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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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What Is ChatGPT Doing … and Why Does It Work?

Stephen Wolfram

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. It’s just something that’s mathematically simple, and we’re used to the fact that lots of data we measure turns out to be well fit by mathematically simple things.

Computer 145
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On the frontline of the biomedical revolution

Futurum

There’s a lot of exciting science out there, but for it to be useful for society, it needs to be translated into accessible technology that can be commercialised,” says Jin. I loved building things, such as with LEGO, and enjoyed mathematics – I was always quite good at it. “I The other potential limitation is people.

Biology 98
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Indoor STEM Activities for Kids

STEM Sport

Focusing on STEM (science, technology, engineering, and mathematics) activities can be an excellent strategy to keep students engaged in winter. These activities help reinforce mathematical concepts playfully, promoting logical thinking and problem-solving skills, which are essential components of mathematical understanding.

STEM 52
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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 90
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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. From mathematics. Mathematical physics. By the late 1970s, though, there were other initiatives emerging, particularly coming from mathematics and mathematical physics. Synergetics.

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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

Fast numbers-based ways to do particular computations are often viewed as representing “ exact solutions ” to corresponding mathematical problems. Still, there is in a sense one other kind of computational reducibility that we do know about, and that’s been very widely used in mathematical science: the phenomenon of continuity.