Graduate Student Solves Decades-Old Conway Knot Problem
From a high level overview what she did feels mostly like a hacker approach: finding a side channel [1]. I wonder to what extent mathematicians think about side channels.Instead of talking to the service/mathematical object (A) directly, you talk to another service/mathematical object (B) that leaks information about (A). Precisely, the information that you want.The way she leaked that information was through a property called traceness that apparently was underappreciated by knot theorists in terms of sliceness problems. Which makes sense, otherwise it wouldn't be an information leak. Finding an info leak in itself, no matter what discipline your in is already amazing.As far as I understood the quantamagazine article, mathematical object (B) still had to be constructed which only a person well-versed in knot theory could do. So not only did she find an info leak, she basically created something entirely new that few people can do (yep, the hacker analogy breaks here, this part is the "incredible builder" analogy).This is so cool. Side channels are everywhere, even in math. Apparently, for knots it's called traceness.[1] Not sure if side channel is the right word, but I view it as: something that leaks information about another thing. For example, air vibrations leaking information on what instructions the CPU is executing (I'm making this up, one would need very fine-grained air vibration data to see if this would be a side channel).