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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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Don’t Give Up on Algebra: Let’s Shift the Focus to Instruction

National Science Foundation

In its current form, school algebra serves as a gatekeeper to higher-level mathematics. Researchers and policy makers have pushed to open that gate—providing more students access to algebra, focusing in particular on those students historically denied access to higher-level mathematics. Berry & Larson, 2019; Levitt, 2019).

Algebra 76
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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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Why Choose a STEM Career?

CTE Learning

stands for Science, Technology, Engineering, and Mathematics. On the other hand, physical and biological sciences, mathematics, science technology, and agricultural sciences pay around $50,400 on average. With STEM, customary gender roles are broken, and it gives way to equality in every possible way. The acronym “S.T.E.M.”

STEM 52
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Why Choose a STEM Career?

CTE Learning

” stands for Science, Technology, Engineering, and Mathematics. Mathematics is typically in every activity or occupation we do in life. On the other hand, physical and biological sciences, mathematics, science technology, and agricultural sciences pay around $50,400 on average. So what exactly is a STEM based career?

STEM 52
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Launching Version 13.0 of Wolfram Language + Mathematica

Stephen Wolfram

the same integral could still be done, but only in terms of elliptic integrals : Mathematical Functions: A Milestone Is Reached. Special functions are in a sense a way of packaging mathematical knowledge : once you know that the solution to your equation is a Lamé function , that immediately tells you lots of mathematical things about it.

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Computational Foundations for the Second Law of Thermodynamics

Stephen Wolfram

How does one tie all this down with rigorous, mathematical-style proofs? Once one has the idea of “equilibrium”, one can then start to think of its properties as purely being functions of certain parameters—and this opens up all sorts of calculus-based mathematical opportunities. Well, it’s difficult.