I'm surprised it took so long to find a counterexample, but it doesn't surprise me at all to hear it doesn't work.
So much of math and physics is discovering these beautiful, surprisingly non-intuitive things.
And this fits right in that pattern -- it seems intuitive that it wouldn't be true, but nobody's been able to find a counterexample. So it's yet another counterintuitive result that math is built on.
Which is what makes it great when somebody does ten years of work in simulating knots so a counterexample can be found.
Holy topic-specific terminology, Batman!
Thank you!
https://m.youtube.com/watch?v=TUHgGK-tImY
Or may not.
NoMoreNicksLeft•2h ago
Wouldn't this mean that there is a sort of "negative" number implied here? That one knot is +2/+1 and that the other knot is +2/-1, and that their measure (the unknotting number) is only the sum of the abs()?
drakythe•1h ago
Basically the unknotting number combes from how the string crosses itself and when you add two (or more?) knots together you can't guarantee that the crossings will remain the same, which makes a kind of intuitive sense but is extremely frustrating when there isn't a solid mathematical formula that can account for that.
taeric•1h ago
I could see trying to fit this with surreal numbers, as well. Would be fitting, as I think Conway was big into knots?
Regardless, no, not dumb. Numerically modelling things is hard, it turns out. :D
ashivkum•1h ago