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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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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

Because for some reason—that maybe one day we’ll have a scientific-style understanding of—if we always pick the highest-ranked word, we’ll typically get a very “flat” essay, that never seems to “show any creativity” (and even sometimes repeats word for word). At some level we didn’t.

Computer 145