Mathematicians Disprove Long-Standing Knot Theory Conjecture About Unknotting Numbers
By
JohnHammersley
An everything bagel for the brain. Substantive, layered, well-seasoned.
Summary
Mathematicians Mark Brittenham and Susan Hermiller published a groundbreaking preprint disproving a long-standing conjecture in knot theory that the unknotting number is additive under connected sum. Their counterexample, which involves creating a knot with unknotting number 2 from two knots each with unknotting number 1, challenges fundamental assumptions in the field and has generated significant attention in the mathematical community.
Key quotes
· 5 pulledThe unknotting number of a knot is the minimum number of times you need to change a crossing in a diagram of the knot to turn it into the unknot.
The conjecture was that the unknotting number is additive under connected sum: u(K#L) = u(K) + u(L).
They found a counterexample: two knots K and L, each with unknotting number 1, such that their connected sum K#L has unknotting number 2.
This is a surprising result because it goes against what many mathematicians believed for a long time.
The discovery has generated excitement in the mathematical community and been covered by major science publications.
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