Are the Digits of Pi Random? 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 […]
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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 […]
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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 […]
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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 […]
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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 […]
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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’ […]
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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. […]
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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 […]
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LLM Challenge with Petabytes of Data to Prove Famous Number Theory Conjecture
In my recent article “Piercing the Deepest Mathematical Mystery” posted here, 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 […]
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Piercing the Deepest Mathematical Mystery
Any solution to the mythical problem in question has remained elusive for centuries. It is deemed more difficult than proving the Riemann Hypothesis, yet its formulation can be understood by kids in elementary school. The question is whether or not the digits of mathematical constants such as π, behave like a random sequence. This article […]
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