Checking for Randomness: Replacing Test Batteries with a Single Test
In cybersecurity applications where replicability is critical, or when building pseudo-random number generators, it is typical to perform a large number of various tests to check if a sequence of bits is random enough for practical purposes. This is also true in scientific research, to assess whether or not the digits of π or other […]
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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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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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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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Visualizing Trading Strategies that Consistently Outperform the Stock Market
In this short paper, I discuss two topics. First, strategies to trade the S&P 500 index with few trades over long time periods, offering best exit, entry and re-entry points during the journey, to beat the baseline return. The baseline consists of staying long the whole time. The dataset has 40 years’ worth of daily […]
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A Synthetic Stock Exchange Played with Real Money
Not only that, but you can predict — more precisely compute with absolute certainty — what the value of any stock will be tomorrow. Transaction fees are well below 0.05% and the market, at least in the version presented here, is fair: in other words, a zero-sum game if you play by luck. If instead […]
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Generating and Videolizing Agglomerative Processes
This short article explains how to efficiently simulate the evolution of agglomerative processes, and visualize their behavior with data animations. I use a generic, simple model for illustration purposes: atoms, initially consisting of one electron, collide and merge over time, with a pre-specified maximum number of electrons per atom: the maximum limit. Given enough time, […]
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New Book: Gentle Introduction To Chaotic Dynamical Systems
In less than 100 pages, the book covers all important topics about discrete chaotic dynamical systems and related time series and stochastic processes, ranging from introductory to advanced, in one and two dimensions. State-of-the art methods and new results are presented in simple English. Yet, some mathematical proofs appear for the first time in this […]
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Introduction to Discrete Chaotic Dynamical Systems
Entitled “Introduction to Discrete Chaotic Dynamical Systems”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. This article is an extract from my book “Gentle Introduction to Chaotic Dynamical Systems”, available here. This is chapter 2 of my upcoming book on dynamical systems and related stochastic processes, expected to be […]
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