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Who Can Understand the Proof? A Window on Formalized Mathematics
Stephen Wolfram
For more than a century people had wondered how simple the axioms of logic (Boolean algebra) could be. On January 29, 2000, I found the answer—and made the surprising discovery that they could be about twice as simple as anyone knew. (I also showed that what I found was the simplest possible.)
The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics
Stephen Wolfram
One of the many surprising (and to me, unexpected) implications of our Physics Project is its suggestion of a very deep correspondence between the foundations of physics and mathematics. We might have imagined that physics would have certain laws, and mathematics would have certain theories, and that while they might be historically related, there wouldn’t be any fundamental formal correspondence between them.
But what our Physics Project suggests is that underneath everything we physically experience there is a single very general abstract structure—that we call the ruliad—and that our physical laws arise in an inexorable way from the particular samples we take of this structure.