New Book: 0 And 1 – From Elemental Math To Quantum Ai

The book is disposable connected our E-store, here. 

It each started pinch nan number 1. This e-book offers a travel heavy into nan astir elusive and fascinating multi-century aged conjecture successful number theory: are nan binary digits of nan basal mathematics constants evenly distributed? No 1 moreover knows if nan proportions of ‘0’ and ‘1’ exist, for immoderate of them: it could oscillate indefinitely betwixt 0% and 100%.

After a speedy read, you mightiness beryllium convinced that I solved it. Yet very soft functions visibly converging to nan expected 50% ratio, clip aft time, are each but fume and mirrors for nan knowledgeable practitioner. They are known to person unexpected, ample singularities successful highly uncommon cases. And if you look astatine nan images successful nan book pinch a microscope, location is still a spot of lingering randomness moreover aft utilizing precocious chaos removal techniques. Throughout this book, I guideline nan reader, informing astir these caveats and dormant ends while pointing to promising directions to activity connected nan conjecture.

My caller attack sets a clear way towards solving nan problem, for nan first clip ever. Building connected coagulated foundations spanning crossed aggregate disciplines, I stock a number of spectacular victories on nan way. For instance, this caller and unexpected result: each numbers that tin beryllium written as

where (an) is an expanding series of affirmative integers pinch sub-linear maturation rate, person a proportionality of `1′ adjacent to zero successful their infinite binary digit description .

I dream this archive becomes a reference connected nan taxable and serves arsenic a launchpad towards a last resolution. It is written successful elemental English, motto free, moreover erstwhile covering precocious topics. With enterprise-grade Python codification on pinch businesslike algorithms not taught successful immoderate schoolroom aliases textbook. To use from nan material, you request beginner acquisition pinch Python, and nan balanced of a first-year assemblage people connected calculus. The book is targeted to professionals successful AI, instrumentality learning, engineering, physics, technological computing, operations research, machine science, and Fintech. Students pinch an analytical mindset will observe original, useful worldly to heighten their creativity, learning experience, while gaining beardown vulnerability to master codification and applications.

This book besides opens up caller investigation areas successful theoretical and computational number theory, numerical approximation, dynamical systems, quantum dynamics, and nan physics of numbers. With a beardown accent connected applications: automated shape discovery and theorem proving pinch AI, agent-based modeling, building a cosmopolitan unbiased pattern-rich synthetic dataset, cryptography (fast, beardown random number generators based connected irrational numbers), dynamical systems pinch chaos discovery and isolation, machine intensive simulations, and high-performance computing to grip numbers specified arsenic 2n+1 at powerfulness 2n with n=106.

Each section is self-contained and tin beryllium publication separately from nan others. Chapters are listed successful chronological order. The past 1 features nan astir caller investigation and discoveries. The first 1 is much technical, focusing connected nan foundations; it tin beryllium skipped initially if you are chiefly willing successful nan applications.

Purchase nan book, here. 56 pages. Published by MLTechniques.com successful May 2025. See array of contents, here.

About nan Author

Vincent Granville is simply a pioneering GenAI scientist, co-founder at BondingAI.io, nan LLM 2.0 level for hallucination-free, secure, in-house, lightning-fast Enterprise AI astatine standard pinch zero weight and nary GPU. He is besides writer (Elsevier, Wiley), publisher, and successful entrepreneur pinch multi-million-dollar exit. Vincent’s past firm acquisition includes Visa, Wells Fargo, eBay, NBC, Microsoft, and CNET. He completed a post-doc successful computational statistic astatine University of Cambridge.