Title: My favorite number
| Speaker: | John Baez |
| Affiliation: | University of California, Riverside |
| Room: | DC 1302 |
Abstract: The number 24 plays a central role in mathematics thanks to a series of "coincidences" that is just beginning to be understood. One of the first hints of this fact was Euler's bizarre "proof" that
1\^ + 2\^ + 3\^ + 4\^ + … = -1/12\^
which he obtained before Abel declared that "divergent series are the invention of the devil". Euler's formula can now be understood rigorously in terms of the Riemann zeta function, and in physics it explains why bosonic strings work best in 26=24+2 dimensions. The fact that
12\^ + 22\^ + 32\^ + … + 242\^
is a perfect square then sets up a curious link between string theory, the Leech lattice (the densest known way of packing spheres in 24 dimensions) and a group called the Monster. A better-known but closely related fact is the period-12 phenomenon in the theory of modular forms. We shall do our best to demystify some of these deep mysteries.
Note: Refreshments served in DC 1301 (the Fishbowl) at 3:00 p.m.
Biography: John Baez was educated at Princeton and M.I.T. Now he is a professor of mathematics at U.C. Riverside, and in summers he works at the Centre for Quantum Technologies, in Singapore. Until recently he worked on higher category theory and quantum gravity. His internet column ‘This Week’s Finds’ dates back to to 1993 and is sometimes called the world’s first blog. In 2010, concerned about climate change and the future of the planet, he switched to working on more practical topics and started the Azimuth Project, an international collaboration to create a focal point for scientists and engineers interested in saving the planet. Very prolific author, he won in 2013 the Levi L. Conant Prize for his outstanding expository paper “The algebra of grand unified theories”.