Before mathematics can prove anything, it has to agree on the rules of the game: what counts as a valid argument, what a set really is, and what it means for a statement to be true. Foundations and logic is the part of mathematics that studies mathematics itself — the bedrock the whole tree is built on.

Three areas to explore

Start with proof & logic — how to reason watertight, from "if–then" to proof by induction. Make it formal with mathematical logic, where proof itself becomes an object of study — right up to Gödel's stunning limits on what any system can prove. And meet the raw material everything is built from in set theory, the surprisingly deep mathematics of collections, infinity and size.