They buried the how extremely deep in the article. Fished it out for y'all. > The day after hearing about the Conway knot problem, Piccirillo, then 27, sat dow

They buried the how extremely deep in the article. Fished it out for y'all. > The day after hearing about the Conway knot problem, Piccirillo, then 27, sat down at her desk and began looking for a solution. Because much of her graduate work involved building pairs of knots that were different but shared some 4-D properties, she already knew that any two knots that share the same 4-D space also share sliceness — they’re either both slice or both not slice. Since her goal was to prove that the Conway knot wasn’t slice, her first step was come up with an entirely different knot with the same four-dimensional space, she explains. “Then I’ll try to show that the other knot isn’t slice.” > She spent spare time over the next several days hand-sketching and manipulating configurations of the 4-D space occupied by the Conway knot. “I didn’t allow myself to work on it during the day,” she told Quanta Magazine earlier this year, “because I didn’t consider it to be real math. I thought it was, like, my homework.” > The next step was to try to prove that the knot she drew was not slice. “There are lots of tools already in the literature for doing that,” she says. She would feed the knot iterations into a computer, “and based on the data of the knot, maybe based on how its crossings look or other data that you can pull from the knot, the algorithm spits out an integer.” In less than a week, Piccirillo had created a knot that hit the sweet spot: It had the same 4-D properties as the Conway knot, and it was found by the algorithm to be not slice. > She had suddenly succeeded where countless mathematicians had failed for five decades. She had solved the Conway knot problem.