article thumbnail

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

Stephen Wolfram

And if we’re going to make a “general theory of mathematics” a first step is to do something like we’d typically do in natural science, and try to “drill down” to find a uniform underlying model—or at least representation—for all of them. and at t steps gives a total number of rules equal to: &#10005. &#10005.

article thumbnail

The Concept of the Ruliad

Stephen Wolfram

For integers, the obvious notion of equivalence is numerical equality. Then (by the assumed properties of equality) it follows that. But it’s a fundamental claim that we’re making—that can be thought of as a matter of natural science—that in our universe only computation can occur, not hypercomputation.

Physics 121