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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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Numbers and networks: how can we use mathematics to assess the resilience of global supply chains?

Futurum

Numbers and networks: how can we use mathematics to assess the resilience of global supply chains? At Brigham Young University in the US, Dr Zach Boyd is using his mathematical skills to determine how best to protect our supply chains. BUILDING MATHEMATICAL MODELS. FIELD OF RESEARCH: Mathematics. Published: July 13, 2022.

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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

And in it this computation is going on: &#10005. Let’s change the rule for the computation a bit. But that ignores the phenomenon of computational irreducibility. But it’s a fundamental fact of the computational universe that the result doesn’t have to be simple: &#10005. Imagine you have some sophisticated AI.

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The Concept of the Ruliad

Stephen Wolfram

Think of it as the entangled limit of everything that is computationally possible: the result of following all possible computational rules in all possible ways. And it’s one that I think has extremely deep implications—both in science and beyond. (And—it The full ruliad is in effect a representation of all possible computations.

Physics 122