As a Princeton University graduate student in 2001, Subhash Khot was visiting his family in India and thinking about his research on the limits of computation when he came up with a good, if seemingly modest, idea. He was thinking about an analytic theorem that Johan Håstad, one of his mentors, had formulated (and Jean Bourgain had proved) and how it could be applied to the “hardness of approximation.” But there was a missing ingredient.

While most computer scientists work to expand the capabilities of computers, computational complexity experts like Khot try to determine which problems are impossible for computers to solve within a reasonable time frame. Once a problem has been classified as “hard” in this way, the natural next question to ask is about its hardness of approximation: whether a computer can efficiently find an approximate solution good enough to put to practical use.

In thinking about the analytic theorem and these hardness questions, Khot realized that the missing ingredient was an existing problem called Unique Games. “I posited that the problem is indeed computationally hard, which became the Unique Games Conjecture,” Khot told Quanta in an email. He found that assuming that the Unique Games problem was hard made it much easier to show that another problem he was working on was also hard.

“I was happy of course and I told my family that I had an idea that was worth pursuing,” said Khot. “I certainly did not think that it would have such a wide range of applications.” After returning to Princeton, he was surprised to discover that his assumption worked for several of his other problems too. It seemed like a useful idea, and he wrote a paper that appeared the following spring.

In his paper, Khot found connections between his conjecture and an important hardness of approximation paper by Irit Dinur and Shmuel Safra, which fueled excitement in the field. “I think I was at the right place at the right time,” Khot said. In the following years, the connections extended to other big problems, further elevating the conjecture’s profile and influence. In 2014, Khot, who is now a professor at New York University’s Courant Institute of Mathematical Sciences, was awarded the Rolf Nevanlinna Prize, one of the top honors in theoretical computer science.