Science and Math Colloquium Series
All lectures are free and open to the public. A brief reception will precede each talk in the Ferguson Auditorium Lobby.
5:00 - 6:00 p.m.
Christopher Shaw, Department of Science and Mathematics, Columbia College Chicago
"Two Ideas That Shook the Foundations of Mathematics"
Mathematicians have long worked toward building a comprehensive system of laws that govern the universe of mathematics. In this talk we will discuss two surprising ways in which this pursuit is guaranteed to be futile, each resulting from the novel work of a mathematician named Kurt Gödel in 1931. The first, independence, is that it is impossible to construct a system of axioms that is strong enough to entail all mathematical truths. The second, incompleteness, is that in any system that formalizes a significant part of mathematics, it is impossible to verify within that system that its laws are consistent.
This talk will tell the story of the fascinating proof of Gödel’s Second Incompleteness Theorem, and explore the concept of independence through the lens of the Continuum Hypothesis, which was shown by Paul Cohen to be independent of the most widely accepted system of axioms in 1963.