Lawvere examines the ideas of toposes and generalised spaces for the geometric insight into reality that they provide.
Foundations of Math
Michael Wright chairs a discussion with conference attendees about ideals apparent in Grothendieck’s work, including geometry, logic, and the philosophy of generalisation.
McLarty considers the difference between introducing new abstract concepts that generalise old ones, and discarding irrelevant, obfuscating assumptions in order to clarify or unify topics. In particular, he focuses on the latter motivation of Grothendieck and Noether.
Cartier reflects on the advantages and disadvantages afforded by set- and category-theoretic formalisations of mathematics.
Crane explores the troubled foundations of geometry, quantum field theory and general relativity, and introduces his notion of the quantum topos.
Lecture with Chris Isham on the topic of Foundations of Math
Interview with Fw Lawvere on the topic of Foundations of Math