Spectacular Connection Between LLMs, Quantum Systems, and Number Theory

In my recent research on cracking the deepest mathematical mystery, with version 2.0 published yesterday and available here as paper 51, 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 between 0% and 100% 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 (versus 10,000 in the original version). No one before has ever analyzed the digits of such titanic numbers!

To read the full article, participate in the AI challenge to test reasoning, math and pattern detection capabilities of LLMs, get the Python code, read about ground-breaking research, and see all the applications, follow this link.

If you already looked at the Python code in version 1.0, note that the new version is 10 times faster with the Gmpy2 library, and now handles numbers even far bigger. I also tested it with different seeds, one of them producing the dynamics shown in the picture below, leading to chaos in much fewer iterations, making it more suitable for cryptography.