New knot theory discovery overturns long-held mathematical assumption (scientificamerican.com)

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Wow, this problem has been around for a long time. Exciting to see this finally figured out.

I’m curious what specific conclusions this may undo.

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

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?)

This is when you read articles like these that you realize how great the articles on quanta magazine are.

Gem of an old video going over the basics of knot theory. https://www.youtube.com/watch?v=QcLfb0PhfO0

It was made on a supercomputer from the 90's