Berkeley mathematician Nikhil Srivastava on Kadison–Singer problem

Mayank Chhaya-

As it often happens in science, mathematicians Nikhil Srivastava, Adam Marcus and Daniel Spielman accidentally ended up solving a particularly challenging problem vexing mathematicians since 1959. Working on an area called graph sparsification they used methods of linear algebra. Quite fortuitously, they ended up solving what is known as the Kadison-Singer problem which has a link to Paul Dirac, regarded as one of the greatest physicists of all time and among the pioneers of quantum theory in the late 1920s and early 1930s.

Their work has won them the inaugural Ciprian Foias Prize for the “highly original work” in Operator Theory by the American Mathematical Society (AMS). Srivastava, who holds a doctorate in computer science, is an associate professor of mathematics at the University of California, Berkeley. This is the third prize for Dr. Srivastava who had earlier jointly won is the George Polya Prize in 2014, and the Held prize in 2021.

He spoke to Mayank Chhaya Reports from Mexico City, where he is on a break, to explain how he and his two colleagues ended up solving a more than six-decades-old problem. The trio was not initially aware of what they might be doing to the Kadison-Singer problem. Once they were informed of the connection between potential improvements to graph sparsification and the Kadison-Singer problem in 2008, it gave us even more motivation to solve the problem, which took another five years. It was not entirely accidental in that they might not have put in as much effort had they not known it was a famous problem.