Invitation to Crack Codes Using AI
Could you use AI to crack a cypher? For instance, predict the next bits in bitstreams produced by a high-quality PRNG (pseudo-random generator). Or correctly guessing the next bit in sub-sequences of 100,000 consecutive binary digits of π starting at arbitrary positions, with a success rate above 55%. Without knowing that the digits come from […]
Read More
Quantum, chaotic and fractal types of algorithmic convergence
For centuries, mathematicians worked on problems where the convergence is either smooth or does not happen. Now the concept of chaotic convergence is mainstream, popularized by the stochastic gradient descent in deep neural networks, central to LLMs. In my most recent book here, I discuss many cases involving various types of chaotic convergence. In some […]
Read More
How Random are the Digits of π? State of the Art & Free Book on the Topic
Over the last 10 years, I spent a lot of time analyzing the digits of the classic math constants such as π, e, log 2, √2 and so on. Not testing them for randomness but trying to formally prove that they are undistinguishable from random bit streams. And trying to identify which constants are the […]
Read More
Spectacular New Discovery about the Digits of π
Everyone believes that the digits of constants such as π or √2 cannot be distinguished from a sequence of random bits. The first few trillion successfully pass all tests of randomness. However, proving that they indeed behave perfectly randomly is arguably one of the oldest and most difficult unsolved math conjectures. So far, nobody succeeded […]
Read More
New Book: Breakthroughs on the Digit Distribution of Classic Constants
Since the first edition entitled “0 and 1 — From Elemental Math to Quantum AI” and released in early 2025, a lot of progress has been made. Fascinating new results have been uncovered and proved by the author, many still leading to interesting quantum dynamics. In 100 pages, the new material presented here goes far […]
Read More
Simple Normality Test with Application to Random Number Generation
Numbers such as π, e, log 2 or √2 have binary digits (bits) that look randomly distributed. They are very good candidates to generate randomness especially in cryptography. One way to assess their randomness is by proving that they are normal numbers. Such a proof has remained elusive for centuries. Here I focus on a […]
Read More
How Synthetic Primes Reveal the Quantum States in the Riemann Hypothesis
This research paper showcases spectacular discoveries across multiple disciplines. The main question — yet unanswered — is how the mathematical engineering behind the scenes could be applied to modern AI, deep neural networks (DNNs) and LLMs in particular, to dramatically accelerate the convergence of some slow algorithms. Most notoriously, the laborious and expensive training attached […]
Read More
New Book: 0 and 1 – From Elemental Math to Quantum AI
The book is available on our E-store, here. It all started with the number 1. This e-book offers a trip deep into the most elusive and fascinating multi-century old conjecture in number theory: are the binary digits of the fundamental math constants evenly distributed? No one even knows if the proportions of ‘0’ and ‘1’ […]
Read More
Quantum Dynamics, Logistic Map, and Digit Distribution of Special Math Constants
Using the logistic map instead of the base quadratic system as in paper #53 (here), I obtain very similar quantum dynamics, this time for the function sin2(√x) instead of exp(x). When x is a small integer or a product of consecutive primes, my framework reveals new insights on the digit distribution of major math constants. […]
Read More
Universal Dataset to Test, Enhance and Benchmark AI Algorithms
This scientific research has three components. First, my most recent advances towards solving one of the most famous, multi-century old conjectures in number theory. One that kids in elementary school can understand, yet incredibly hard to prove. At the very core, it is about the spectacular quantum dynamics of the digit sum function. Then, I […]
Read More