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 116

Mathematics Physics Computer Algebra 116

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.) Mathematically this can be thought of as being like decomposing the ruliad structure in terms of fibrations and foliations.). The View from Mathematics.

Physics 117

Physics Mathematics Computer Construction 117

Stephen Wolfram

JANUARY 31, 2023

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

Energy Physics Argumentation Mathematics 90

Stephen Wolfram

FEBRUARY 2, 2023

It’s a story I’ve told elsewhere , but one of the important elements for our purposes here is that in designing the system I called SMP (for “Symbolic Manipulation Program”) I ended up digging deeply into the foundations of computation, and its connections to areas like mathematical logic.

Physics 95

Physics Computer Mathematics Sciences 95