John Baez

Grothendieck's Approach to Mathematics, Chapman University

May 25, 2022

Motivating Motives

Underlying the Riemann Hypothesis there is a question whose full answer still eludes us: what do the zeros of the Riemann zeta function really mean? As a step toward answering this, André Weil proposed a series of conjectures that include a simplified version of the Riemann Hypothesis in which the meaning of the zeros becomes somewhat easier to understand. Grothendieck and others worked for decades to prove Weil's conjectures, inventing a large chunk of modern algebraic geometry in the process. This quest, still in part unfulfilled, led Grothendieck to dream of 'motives': mysterious building blocks that could explain the zeros (and poles) of Weil's analogue of the Riemann zeta function. This talk by a complete amateur will try to sketch some of these ideas in ways that other amateurs can enjoy.

Here's a video of this talk:

You can see my slides here — they're a series of webpages, so click "Next" to move on to the next slide.

You can also see my slides as a PDF, without the animations.

I'm also writing a series of blog articles that goes into more detail:

© 2022 John Baez, except for animations by Dan Rockmore