What is the name of this fundamental math theory?

Question

I remember reading a while back on Wikipedia about a theory that says all of Mathematics can be reduced to a set of string manipulation rules and don't need to have any actual meaning. So e.g. if 2+2=4 then wherever we see 2+2 we replace it with 4 and so solve bigger equations.

I thought it was called String Manipulation theory, but that doesn't seem to be the case.

(It's not limited to calculus, but I couldn't find any other appropriate tag).

Answer 1

The theory that you described, "all of mathematics can be reduced to a set of string manipulation rules and do[es]n't need to have any actual meaning," doesn't seem to be a math theory (as in your title) at all but rather a philosophical theory about the nature of mathematics. Specifically, it seems to be a (rather extreme) version of formalism. By googling "formalism", you should be able to find more than you ever wanted to know about this topic.

Answer 2

You are presumably referring to syntax — the part of formal logic that deals with the study of (formal) mathematical statements and deductive proofs.

A related notion is that of string rewriting, which also has uses outside of formal logic.