New knot theory discovery overturns long-held mathematical assumption

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.

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.

If anybody is reading this, please hit "parent" a few times to see what everybody actually said.

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.

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.