Science Night Live: Symmetry And The Primes

First we learn to count; next we learn to multiply. From the interaction of these two elementary operations emerge the prime numbers, the building blocks of the integers.

The patterning of the primes continually reveals itself to be richer than mathematicians could ever have expected. A well-placed application of 18th century number theory exploits the richness of this patterning to build the public-key cryptography algorithms that secure many of our electronic communications. Number theory in the 21st century, while still grounded in the study of the primes, takes form through surprising connections with geometry, topology, algebra, and analysis, and even suggests bizarre and tantalizing analogies with fundamental physics.

These astonishing connections express previously hidden symmetries in the prime numbers, which we are only in the very first stages of understanding. In this talk we will explore how elementary questions of arithmetic lead us to this strange mathematical landscape.