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Graduate Student Solves Decades-Old Conway Knot Problem

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Lisa Piccirillo

Lisa Piccirillo's solution to the Conway knot problem helped her land a tenure-track position at the Massachusetts Institute of Technology.

Credit: Quanta

In the summer of 2018, at a conference on low-dimensional topology and geometry, Lisa Piccirillo heard about a nice little math problem. It seemed like a good testing ground for some techniques she had been developing as a graduate student at the University of Texas, Austin.

"I didn't consider it to be real math," she says. "I thought it was, like, my homework."

The question asked whether the Conway knot — a snarl discovered more than half a century ago by the legendary mathematician John Horton Conway — is a slice of a higher-dimensional knot. The Conway knot, which has 11 crossings, had thumbed its nose at mathematicians for decades.

Before the week was out, Piccirillo had an answer: The Conway knot is not "slice." A few days later, she met with Cameron Gordon, a professor at UT Austin, and casually mentioned her solution.

"I said, 'What?? That's going to the Annals right now!'" Gordon says, referring to one of the discipline's top journals.

Piccirillo's proof, "The Conway Knot Is Not Slice," was published in Annals of Mathematics in February. The paper, combined with her other work, has secured her a tenure-track job offer from the Massachusetts Institute of Technology that will begin on July 1, only 14 months after she finished her doctorate.

"I don't think she'd recognized what an old and famous problem this was," Gordon says.

From Quanta
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