Mathematical Theory

From the coauthor of Algorithms to Live By, an exploration of the quest to use mathematics to describe the ways we think, from its origins three hundred years ago to the ideas behind modern AI systems and the ways in which they still differ from human minds. Everyone has a basic understanding of...

The Structure of Reality: Constraint, Coherence, and Control This work defines the structure by which all systems are generated, sustained, and transformed. Fragments of this structure appear across traditions—in Sefer Yetzirah, Sefer ha-Razim, and Ghāyat al-Ḥakīm—as well as in mathematics and natural systems, each describing part of the process without presenting a complete account. Drawing on the research developed by Dr. Erik Gray and known as The Foundations Corpus, this work resolves these fragments into a single operational framework that makes explicit the conditions under ...

Alexander Unzicker is a theoretical physicist and writes about elementary questions of natural philosophy. His critique of contemporary physics Bankrupting Physics (Macmillan) received the ‘Science Book of the Year’ award (German edition 2010). With The Mathematical Reality, Unzicker presents his most fundamental work to date, which is the result of years of study of natural laws and their historical development.The discovery of fundamental laws of nature has influenced the fate of Homo sapiens more than anything else. Has modern physics already understood these laws? Many puzzles ...

On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules.

Are you ready to become a master of strategic thinking? Look no further than The Game Theory Bible, your comprehensive guide to navigating complex decision-making scenarios. With 17 chapters covering everything from basic concepts to real-life applications, this eBook is packed with insights that will change the way you approach problem-solving. Whether you're a business owner looking to gain an edge over the competition or a student hoping to excel in game theory courses, this book gives you the tools you need to succeed. In Chapter 2, you'll learn the fundamental principles of game theory...

Werner Heisenberg entered the atom and found Plato waiting inside. At the foundations of quantum physics lies a strange revelation: matter is not what it seems. The deeper science looks into the physical world, the less reality resembles tiny solid objects moving through empty space. Instead, it reveals uncertainty, probability, measurement, mathematical structures, and invisible forms beneath appearance. In Heisenberg and the Platonic Foundations of Quantum Physics, Clayton Louis Turnage explores the philosophical imagination behind one of the founders of quantum mechanics. From matrix ...

From the coauthor of Algorithms to Live By, an exploration of the quest to use mathematics to describe the ways we think, from its origins three hundred years ago to the ideas behind modern AI systems and the ways in which they still differ from human minds Everyone has a basic understanding of...

Nearly a hundred years after its publication, Kurt Gödel's famous proof that every mathematical system must contain propositions that are true - yet never provable - continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life. 

Fractals Explained: The Geometry of Chaos, Self Similarity, Scaling Laws, and the Hidden Patterns of Nature explores one of the most fascinating revolutions in modern mathematics and science. From the jagged outline of coastlines to the branching of trees and the structure of the human lung, fractals reveal that nature is built on repeating patterns that echo across scales. This book introduces readers to fractal geometry in clear, accessible language while preserving the depth and rigor that make the subject so powerful. If you have ever wondered how simple equations can generate infinite ...

William Stanley Jevons was an English economist and logician. In Brief Account of a General Mathematical Theory of Political Economy, which is essentially a condensed version of his most important piece of work, The Theory of Political Economy, first published in 1850, Javons discusses the marginal utility theory of value, pushing economic thought into the modern era. This piece is a must for both budding young mathematicians and aspiring economists with an interest in the recent history of their fields.

A "powerful, passionate, and inspiring" (New York Times) journey through the beauty and power of mathematics New York Times Bestseller What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso...

For centuries, humanity has studied consciousness, biology, physics, and mind as if they belonged to different worlds. They never did. They only looked that way because human perception is a narrow rendering of a far larger structure — a structure that can finally be modeled, described, and proven. In The Ω-Field, Dr. Erik Gray introduces the first complete framework that unifies the deepest patterns of human life — perception, identity, thought, emotion, death, memory, culture, evolution, intuition, intelligence — inside a single mathematical field. This is not a metaphor. It is a ...

What if humanity’s oldest book of wisdom could become a scientific instrument for navigating the future? The Neo-I Ching: A Mathematical System for Navigating Change, Ethics, and Civilizational Stability transforms the ancient I Ching into a modern framework for understanding complex systems, forecasting regime shifts, and ethically guiding interventions in a world shaped by artificial intelligence, climate disruption, information warfare, pandemics, and geopolitical volatility. Blending complexity science, Bayesian modeling, systems theory, ethics-aware optimization, and civilizational ...

For centuries, humanity has studied consciousness, biology, physics, and mind as if they belonged to different worlds. They never did. They only looked that way because human perception is a narrow rendering of a far larger structure — a structure that can finally be modeled, described, and proven. In The Ω-Field, Dr. Erik Gray introduces the first complete framework that unifies the deepest patterns of human life — perception, identity, thought, emotion, death, memory, culture, evolution, intuition, intelligence — inside a single mathematical field. This is not a metaphor. It is a ...

The Life and Legacy of Jules Henri Poincaré A Master of Pattern Recognition, He Laid the Groundwork for Chaos Theory, Relativity, and More Step into the life of one of history’s most quietly transformative minds—Jules Henri Poincaré, the mathematician, physicist, philosopher, and polymath who bridged the old world of Newtonian mechanics and the modern age of chaos and relativity. In this sweeping and intimate biography, The Life and Legacy of Jules Henri Poincaré traces the journey of a man whose insights redefined the laws of the universe—often before the world was ready to ...

In this must-have for anyone who wants to better understand their love life, a mathematician pulls back the curtain and reveals the hidden patterns—from dating sites to divorce, sex to marriage—behind the rituals of love. The roller coaster of romance is hard to quantify; defining how lovers...

Think in Sets – A Beginner’s Guide to Discrete Maths is a friendly, simple, and clear introduction to the most important subject in computer science: Discrete Mathematics. Written especially for beginners, this book removes fear and confusion and replaces them with confidence and clarity. Whether you are a first-year engineering student, a computer science learner, or someone returning to math after years, this book explains each concept in an easy, intuitive, and learner-friendly way—without sacrificing correctness.

For the past few decades, the financial world has often displayed an unreasonable willingness to believe that "the model is right, the market is wrong," in spite of the fact that these theoretical machinations were largely responsible for the stock market crash of 1987, the LTCM crisis of 1998, the credit crisis of 2008, and many other blow-ups, large and small.

Unveiled the hidden structural mysteries of Albrecht Dürer's masterpiece in this deep dive into alchemical thresholds and philosophical inquiry. Moving beyond traditional interpretations of artistic depression, this interdisciplinary exploration reveals the engraving as a state of suspended readiness and profound attentiveness. By drawing striking parallels with Daoist philosophy, shamanic practices, and musical composition, this study offers a transformative lens for encountering reality, inviting readers into a contemplative space of sober emptiness. The text establishes a comparative ...

A brilliant mathematician examines the complexity of gender and society and forges a path out of inequality. Why are men in charge? After years in the male-dominated field of mathematics and in the female-dominated field of art, Eugenia Cheng has heard the question many times. In x + y, Cheng...