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 114

Mathematics Physics Computer Algebra 114

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 116

Physics Mathematics Computer Construction 116

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 88

Energy Physics Argumentation Mathematics 88

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 52

Mathematics Physics Computer Algebra 52

STEM Sport

DECEMBER 12, 2023

Focusing on STEM (science, technology, engineering, and mathematics) activities can be an excellent strategy to keep students engaged in winter. As the air rushes out of the balloon, it propels the balloon forward, vividly illustrating Newton’s Third Law of Motion – for every action, there is an equal and opposite reaction.

STEM 52

STEM Chemistry Problem Solving Biology 52

Stephen Wolfram

MARCH 15, 2023

And indeed it increasingly seems as if the “secret” that nature uses to make the complexity it so often shows is exactly to operate according to the rules of simple programs. And indeed over the past three centuries there’s been lots of success in doing this, mainly by using mathematical equations.

Computer 102

Computer Biology Mathematics Economics 102