I’ve got Euclid’s, I’ve got Al Gore, I’ve got Rhythm, who could ask for anything more?

3:00pm, Wednesday 18 March 2026

Abstract

Inspired by Gershwin, the title refers to the oldest (?) mathematical algorithm: the Euclid’s algorithm for division. This allows us to divide two numbers, keep track of remainders, rinse ‘n’ repeat, and recover GCDs. I will discuss other algebraic settings: some rings are known to be Euclidean (meaning they have this algorithm), some are known not to be; many are unknown. I will end with a summary of recent work done by Bagger, Booker, Kerr, McGown, Starichkova, and me that resolves completely the case of cyclic cubic fields.