| 1999 Why does evolution not make our life longer? | |
| 2000 Why does it hurt the next day after doing significant exercise? | |
| 2001 Can a woman give birth to twins with different fathers? | |
| 2002 Are there organisms with fewer than 1000 neurons? | |
| 2003 How come large herbivores have such thin legs? | |
| 2004 A new species of small bird? | |
| 2005 Why dont mammals have more than 4 limbs? | |
| 2006 Why do smaller mammals move intermittently? | |
| 2007 Are the social-distancing measures implemented against SARS-CoV-2 also suppressing the spread of other viruses? | |
| 2008 Why do the fastest runners tend to be black? | |
| 2009 Life without DNA? | |
| 2010 What is the benefit of fever during infections? | |
| 2011 Why isnt a virus alive? | |
| 2012 Why do men have nipples? | |
| 2013 Why are there no organisms with metal body parts, like weapons, bones, and armour? (Or are there?) | |
| 2014 Human perception of time depending on age | |
| 2015 Do large animals experience a meaningful delay when moving their most distant appendages? | |
| 2016 Why does cracking a joint make noise? | |