Building Telescopes for Mathematicians

Computers play an increasingly important role as research tools for mathematicians. The advent of cloud computing has made massively parallel computation available at an unprecedented scale.

In this lecture, Andrew Sutherland will discuss how mathematicians can harness this new resource as a powerful observational instrument that illuminates previously inaccessible regions of the mathematical universe. He will describe what is believed to be the single largest scientific computation ever conducted on a cloud computing platform, using 580,000 cores to complete a 300-year computation in less than 12 hours. This computation was part of an effort to build a database of mathematical objects that lie on one side of the conjectured “Langlands correspondence,” and to address open questions in arithmetic geometry by finding several objects that were predicted, but notably absent, from previous tabulations. While the increasing availability of computational resources played an essential role in this work, algorithmic advances driven by mathematical breakthroughs have easily outpaced Moore’s law over the last two decades.

Sutherland is a principal research scientist in the mathematics department at the Massachusetts Institute of Technology, where he received his Ph.D. in 2007. He has played a leading role in many computationally focused research collaborations in number theory, including the Polymath project on Bounded Gaps Between Primes and the L-functions and Modular Forms Database. He has received numerous awards for his work, including the 2012 Selfridge prize, and he is a principal investigator in the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation.