3.0

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With the appearance of Zermelo-Fraenkel set theory (ZF) in the early 20th century and the subsequent identification of first-order logic, the problem of an adequate foundations for mathematics was thought to have been solved. The emergence of category theory (Cat) in the latter half of the century and more recently of homotopy type theory (HoT) has been seen to undermine ZF’s foundational status and to threaten to replace it. In this course we will (1) see how ZF serves as a foundation, (2) learn a bit of Cat and HoT, and (3) discuss what the foundations can and should be (if any).