Berkeley mathematician Nikhil Srivastava on the Kadison-Singer problem

Mayank Chhaya-

As often happens in science, mathematicians Nikhil Srivastava, Adam Marcus, and Daniel Spielman accidentally ended up solving a particularly difficult problem that had plagued mathematicians since 1959. Working in an area called graph parsimony, they used methods of linear algebra. Quite by chance, they ended up solving what is called the Kadison-Singer problem which has a connection with Paul Dirac, considered one of the greatest physicists of all time and among the pioneers of the theory quantum in the late 1920s and early 1930s.

Their work won them the first Ciprian Foias Prize for “highly original work” in operator theory by the American Mathematical Society (AMS). Srivastava, with a doctorate in computer science, is an associate professor of mathematics at the University of California, Berkeley. This is the third award for Dr Srivastava who previously jointly won 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 hiatus, to explain how he and his two colleagues ended up solving a problem that was more than six decades old. The trio were initially unaware of what they might do to the Kadison-Singer issue. Once they were made aware of the link between potential graph sparseness improvements and the Kadison-Singer problem in 2008, it gave us even more motivation to solve the problem, which took another five years. It wasn’t entirely accidental in that they might not have put in so much effort if they hadn’t known it was a famous issue.

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