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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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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 121
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A 50-Year Quest: My Personal Journey with the Second Law of Thermodynamics

Stephen Wolfram

Statistical Mechanics and Simple Programs Back in 1973 I never really managed to do much science on the very first computer I used. And finally I gave what the 22-year-old me thought at the time was the most plausible explanation: All of this was in a sense rooted in a traditional mathematical physics style of thinking.

Physics 95