Dan Spielman, a Yale computer scientist, wasn’t looking for a new problem. He was already deeply immersed in a tricky effort to model complex online communities like Facebook, hoping to gain insight into how they form and interact.

But when a colleague in Jerusalem observed that aspects of Spielman’s research brought to mind the famous — and unsolved — Kadison-Singer math problem, Spielman saw irresistibly low-hanging fruit — or so it seemed.