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New knot theory discovery overturns long-held mathematical assumption

(www.scientificamerican.com)
141 points baruchel | 1 comments | 02 Sep 25 11:35 UTC | HN request time: 0.356s | source
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viraptor ◴[04 Sep 25 06:02 UTC] No.45124051[source]▶
Is this something people have been actively trying to disprove? The example provided seems to not be hard to bruteforce - given it's only 5 moves. Does anyone know why there's no older counter example? (Or am I totally underestimating how the number of options explodes in 5 moves?)
replies(3): >>45124262 #>>45124346 #>>45129087 #
1. adgjlsfhk1 ◴[04 Sep 25 06:38 UTC] No.45124262[source]▶
I think this is a combination of things.

1: knot theory is somewhat obscure. it generally only comes up in undergrad in a topology class for a week or two so there aren't a ton of people interested

2. It's 5 cuts on a joining of 2 knots with 6 crossings. it's brute forcable, but not trivially (i.e. you have to code it up and possibly wait a while)

3. for conjectures that feel intuitively true more effort goes into finding the proof than looking for a counterexample that feels unlikely to exist.