Euler discovered how to assign a finite value to certain divergent sums, such as 1 + 2 + 4 + 8 + … that he determined should equal -1. How does one make sense of this?!? The 19th century mathematicians discovered a systematic approach to such madness. Contemporary number theorists have yet another approach, using an exotic number system that is not taught in schools. Dr. Conrad spoke to the Forum on how to calculate in this exotic world, and use it to understand a remarkable concrete fact about ordinary numbers.
Brian Conrad is Professor of Mathematics at Stanford University, specializing in number theory and arithmetic geometry. He has previously taught at the University of Michigan and at Columbia University. Conrad, together with Christophe Breuil, Fred Diamond and Richard Taylor, proved the modularity theorem, also known as the Taniyama-Shimura Conjecture in 1999. He has held a joint postdoctoral position at Harvard University and the Institute for Advanced Study. Conrad received his bachelor’s degree from Harvard University and his Ph.D. from Princeton University under Andrew Wiles.