Often times it is useful for mathematicians to have multiple ways to approach a given problem. It is not uncommon to find solutions for a given problem making use of very different areas of mathematics.
I am particularly interested in other ways to formulate the P vs. NP problem. For instance, there are objects known as modular machines which are Turing-equivalent whose underlying mode of operation rely heavily on principles of number theory. I am wondering then, if there is a way to formulate the P vs. NP problem as a number theoretical one.
More generally, are there equivalent problems to P vs. NP in other fields of mathematics? That is, can we reformulate P vs. NP in other mathematical disciplines?
I'm looking for something along the lines of this answer on a question from CS.SE.