for all infinite sets X X and Y Y. Proving this required most of the concepts and results from the second half of the course: well ordered sets, the Cantor–Bernstein theorem, the Hartogs theorem, Zorn ...

Previously: Part 8. Next: Part 10. It’s the penultimate week of the course, and up until now we’ve abstained from using the axiom of choice. But this week we gorged on it. The section I most enjoyed ...

Previously: Part 6. Next: Part 8. As the course continues, the axioms fade into the background. They rarely get mentioned these days. Much more often, the facts we’re leaning on are theorems that were ...

every family of well ordered sets has a least member — informally, “the well ordered sets are well ordered”; ...

Are you interested in using category-theoretic methods to tackle problems in topics like quantum computation, machine learning, numerical analysis or graph theory? Then you might like the Adjoint ...

You can now apply for the 2025 Summer Research Associate program at the Topos Institute! This is a really good opportunity. Details and instructions on how to apply are in the official announcement. A ...

Thurston gave a concrete procedure to construct triangulations of the 2-sphere where 5 or 6 triangles meet at each vertex. How can you get the icosahedron using this procedure? Gerard Westendorp has a ...

Thurston’s paper Shapes of polyhedra and triangulations of the sphere is really remarkable. I’m writing about it in my next column for the Notices of the American Mathematical Society. Here’s a draft ...

This is the homepage for the UT Geometry and Quantum Field Theory Seminar. At the organizational meeting we will flesh out the details of our plans for the semester. Below are some suggestions to get ...

Nov 15, 2024 The penultimate week of this axiomatic set theory course, based on Lawvere’s Elementary Theory of the Category of Sets.