By the way, what about if you find a mathematical theory that show that:

computer programs and matematical proofs  are no longer something out
of math, but mathematical structures and both are essentially the same
thing: both are paths from premises to conclussion in a  space with
topological properties

And the theory stablish topological relations between these paths so
that proofs and computer algorithms are classified according with
these relations.

That is homotopy type theory.

I´m starting to learn something about it, It is based on type theory,
category theory and topology. The book introduction is nice (HOTT link
at the bottom of the page). It seems to be a foundation of computer
science and math that unify both at a higher level, since proofs and
programs become legitimate mathematical structures

The book:


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