I will review the endeavors of many great mathematicians of the late 19th century and beginning of the 20th century, and their motivating philosophies in pursuing a consistent and complete axiomatic system for mathematics. On the way, they encountered many paradoxes, such as Russell's, with important implications for our mathematical understanding.

In this context, it would be good to know then what an axiomatic system might be and what we mean by a model in which it is verified. I will end by presenting more logical conundrums, and in particular, discuss G\"odel's Incompleteness Theorems.

Tuesday, April 16, 2019 - 12:00 to 13:00

Thackeray 703