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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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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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Expression Evaluation and Fundamental Physics

Stephen Wolfram

Since the standard Wolfram Language evaluator evaluates arguments first (“leftmost-innermost evaluation”), it therefore won’t terminate in this case—even though there are branches in the multiway evaluation (corresponding to “outermost evaluation”) that do terminate. If you set , then you set , you should get (not ) if you asked for.

Physics 108
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Even beyond Physics: Introducing Multicomputation as a Fourth General Paradigm for Theoretical Science

Stephen Wolfram

Many would say that modern exact science was launched in the 1600s with the introduction of what we can call the “ mathematical paradigm ”: the idea that things in the world can be described by mathematical equations—and that their behavior can be determined by finding solutions to these equations.

Physics 65
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Multicomputation: A Fourth Paradigm for Theoretical Science

Stephen Wolfram

Many would say that modern exact science was launched in the 1600s with the introduction of what we can call the “ mathematical paradigm ”: the idea that things in the world can be described by mathematical equations—and that their behavior can be determined by finding solutions to these equations.

Science 64
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What should mathematics majors know about computing, and when should they know it?

Robert Talbert, Ph.D.

As I teach my Linear Algebra and Differential Equations class this semester, which uses more computing than ever, I'm thinking even more about these topics. In the original article, I gave a list of what computing skills mathematics majors should learn and when they should learn them.

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Remembering the Improbable Life of Ed Fredkin (1934–2023) and His World of Ideas and Stories

Stephen Wolfram

. “Lick” Licklider —who persuaded Ed to join BBN to “teach them about computers”. It didn’t really come to light until he was at BBN, but while at Lincoln Lab Ed had made what would eventually become his first lasting contribution to computer science. Then McCarthy started to explain ways a computer could do algebra.