Erica Klarreich in 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 allow myself to work on it during the day,” she said, “because I didn’t consider it to be real math. 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. “Sliceness” is one of the first natural questions knot theorists ask about knots in higher-dimensional spaces, and mathematicians had been able to answer it for all of the thousands of knots with 12 or fewer crossings — except one. 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.