Metamathematics
Foundations & Physicalization
"What is mathematics?" is a question that has been debated since antiquity. This book presents a groundbreaking and surprising answer to the question—showing through the concept of the physicalization of metamathematics how both mathematics and physics as experienced by humans can be seen to emerge from the unique underlying computational structure of the recently formulated ruliad. Written with Stephen Wolfram's characteristic expositional flair and richly illustrated with remarkable algorithmic diagrams, the book takes the reader on a unprecedented intellectual journey to the center of some of the deepest questions about mathematics and its nature—and points the way to a new understanding of the foundations and future of mathematics, taking a major step beyond ideas from Plato, Kant, Hilbert, Gödel and others.
Information and Media Inquiries
December 2022 Publication
Publicity and Interviews: swmedia@wolfram.com
Trim Size: 7.44" x 9.69"
NonFiction
Distribution by Ingram, Amazon and Baker & Taylor
Contents
 Preface
 The Physicalization of Metamathematics and Its Implications for the
Foundations of Mathematics  Mathematics and Physics Have the Same Foundations · The Underlying Structure of Mathematics and Physics · The Metamodeling of Axiomatic Mathematics · Some Simple Examples with Mathematical Interpretations · Metamathematical Space · The Issue of Generated Variables · Rules Applied to Rules · Accumulative Evolution · Accumulative String Systems · The Case of Hypergraphs · Proofs in Accumulative Systems · Beyond Substitution: Cosubstitution and Bisubstitution · Some First Metamathematical Phenomenology · Relations to Automated Theorem Proving · Axiom Systems of PresentDay Mathematics · The ModelTheoretic Perspective · Axiom Systems in the Wild · The Topology of Proof Space · Time, Timelessness and Entailment Fabrics · The Notion of Truth · What Can Human Mathematics Be Like? · Going below Axiomatic Mathematics · The Physicalized Laws of Mathematics · Uniformity and Motion in Metamathematical Space · Gravitational and Relativistic Effects in Metamathematics · Empirical Metamathematics · Invented or Discovered? How Mathematics Relates to Humans · What Axioms Can There Be for Human Mathematics? · Counting the Emes of Mathematics and Physics · Some Historical (and Philosophical) Background · Implications for the Future of Mathematics · Some Personal History: The Evolution of These Ideas · Notes & Thanks · Graphical Key · Glossary · Annotated Bibliography
 The Concept of the Ruliad
 The Entangled Limit of Everything · Experiencing the Ruliad · Observers Like Us · Living in Rulial Space · The View from Mathematics · The View from Computation Theory · What's beyond the Ruliad? · Communicating across Rulial Space · So Is There a Fundamental Theory of Physics? · Alien Views of the Ruliad · Conceptual Implications of the Ruliad · Appendix: The Case of the "Multiplicad" · Thanks & Note
 The Empirical Metamathematics of Euclid and Beyond
 Towards a Science of Metamathematics · The Most Famous Math Book in History · Basic Statistics of Euclid · The Interdependence of Theorems · The Graph of All Theorems · The Causal Graph Analogy · The Most Difficult Theorem in Euclid · The Most Popular Theorems in Euclid · What Really Depends on What? · The Machine Code of Euclid: All the Way Down to Axioms · Superaxioms, or What Are the Most Powerful Theorems? · Formalizing Euclid · All Possible Theorems · Math beyond Euclid · The Future of Empirical Metamathematics · Thanks · Note Added
 Implications for Mathematics and Its Foundations, Section 12.9 from
A New Kind of Science (2002)  Notes
 Index
About the Author
Stephen Wolfram is a distinguished scientist and bestselling author, and the creator of some of the world's most respected software systems, including Mathematica, WolframAlpha and the Wolfram Language. For more than 30 years he has been the CEO of the global technology company Wolfram Research.
Other books by Stephen Wolfram

Title: Metamathematics:
Foundations & Physicalization  Author: Stephen Wolfram
 Hardcover: $44.95
 Publisher: Wolfram Media, Inc.
 Publication Date: December, 2022
 ISBN13: 9781579550769 (hardcover)
 ISBN13: 9781579550783 (eBook)