In my recent article “Piercing the Deepest Mathematical Mystery”, I paved the way to proving a famous multi-century old conjecture: are the digits of major mathematical constant such as π, e, log 2, or √2 evenly distributed? No one before ever managed to prove even the most basic trivialities, such as whether the proportion of ‘0’ or ‘1’ exists in the binary expansions of any of these constants, or if it oscillates indefinitely between 0% and 100%.
Here I provide an overview of the new framework built to uncover deep results about the digit distribution of Euler’s number e, discuss the latest developments, share a 10x faster version of the code, and feature new potential research areas in LLMs, AI, quantum dynamics, high performance computing, cryptography, dynamical systems, number theory and more, arising from my discovery. Perhaps the most interesting part is testing LLMs and other AI tools to assess their reasoning capabilities on a fascinating math problem with no solution posted anywhere.
In my recent paper 51 on cracking the deepest mathematical mystery, available at https://mltblog.com/3zsnQ2g, I paved the way to solve a famous multi-century old math conjecture. The question is whether or not the digits of numbers such as π are evenly distributed. Currently, no one knows if the proportion of '1' even exists in these binary digit expansions. It could oscillate forever without ever converging. Of course, mathematicians believe that it is 50% in all cases. Trillions of digits have been computed for various constants, and they pass all randomness tests. In this article, I offer a new framework to solve this mystery once for all, for the number e.
Rather than a closure on this topic, it is a starting point opening new research directions in several fields. Applications include cryptography, dynamical systems, quantum dynamics, high performance computing, LLMs to answer difficult math questions, and more. The highly innovative approach involves iterated self-convolutions of strings and working with numbers as large as 2^n + 1 at power 2^n, with n larger than 100,000. No one before has ever analyzed the digits of such titanic numbers!
To read the full article, participate in the AI & LLM challenge, get the very fast Python code, read about ground-breaking research, and see all the applications, visit https://mltblog.com/3DgambA
