Mathematics Grapples with Infinity, from Achilles to Woodin

Abstract

Achilles and the Tortoise’s race bothered the Greeks but their math embraced infinity. The speaker will illustrate the concept of “countable” infinities and Cantor’s great result that the points on a line cannot be counted. Nowadays, a branch of math called set theory builds huge towers and embraces vast infinities, what Woodin calls the “V-view”, believing in the reality of V, the “collection of all sets”. The talk is aimed for a general audience without experience with math.

About the Speaker

Prof. David Mumford is Professor Emeritus of Applied Mathematics at Brown University and Professor Emeritus of Mathematics at Harvard University. He is an internationally renowned mathematician, particularly recognized for his work in algebraic geometry and research into vision, both computationally and biologically. He developed the concept of Deligne-Mumford stacks and introduced the Mumford–Shah functional in image segmentation. Additionally, he revived the classical theory of theta functions, linking them to finite analogues of the Heisenberg group, and pioneered research into moduli spaces and unexpected behaviors in algebraic geometry. Prof. Mumford's numerous contributions have earned him various awards and honors, including the Wolf Prize in Mathematics in 2008, the Shaw Prize in Mathematical Sciences in 2006, and the Fields Medal in 1974. He became a Fellow of the American Mathematical Society in 2012 after being elected as a Member of the National Academy of Sciences in 1975 and as a Foreign Member of the Royal Society in 2008.