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New knot theory discovery overturns long-held mathematical assumption

(www.scientificamerican.com)
141 points baruchel | 2 comments | 02 Sep 25 11:35 UTC | HN request time: 0.566s | source
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argomo ◴[04 Sep 25 04:42 UTC] No.45123645[source]▶
Maybe the article is dumbing it down too much, but the conclusion seems unsurprising. Why shouldn't a single unknotting do double-duty in some cases?

It feels akin to the classic trick of joining a tetrahedron to a square pyramid: 4 faces + 5 faces == 5 faces total!

https://m.youtube.com/watch?v=rXIzUtLG2jE

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nyeah ◴[04 Sep 25 12:25 UTC] No.45126466[source]▶
They only had research mathematicians working on the problem. Until now they didn't have HN commenters. So work went very slowly.
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Hnrobert42 ◴[04 Sep 25 12:28 UTC] No.45126490[source]▶
Do you feel this substantively contributes to the conversation?
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nyeah ◴[04 Sep 25 12:49 UTC] No.45126660[source]▶
Yes. I feel that way very strongly. What contains no substance is a discussion of how we are smarter about knot theory than the knot theorists ... without even connecting to what makes the problem difficult.

Maybe you meant to ask something else. But you asked about substance.

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Hnrobert42 ◴[04 Sep 25 13:24 UTC] No.45127013[source]▶
GP explicitly stated they might be misunderstanding. If you see how they misunderstood, perhaps you could explain. An appeal to authority isn't much of an explanation.
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1. cyphar ◴[04 Sep 25 13:57 UTC] No.45127350[source]▶
Which part of this comment:

> Maybe the article is dumbing it down too much, but the conclusion seems unsurprising. Why shouldn't a single unknotting do double-duty in some cases?

is them "explicitly stat[ing] they might be misunderstanding"? At best they said that the article is at fault for oversimplifying the topic.

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2. argomo ◴[04 Sep 25 18:05 UTC] No.45130249[source]▶
Author of the comment you're quoting, and it is indeed my roundabout way of suggesting I'm missing something.

Clearly, I'm not a knot theory expert, but the way the article presents it makes me wonder what extra nuance motivated the original (now falsified) conjecture.