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New Knot Theory Discovery Overturns Long-Held Mathematical Assumption

New Knot Theory Discovery Overturns Long-Held Mathematical Assumption

4 comments

·September 2, 2025
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cka

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

baruchel

Without paywall: https://www.removepaywall.com/search?url=https://www.scienti...

altairprime

Linked paper: https://arxiv.org/abs/2506.24088

“Unknotting number is not additive under connected sum” (2025 v1)

> We give the first examples of a pair of knots K1,K2 in the 3-sphere for which their unknotting numbers satisfy u(K1#K2)<u(K1)+u(K2) . This answers question 1.69(B) from Kirby's problem list, "Problems in low-dimensional topology", in the negative.

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