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

Stephen Wolfram

One can view a symbolic expression such as f[g[x][y, h[z]], w] as a hierarchical or tree structure , in which at every level some particular “head” (like f ) is “applied to” one or more arguments. So how about logic, or, more specifically Boolean algebra ? We’ve looked at axioms for group theory and for Boolean algebra.

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Can AI Solve Science?

Stephen Wolfram

My first big success came in 1981 when I decided to try enumerating all possible rules of a certain kind (elementary cellular automata) and then ran them on a computer to see what they did: I’d assumed that with simple underlying rules, the final behavior would be correspondingly simple. Yes, there can be a lot of flexibility in this model.

Science 122
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Even beyond Physics: Introducing Multicomputation as a Fourth General Paradigm for Theoretical Science

Stephen Wolfram

Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. In physics, those “topological phenomena” presumably correspond to things like elementary particles , with all their various elaborate symmetries.

Physics 65
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Multicomputation: A Fourth Paradigm for Theoretical Science

Stephen Wolfram

Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. In physics, those “topological phenomena” presumably correspond to things like elementary particles , with all their various elaborate symmetries.

Science 64
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The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica

Stephen Wolfram

In addition to whole courses, we have “miniseries” of lectures about specific topics: And we also have courses —and books—about the Wolfram Language itself, like my Elementary Introduction to the Wolfram Language , which came out in a third edition this year (and has an associated course, online version, etc.): is PositionSmallest.

Computer 102