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While it is proven the ZFC is incomplete, and arithmetic foundations is also incomplete. I was looking for a foundation that would achieve Hilbert's dream.

Premise 1 : Kurt Gödel incompleteness theorem uses self reference and based on the logic in Betrand Russel Principia Mathematica.

Premise 2 : Geometric Complexity theory bypasses self referential barrier and works on complexity classes based on symmetries.

Premise 3 : Both Mathematics and Theoretical Physics aim to understand the working of the Universe.

Premise 4 : Lie groups are core for most of modern Particle Physics.

So based on premise 3, It is possible that foundations of math and physics are same. Including Premise 1, 2 and 4, the way to move past self reference based undecidability is to use symmetry, and continuous symmetry is core for modern physics. So can the foundation of mathematics instead of based on axioms can be based on an abstract object, similar to lie groups, then using symmetry breaking as done to connect string theory to standard model, is used to connect the object properties to all math subfields?

panday
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It is not the case that the underpinnings of mathematics and theoretical physics are the same. That's just not a true statement. Theoretical physics is about the universe, mathematics doesn't care about the universe.

Additionally, I'm not sure what you're talking about when you say that geometric complexity theory avoids self-reference. Geometric complexity theory is an approach to P vs NP

Stella Biderman
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