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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 can first-year STEM university students be better supported?

Futurum

At the University of Pittsburgh at Greensburg in the US, biologists Barbara Barnhart and Dr Olivia Long are using their Science Seminar programme to ease this transition for first year students studying biology, chemistry and biochemistry degrees. What do students learn from studying this?

Biology 81
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STEM in Science Classrooms – Difference Between Science and Technology

STEM Education Guide

STEM, an acronym for Science, Technology, Engineering, and Mathematics, is an essential component of the educational experience. Science in STEM It encompasses fields such as geology, chemistry, physics, biology, and astronomy. The institution began to ramp up programs in support of STEM subjects in a boatload of American schools.

Science 52
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Can AI Solve Science?

Stephen Wolfram

Three centuries ago science was transformed by the idea of representing the world using mathematics. And that’s for example why things like mathematical formulas have been able to be as successful in science as they have. But what I want to do here is to discuss what amount to deeper questions about AI in science.

Science 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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The Concept of the Ruliad

Stephen Wolfram

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.) For integers, the obvious notion of equivalence is numerical equality. For hypergraphs, it’s isomorphism. Experiencing the Ruliad.

Physics 122
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The Problem of Distributed Consensus

Stephen Wolfram

In the basic definition of a standard cellular automaton, the rule “takes its arguments” in a definite order. And in 1952 John von Neumann , in his “ Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components ”, began to give a mathematical structure for analyzing this. There is one immediate issue here.