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Expression Evaluation and Fundamental Physics

Stephen Wolfram

And it’s all based on ideas from our Physics Project —and on a fundamental correspondence between what’s happening at the lowest level in all physical processes and in expression evaluation. And this is where we can start making an analogy with physics. And now there’s a deep analogy to physics.

Physics 100
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How To Make Someone Not Hate Math

ED Surge

A respected math teacher at a K-12 public charter school in Apple Valley, California, Holifield was in steep physical decline. He explained how math was useful for real jobs, such as those who test the level of land for construction or create maps, and how as students they could already perform that math. It was fun, she recalls.

Math 215
educators

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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. 23 The Physicalized Laws of Mathematics. 29 Counting the Emes of Mathematics and Physics. 1 | Mathematics and Physics Have the Same Foundations. 3 The Metamodeling of Axiomatic Mathematics. Graphical Key.

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

Stephen Wolfram

One might have thought it was already exciting enough for our Physics Project to be showing a path to a fundamental theory of physics and a fundamental description of how our physical universe works. Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models.

Physics 65
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The Concept of the Ruliad

Stephen Wolfram

It’s yet another surprising construct that’s arisen from our Physics Project. In the language of our Physics Project, it’s the ultimate limit of all rulial multiway systems. And here is a rulial multiway system made from hypergraph rewriting of the kind used in our Physics Project , using all rules with signature : &#10005.

Physics 116
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Five Most Productive Years: What Happened and What’s Next

Stephen Wolfram

I had begun my career in the 1970s as a teenager studying the frontiers of existing physics. And at first I couldn’t see how computational rules could connect to what is known in physics. But I didn’t stop thinking “one day I need to get back to my physics project”. But now with the Physics Project I was doing this.

Physics 110
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The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica

Stephen Wolfram

Then for each function (or other construct in the language) there are pages that explain the function, with extensive examples. So did that mean we were “finished” with calculus? Somewhere along the way we built out discrete calculus , asymptotic expansions and integral transforms. But even now there are still frontiers.