Welcome to Quantum Magazine's podcast.

Each episode, we bring you stories about developments in science and mathematics.

I'm Susan Vallett.

The Conway knot was discovered more than a half a century ago by legendary mathematician John Horton Conway.

But is it 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 were 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.

That was until a grad student got a hold of it.

In the summer of 2018, Lisa Picharillo was at a conference about

low dimensional topology and geometry. She had heard a talk by Rice University's

Shelley Harvey about a math problem that seemed like a good testing ground for some techniques

Picharillo 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 for a week

because I didn't consider it to be real math. I thought it was like my homework and I wasn't allowed

to use real math time to work on it.

I expected that either what I was going to try wasn't going to work because this knot is actually pathological or like, well, you know,

Shelley Harvey mentioned it in a talk, but it's just one knot.

Like nobody really cares.

The question asked whether the Conway knot is a slice of a higher dimensional knot.

Before the week was out, Picharillo had an answer.

The Conway knot is not slice.

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