Solving for the unobservable

Though you probably didn't notice, Dan Spielman ’92, the Henry Ford II Professor of Computer Science and Mathematics at Yale, quietly changed mathematics in 2013. While looking for ways to model online communities like Facebook, Spielman and his research colleauges Adam Marcus and Nikhil Srivastava discovered the answer to a 50-year old paradox: the Kadison-Singer Problem. In recognition of this feat, the trio yesterday received the George Pólya Prize in mathematics, a biannual award from the Society for Industrial and Applied Mathematics for excellence in the field.

The Kadison-Singer Problem explores whether or not it is possible to learn specific information from a scenario in which it’s impossible to observe all relevant factors. Kadison and Singer conjectured that it was. This is a foundational principle in most abstract math and science. The classic example comes from quantum physics, in which one calculates the momentum of a particle by measuring spin and position, even though momentum can't actually be measured. In 2013, Spielman, Marcus, and Srivastava ultimately proved that one could safely make the assertions Kadison and Singer hypothesized.

“We could never get excited on working on other problems,” Spielman told YaleNews. “The Kadison-Singer problem was just too interesting and compelling: Every approach we pursued revealed beautiful structures. When you are following an approach to a math problem and you discover something beautiful, you take it as an indication that you are on the right path. We kept getting that feeling.”