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The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

1 Mathematics and Physics Have the Same Foundations. 2 The Underlying Structure of Mathematics and Physics. 3 The Metamodeling of Axiomatic Mathematics. 4 Simple Examples with Mathematical Interpretations. 15 Axiom Systems of Present-Day Mathematics. 21 What Can Human Mathematics Be Like? Graphical Key.

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Grades 7-12: Sign Up by Feb. 15 for MIT’s Spring (Virtual) HSSP, Saturdays, Feb. 26-Apr. 2

Newton STEM

All online registrations completed by February 15 will be considered equally in the course-assignment lottery, and registrations after that will be taken first-come/first-served. AI and Science: An Introduction to AI and its Role in Modern Research. Using Computer Science to Model our World. STEM Lecture Series.

Algebra 45
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Grading in my Discrete Mathematics class: a 3x3x3 reflection

Robert Talbert, Ph.D.

Here's the one from Winter 2021 for calculus and here's the one for modern algebra. This semester I taught two sections of Discrete Structures for Computer Science 1, an entry-level course for Computer Science majors on the mathematical foundations of computing.

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Can AI Solve Science?

Stephen Wolfram

But what I want to do here is to discuss what amount to deeper questions about AI in science. Three centuries ago science was transformed by the idea of representing the world using mathematics. What if all we ever want to know about are things that align with computational reducibility?

Science 122
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The Problem of Distributed Consensus

Stephen Wolfram

But what kind of integro-differential-algebraic equation can reproduce the time evolution isn’t clear. And in 1952 John von Neumann , in his “ Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components ”, began to give a mathematical structure for analyzing this.

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The Concept of the Ruliad

Stephen Wolfram

And—it should be said at the outset—we’re still only at the very beginning of nailing down those technical details and setting up the difficult mathematics and formalism they involve.) For integers, the obvious notion of equivalence is numerical equality. For hypergraphs, it’s isomorphism. Experiencing the Ruliad.

Physics 122