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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

This is the first of a series of pieces I’m planning in connection with the upcoming 20th anniversary of the publication of A New Kind of Science. “There’s a Whole New Field to Build…” For me the story began nearly 50 years ago —with what I saw as a great and fundamental mystery of science. From mathematics.

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The Concept of the Ruliad

Stephen Wolfram

And it’s one that I think has extremely deep implications—both in science and beyond. And—it should be said at the outset—we’re still only at the very beginning of nailing down those technical details and setting up the difficult mathematics and formalism they involve.) Experiencing the Ruliad. But in the ruliad there are no choices.

Physics 122
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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

Stephen Wolfram

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. There were still mathematical loose ends, as well as issues such as its application to living systems and to systems involving gravity.

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

Stephen Wolfram

Or you could do what is the essence of theoretical science: make a model that gives some kind of procedure for computing the answer rather than just measuring and remembering each case. Then we might make a mathematical guess, like that perhaps we should use a straight line as a model: We could pick different straight lines.

Computer 145