These talks will be self-contained presentations of mathematical concepts and theorems. They are intended to be accessible to all mathematics
students.  Coffee, tea and drinks will be provided.
 

Most mathematicians use the continuum of real numbers (the "number line"), but no one really understands it. Ever since 1874, when Cantor discovered that there are more real numbers than integers, the central question of set theory has been: how many real numbers are there?

Cantor believed the answer to be: the smallest infinity beyond the infinity of integers. This *continuum hypothesis*, as it is called, was number 1 on Hilbert's famous list of problems in 1900. It is still open, and perhaps may never be settled.

In this talk I'll explain the basic theory of real numbers and sets which, if not actually making the continuum clear, at least shows why it is mysterious. I'll also mention some recent developments, aimed at *disproving* the continuum hypothesis.