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class="nav-list"> <li><a href="/products/" class="titles">Titles</a></li> <li><a href="/translations/" class="translations">Translations</a></li> <li><a href="/resources/" class="resources">Author Resources</a></li> <li><a href="/contact/" class="contact">Contact</a></li> </ul> </div> <ul id="nav-desktop" class="nav-list"> <li><a href="/products/" class="titles">Titles</a></li> <li><a href="/translations/" class="translations">Translations</a></li> <li><a href="/resources/" class="resources">Author Resources</a></li> <li><a href="/contact/" class="contact">Contact</a></li> <li class="desktop-search-wrapper"> <button id="desktop-search-icons" class="desktop-button nav-search-button"> <svg viewBox="0 0 20 20" height="16px" width="16px"> <title>Open search form</title> <path class="open" d="m1 3l2-2l7 7l7 -7l2 2l-7 7l7 7l-2 2l-7 -7l-7 7l-2 -2l7 -7z" /> <path class="closed" d="M8 1a7 7 0 0 0-7 7 7 7 0 0 0 7 7 7 7 0 0 0 3.84-1.16L17 19l2-2-5.15-5.15A7 7 0 0 0 15 8a7 7 0 0 0-7-7zm0 2a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5z" /> </svg> </button> <div id="desktop-search-form" class="nav-search-form"> <form action="https://search.wolfram.com/" method="GET"> <input name="query" placeholder="Search all Wolfram sites"> </form> </div> </li> </ul> </div> </nav>  <main> <div class="page-wrapper"> <div class="basic-6040"> <div class="order-1__900"> <section id="product-intro"> <h2 class="heirs-no-widows"> <span class="line-1">Metamathematics</span> <span class="line-2">Foundations & Physicalization</span> </h2> <p>"What is mathematics?" is a question that has been debated since antiquity. This book presents a groundbreaking and surprising answer to the question鈥攕howing 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鈥攁nd points the way to a new understanding of the foundations and future of mathematics, taking a major step beyond ideas from Plato, Kant, Hilbert, G枚del and others.</p> <p class="buttons"> <a href="https://wolfr.am/Metamath-amazon" target="_blank" class="button" data-walid="WM-SW-Metamathematics-Amazon">Buy from Amazon</a> <a href="https://store.wolfram.com/view/book/metamathematics" class="button" data-walid="WM-SW-Metamathematics-Wolfram">Buy from Wolfram</a> <a href="https://www.wolframscience.com/metamathematics/ " class="button" data-walid="WM-SW-Metamathematics-ReadOnline">Read Online</a> </p> </section> <section id="product-info"> <h3 class="basic-h3">Information and Media Inquiries</h3> <p>December 16, 2022 Publication<br>Publicity and Interviews: <a href="mailto:sw-media@wolfram.com">sw-media@wolfram.com</a><br>Trim Size: 7.44" x 9.69"<br>Non-Fiction</p><p>Distribution by Ingram, Amazon and Baker & Taylor</p> <p>UK Distribution: <a href="https://books.turnaround-uk.com/metamathematics.html" target="_blank">Turnaround Publisher Services</a></p> </section> <section id="product-toc"> <h3 class="basic-h3">Contents</h3> <ul class="nested-list"> <li>Preface</li> <li class="sections">The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics</li> <li class="chapters">Mathematics and Physics Have the Same Foundations 路 The Underlying Structure of Mathematics and Physics 路 The Metamodeling of Axiomatic Mathematics 路 Some Simple Examples with Mathematical Interpretations 路 Metamathematical Space 路 The Issue of Generated Variables 路 Rules Applied to Rules 路 Accumulative Evolution 路 Accumulative String Systems 路 The Case of Hypergraphs 路 Proofs in Accumulative Systems 路 Beyond Substitution: Cosubstitution and Bisubstitution 路 Some First Metamathematical Phenomenology 路 Relations to Automated Theorem Proving 路 Axiom Systems of Present-Day Mathematics 路 The Model-Theoretic Perspective 路 Axiom Systems in the Wild 路 The Topology of Proof Space 路 Time, Timelessness and Entailment Fabrics 路 The Notion of Truth 路 What Can Human Mathematics Be Like? 路 Going below Axiomatic Mathematics 路 The Physicalized Laws of Mathematics 路 Uniformity and Motion in Metamathematical Space 路 Gravitational and Relativistic Effects in Metamathematics 路 Empirical Metamathematics 路 Invented or Discovered? How Mathematics Relates to Humans 路 What Axioms Can There Be for Human Mathematics? 路 Counting the Emes of Mathematics and Physics 路 Some Historical (and Philosophical) Background 路 Implications for the Future of Mathematics 路 Some Personal History: The Evolution of These Ideas 路 Notes & Thanks 路 Graphical Key 路 Glossary 路 Annotated Bibliography</li> <li class="sections">The Concept of the Ruliad</li> <li class="chapters">The Entangled Limit of Everything 路 Experiencing the Ruliad 路 Observers Like Us 路 Living in Rulial Space 路 The View from Mathematics 路 The View from Computation Theory 路 What's beyond the Ruliad? 路 Communicating across Rulial Space 路 So Is There a Fundamental Theory of Physics? 路 Alien Views of the Ruliad 路 Conceptual Implications of the Ruliad 路 Appendix: The Case of the "Multiplicad" 路 Thanks & Note</li> <li class="sections">The Empirical Metamathematics of Euclid and Beyond</li> <li class="chapters">Towards a Science of Metamathematics 路 The Most Famous Math Book in History 路 Basic Statistics of Euclid 路 The Interdependence of Theorems 路 The Graph of All Theorems 路 The Causal Graph Analogy 路 The Most Difficult Theorem in Euclid 路 The Most Popular Theorems in Euclid 路 What Really Depends on What? 路 The Machine Code of Euclid: All the Way Down to Axioms 路 Superaxioms, or What Are the Most Powerful Theorems? 路 Formalizing Euclid 路 All Possible Theorems 路 Math beyond Euclid 路 The Future of Empirical Metamathematics 路 Thanks 路 Note Added</li> <li class="sections">Implications for Mathematics and Its Foundations, Section 12.9 from A New Kind of Science (2002)</li> <li class="chapters">Notes</li> <li>Index</li> </ul> </section> <section id="product-author"> <h3 class="basic-h3">About the Author</h3> <p><a href="//www.stephenwolfram.com/">Stephen Wolfram</a> is a distinguished scientist and best-selling author, and the creator of some of the world's most respected software systems, including Mathematica, Wolfram|Alpha and the Wolfram Language. For more than 30 years he has been the CEO of the global technology company Wolfram Research.</p> <h3 class="basic-h3">Other Books by Stephen Wolfram</h3> <ul> <li><a href="/products/the-second-law-resolving-the-mystery-of-the-second-law-of-thermodynamics/"><em>The Second Law: Resolving the Mystery of the Second Law of Thermodynamics</em></a></li> <li><a href="/products/what-is-chatgpt-doing-and-why-does-it-work/"><em>What Is ChatGPT Doing ... and Why Does It Work?</em></a></li> <li><a href="/products/twenty-years-of-a-new-kind-of-science/"><em>Twenty Years of A New Kind of Science</em></a></li> <li><a href="/products/combinators-a-centennial-view.html"><em>Combinators: A Centennial View</em></a></li> <li><a href="/products/a-project-to-find-the-fundamental-theory-of-physics/"><em>A Project to Find the Fundamental Theory of Physics</em></a></li> <li><a href="/products/adventures-of-a-computational-explorer/"><em>Adventures of a Computational Explorer</em></a></li> <li><a href="/products/idea-makers/"><em>Idea Makers: Personal Perspectives on the Lives & Ideas of Some Notable People</em></a></li> <li><a href="https://www.wolfram.com/language/elementary-introduction/2nd-ed"><em>An Elementary Introduction to the Wolfram Language</em></a></li> <li><a href="https://www.wolfram-media.com/products/nks/"><em>A New Kind of Science</em></a></li> </ul> </section> </div> <div class="margin-t-3 margin-t-0__900 order-0__900"> <section id="product-cover"> <figure><img src="/products/img/metamathematics-foundations-and-physicalization.png" alt="" width="324" height="422" class="fill-and-center"></figure> </section> <section id="product-details"> <ul> <li><span class="label">Title:</span> <span class="indent no-widows">Metamathematics: Foundations & Physicalization</span></li> <li><span class="label">Author:</span> Stephen Wolfram</li> <li><span class="label">Hardcover:</span> $44.95  456 pages</li> <li><span class="label">eBook:</span> $16.95  456 pages</li> <li><span class="label">Publisher:</span> Wolfram Media, Inc.</li> <li><span class="label">Publication Date:</span> December 16, 2022</li> <li><span class="label">ISBN-13:</span> 978-1-57955-076-9 (hardcover)</li> <li><span class="label">ISBN-13:</span> 978-1-57955-078-3 (eBook)</li> </ul> </section> </div> </div> </div> </main>  <footer id="shared-footer"> <div class="width"> <p class="copyright">漏 2024 Wolfram Media, Inc. 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