Experimental Math

Experimental Math Featured Posts Generative AI Python Synthetic Data

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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Books Experimental Math Featured Posts Python Stochastic Systems Synthetic Data Visualization

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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Experimental Math Featured Posts Machine Learning Python

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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Data Sets Experimental Math Featured Posts Python Synthetic Data

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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Data Sets Experimental Math Featured Posts Machine Learning Natural Language Processing Python Stochastic Systems

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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Books Experimental Math Featured Posts Python

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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Experimental Math Featured Posts Python Statistical Science

Fast Random Generators with Infinite Period for Large-Scale Reproducible AI and Cryptography

Modern GenAI apps rely on billions if not trillions of pseudo-random numbers. You find them in the construction of latent variables in nearly all deep neural networks and almost all applications: computer vision, synthetization, and LLMs. Yet, few AI systems offer reproducibility, though those described in my recent book, do. When producing so many random […]

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Experimental Math Featured Posts Machine Learning Python Statistical Science

Quantum Derivatives, GenAI, and the Riemann Hypothesis

Have you ever encountered a function or cumulative probability distribution (CDF) that is nowhere differentiable, yet continuous everywhere? Some are featured in this article. For a CDF, it means that it does not have a probability density function (PDF), and for a standard function, it has no derivative. At least, not until now. The quantum […]

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Data Sets Experimental Math Featured Posts Python Statistical Science

Number Theory: Longest Runs of Zeros in Binary Digits of Square Root of 2

Studying the longest head runs in coin tossing has a very long history, starting in gaming and probability theory. Today, it has applications in cryptography and insurance. For random sequences or Bernoulli trials, the associated statistical properties and distributions have been studied in detail, even when the proportions of zero and one are different. Yet, […]

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Data Sets Experimental Math Featured Posts Generative AI Synthetic Data Time Series

Sound Generation in Python: Turning Your Data into Music

Not long ago, I published here an article entitled “The Sound that Data Makes”. The goal was turning data — random noise in this case — into music. The hope was that by “listening” to your data, you could gain a different kind of insights, not conveyed by visualizations or tabular summaries. This article is […]

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