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

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

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 105

Computer Biology Mathematics Economics 105