How Outsiders Cracked a 50-Year-Old Math Mystery

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The Kadison Singer Problem

In 2008, Yale computer scientist Daniel Spielman was working on a problem in "network sparsification" — reducing the number of connections between elements of a network without causing the network to lose its defining features.

He happened to mentioned the work to a colleague, who immediately saw a similarity to an unsolved question in math. That question, known as the Kadison-Singer problem, was originally posed by two mathematicians in an apartment near Columbia University, in the late 1950s. 

Some of the most talented mathematicians of the time had labored to find an answer to Kadison-Singer, but it remained a riddle.

While Spielman wasn't very familiar with the problem, he agreed it sounded connected. What's more, he thought, it seemed like something he could solve. It took five years. But working with colleagues Nikhil Srivastava and Adam Marcus, he did it.

"People in the fields where the Kadison-Singer problem had started were maybe kind of in shock," said Erica Klarreich, a writer for wrote about the breakthrough for Quanta Magazine. She said the way the team approached the problem points out the importance of bridging disciplines.

"Two hundred years ago," she continued, "you were just a mathematician and you studied everything. Now people are very specialized and they're trying to figure out how to find their way back that old state of mathematics."

Want to know more about the Kadison-Singer problem? View this video, where Srivastava, one of the trio, explains:

 Hypothesis is written and produced by Alec Hamilton and edited by Matthew Schuerman. Sound design and engineering by Liora Noam-Kravitz and Wayne Shulmister. Original music by Josh Burnett.