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The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

And in what follows we’ll see the great power that arises from using this to combine the achievements and intuitions of physics and mathematics—and how this lets us think about new “general laws of mathematics”, and view the ultimate foundations of mathematics in a different light. So how about logic, or, more specifically Boolean algebra ?

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The Concept of the Ruliad

Stephen Wolfram

For example, we know (as I discovered in 2000) that (( b · c ) · a ) · ( b · (( b · a ) · b )) = a is the minimal axiom system for Boolean algebra , because FindEquationalProof finds a path that proves it. And we can trace the argument for this to the Principle of Computational Equivalence.

Physics 122