Special public lecture:

## Structure and Randomness in the Prime Numbers

*
Terence Tao is a professor at UCLA, 32 years old, and Australia's
only ever winner of the highest award in mathematics: a Fields Medal.*

When: 7 February 2008 at 5:30–6:30pm.

Where: General Lecture Theatre, Main Quadrangle, University of Sydney
– a little to the left of the word "Main" in the map.

#### Abstract:

The prime numbers are a fascinating blend of both structure
(for instance, almost all primes are odd) and randomness.
It is widely believed that beyond the "obvious" structures
in the primes, the primes otherwise behave as if they were
distributed randomly; this "pseudorandomness" then underlies
our belief in many unsolved conjectures about the primes,
from the twin prime conjecture to the Riemann hypothesis.
This pseudorandomness has been frustratingly elusive to actually
prove rigorously, but recently there has been progress in capturing
enough of this pseudorandomness to establish new results about
the primes, such as the fact that they contain arbitrarily long
progressions. We survey some of these developments in this talk.

Aerial view of Main Quad and surrounds. View Larger Map.
School of Mathematics and Statistics, University of Sydney.