Stephen Wolfram

MARCH 7, 2022

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.

Mathematics 120

Mathematics Physics Computer Algebra 120

Stephen Wolfram

MAY 25, 2021

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.

Mathematics 53

Mathematics Physics Computer Algebra 53

Stephen Wolfram

NOVEMBER 10, 2021

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

Physics Mathematics Computer Construction 122