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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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Charting a Course for “Complexity”: Metamodeling, Ruliology and More

Stephen Wolfram

And at first I did so in the main scientific paradigm I knew : models based on mathematics and mathematical equations. But in a quirk of history that I now realize had tremendous significance, I had just spent a couple of years creating a big computer system that was ultimately a direct forerunner of our modern Wolfram Language.

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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

Stephen Wolfram

Computational Foundations for the Second Law of Thermodynamics (forthcoming) 2. But by the end of the 1800s, with the existence of molecules increasingly firmly established, the Second Law began to often be treated as an almost-mathematically-proven necessary law of physics. This is part 3 in a 3-part series about the Second Law: 1.

Energy 88
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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
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What Is ChatGPT Doing … and Why Does It Work?

Stephen Wolfram

See also: “Wolfram|Alpha as the Way to Bring Computational Knowledge Superpowers to ChatGPT” » It’s Just Adding One Word at a Time That ChatGPT can automatically generate something that reads even superficially like human-written text is remarkable, and unexpected. But how does it do it? And why does it work?

Computer 145