Logic as subset of mathematics and mathematics as subset of logic

Question

Is logic a subset of mathematics or is mathematics a subset of logic? I have heard the former view, but is there any argument for the latter?

Answer 1

Mathematical logic is a branch of mathematics. But mathematical logic is by no means all of logic.

There have been recurrent attempts, from Frege through Whitehead/Russell and others, to develop mathematics within what they thought of as logic. The attempts failed, we have moved on.

Answer 2

[(logic) $\cap$ (math) $\neq \varnothing$] $\;\land\;$ [(logic)$\setminus$(math) $\neq \varnothing$] $\;\land\;$ [(math)$\setminus$ (logic) $\neq \varnothing$].

That is, the intersection of logic and math is clearly not empty, but I think it is also the case that neither one completely encompasses (contains) the other.

Also note:
Mathematical Logic is a branch of mathematics, and is also of interest to (some) philosophers.
Likewise,
Philosophy of Math is a branch of Philosophy, which is also of interest to (some) mathematicians.

Answer 3

It is actually the other way around. Philosophy is the root of all sciences, including mathematics. You can think of mathematics as an application of logic.

Answer 4

Also, you can think of both mathematics and logic as subsets of the Philosophy of Proof.