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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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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

The history of physics might make one think that numbers would be a necessary part of the structure of any fundamental theory of our physical universe. But the models of physics suggested by our Physics Project have no intrinsic reference to numbers. We discussed above the example of fundamental physics.

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The Concept of the Ruliad

Stephen Wolfram

It’s yet another surprising construct that’s arisen from our Physics Project. And it’s one that I think has extremely deep implications—both in science and beyond. In the language of our Physics Project, it’s the ultimate limit of all rulial multiway systems. For integers, the obvious notion of equivalence is numerical equality.

Physics 122