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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 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.