Algebra Elementary Equality Mathematics 
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.
Stephen Wolfram
MAY 25, 2021
Instead, what happens is that the universe evolves by virtue of lots of elementary updating events happening throughout the network. Fast numbers-based ways to do particular computations are often viewed as representing “ exact solutions ” to corresponding mathematical problems. Are Numbers Even Inevitable in Mathematics?
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Stephen Wolfram
MARCH 5, 2024
Three centuries ago science was transformed by the idea of representing the world using mathematics. And that’s for example why things like mathematical formulas have been able to be as successful in science as they have. In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be.
Stephen Wolfram
JUNE 28, 2023
They’re mathematically more complex, but each one we successfully cover makes a new collection of problems accessible to exact solution and reliable numerical and symbolic computation. It’s the end of a long journey, and a satisfying achievement in the quest to make as much mathematical knowledge as possible automatically computable.
Stephen Wolfram
DECEMBER 11, 2023
But here we want to think not about what’s “mathematically describable”, but instead about what in general is actually implemented —say by our senses, our measuring devices, or our ways of analyzing things. And one particularly prominent example of this is mathematics, or rather, metamathematics. But other features do not.
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.
Stephen Wolfram
OCTOBER 7, 2021
And the involvement of numbers will often allow us to make immediate use of traditional mathematical methods. or ) must for example be equal to 1 mod 2, 3 and 6. This structure is very dependent on the algebraic properties of. How should we decompose that into “elementary events”? ✕. for some integers u and v.
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