The Unknotting Number is Not Additive

On June 30, 2025, Mark Brittenham and Susan Hermiller uploaded a preprint to the arXiv called Unknotting number is not additive under connected sum (and an updated version on September 15, 2025). In it, they surprised the mathematical community by giving a counterexample to a long-standing conjecture in knot theory. The story was picked up... Read More