SHE SOLVED A 50-YEAR-OLD MATH PROBLEM IN UNDER A WEEK BECAUSE SHE DIDN'T THINK IT COUNTED AS REAL WORK
lisa piccirillo, 2018, graduate student at UT Austin. she hears about the Conway knot at a conference and starts poking at it in the evenings.
her own words: she wouldn't let herself work on it during the day, because she didn't consider it to be real math. she thought of it like homework.
the problem had stood since the 1960s. of every knot with twelve or fewer crossings, mathematicians had determined "sliceness" for all of them except one. that one had a sculpture of itself on a gate at Cambridge's Isaac Newton Institute.
she cracked it in under a week.
the method is the elegant part. she built a different knot that shares the same four-dimensional trace as Conway's, proved hers wasn't slice, and since trace siblings share slice status, Conway's isn't either.
then she mentioned it casually to Cameron Gordon, a senior topologist. he started shouting "why aren't you more excited?" and said it was going to the Annals immediately.
it did. she was at MIT fourteen months out of grad school.
and the reason her field exists at all is genuinely strange.
four dimensions is the only one that breaks. flat n-dimensional space has exactly one smooth structure for every value of n. except four, where there are uncountably infinitely many.
not three. not five. not eleven. four.
nobody fully knows why.