Mathematical logic

Frege's development began with... "an epoch-making little book" called , translated as Concept Script or Conceptual Notation... Just as Aristotle's is the foundation of traditional or syllogistic logic—the logic of the categorical three-term syllogism, Frege's Begriffsschrift is the keystone of modern or mathematical logic.

— Mathematical logic

In 1920 logic was mostly a philosopher's garden. There were also a few mathematicians there, cultivating the logical roots of the mathematical tree. Today, Recursion Theory, Set Theory, Model Theory and Proof Theory, logic's major subdisciplines, have become full-fledged branches of mathematics.

— Mathematical logic