Mathematical Theory

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.

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.

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 ...

In 2019, Giuseppe Carleo and his team pioneered the application of machine learning to quantum physics. This book is an introduction to how AI revolutionizes quantum field theory (QFT), from scalar fields to complex gauge theories describing quarks and gluons. The narrative unfolds in three acts. First, readers discover the mathematical kinship between neural networks and quantum fields—the renormalization group maps onto information flow through neural layers, while gauge symmetry provides blueprints for AI architectures. Through Python code, readers build networks that discover phase ...

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...

“There’s a book I recommend for everybody: It’s Howard Gardner’s Frames of Mind. It has helped me immensely.” – Robert Greene, author of The 48 Laws of Power What do we mean when we call someone smart? That they are good at math and got a high score on the SAT? That they learn...

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...

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.

The Zito Constant introduces a newly proposed mathematical idea — the value of the Riemann zeta function at the Gelfond constant. In this concise and thought-provoking work, author A.C. Zito defines and interprets this quantity as the Dimensional Boundary Constant, symbolizing the threshold between mathematical structure and transcendental expansion. Blending number theory, transcendence, and speculative physics, Zito explores how the zeta function — one of mathematics’ most mysterious objects — may reveal deeper harmonies within higher-dimensional systems. Written in a clear, ...

Everyone has a basic understanding of how the physical world works. We learn about physics and chemistry in school, letting us explain the world around us in terms of concepts like force, acceleration, and gravity—the Laws of Nature. But we don’t have the same fluency with concepts needed to understand the world inside us—the Laws of Thought. While the story of how mathematics has been used to reveal the mysteries of the universe is familiar, the story of how it has been used to study the mind is not.

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...

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 ...

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...

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.

When we command artificial intelligence to "create random abstract art," something peculiar happens. When AI tries to create chaos, it accidentally reveals the hidden order in everything.Ask any AI to generate "random abstract art." What happens next is a paradox that upends everything we thought we knew about creativity, computation, and consciousness.The machine—free from human muscle memory and cognitive bias—should achieve true randomness. Instead, it produces something far stranger: patterns emerging from chaos. Order materializing from disorder. Symmetry where none was ...