Metamathematics

Name: Metamathematics
ISBN: 978-1579550769

by Stephen Wolfram

Publisher

Wolfram Media

Publication

Dec 16, 2022

Format

Hardback

Illustrated

Price

$41.38

Dimensions

10.04 x 7.68 x 1.26 in

ISBN

978-1579550769

ASIN

1579550762

Age

Adult 18+

Rights Sold

🌍 World Wide Rights Available

Description

“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 an 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.

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 Present-Day Mathematics · The Model-Theoretic 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 Metama...

Author(s)

Stephen Wolfram

Stephen Wolfram has had a unique trajectory in science, technology and business. Widely known for his discoveries in basic science and his groundbreaking 2002 book "A New Kind of Science," he has spent more than three decades building what is now Wolfram Language: the knowledge-based computer language that powers Mathematica and Wolfram|Alpha and has contributed to countless inventions and discoveries, as well as to the education of several generations of students.