Undergraduate Colloquium

Bernhard Riemann (1826 - 1866) conjectured in 1859 that the analytic extension of \[ \zeta(s):= 1 + \frac{1}{2^s} +\frac{1}{3^s} + \frac{1}{4^s} + \frac{1}{5^s} + \frac{1}{6^s} + \dots = \prod_{p \ {prime}} \Big(1-\frac{1}{p^s}\Big)^{-1} \] to the complex plane has its zeros ONLY at the negative even integers and complex numbers with real part 1/2.

Because of its connection to the distribution of prime numbers, this is one of the major unsolved problems in mathematics, worth $1M (per the Clay Mathematics Institute).

The talk will explain what all this is about.

Riemann's notes (click for full size)

First nontrivial zeros (click for full size) [source of images]

Colloquium sponsored by the NSM Dean's office DUSEM grant