What Do We Mean By Equality? - Prof Kevin Buzzard - The Archimedeans

Prof. Kevin Buzzard (https://en.wikipedia.org/wiki/Kevin_B...) is an algebraic number theorist who is now working in formal proof verification. He runs the Xena project, which aims to formalise the entire undergraduate pure maths curriculum in the language Lean. He was awarded the Whitehead prize and the Senior Berwick prize by the LMS.

Have you ever read Euclid's "common notions", right at the beginning of book 1 of his Elements? Have you ever read the axioms of set theory? Have you ever read Grothendieck's EGA? Have you ever looked at Voevodsky's work at the IAS, where he was trying to understand work of Voevodsky pre-IAS? Have you ever tried to prove a theorem using a computer proof checker? Do you know what "=" means? It turns out that different mathematicians have different opinions about the matter. Basically, the more high-powered your definition is, the easier it is to cheat. Prof. Kevin Buzzard will talk about how to localise a commutative ring at a multiplicative subset, and how to define a scheme. He will explain all the algebra we need; the talk will be suitable for university first years.

No prerequisites are required.

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