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

Robert Talbert, Ph.D.

In the original article, I gave a list of what computing skills mathematics majors should learn and when they should learn them. If anything, over the past seven years, my feelings about the centrality of computing in the mathematics major have gotten even more entrenched. Mostly this is because of two things.

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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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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.) Mathematically this can be thought of as being like decomposing the ruliad structure in terms of fibrations and foliations.). The View from Mathematics.

Physics 122
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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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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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Remembering the Improbable Life of Ed Fredkin (1934–2023) and His World of Ideas and Stories

Stephen Wolfram

It didn’t help that his knowledge of physics was at best spotty (and, for example, I don’t think he ever really learned calculus). “Lick” Licklider —who persuaded Ed to join BBN to “teach them about computers”. So what happened is Marvin [Minsky] and I basically fleshed out the idea of a mathematical thing.