Reality described by geometry or algebra?

[pivoxa15]

Many people say that geometry is at the heart of physics. However Albert Einstein in his last paper worte that he believed purely algebraic methods will provide a framework for nature i.e unification, TOE etc.

Has he got representation theory on his mind? Or something else?

It raises the question is geometry or algebra at the heart of physics?

 

[George Jones]

Many people say that geometry is at the heart of physics. However Albert Einstein in his last paper worte that he believed purely algebraic methods will provide a framework for nature i.e unification, TOE etc.

The following appeared in an appendix in one of the last editions of Einstein's book The Meaning of Relativity.

"One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers), This does not seem to be in accordance with a continuum theory, and must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the basis of such a theory." (Albert Einstein, 1954)

Has he got representation theory on his mind? Or something else?

I thinks he's talking about the difference between countable and uncountable sets.

It raises the question is geometry or algebra at the heart of physics?

What is geometry? What is algebra? What is algebraic geometry?