Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics.
Although the layperson may think that mathematical logic is
the logic of mathematics, the truth is rather that it more closely
resembles the mathematics of logic. It comprises those parts of logic
that can be modeled mathematically. Earlier appellations were symbolic logic (as
opposed to philosophical logic); and meta-mathematics, which is now restricted
as a term to some aspects of proof theory.