A Simple Way to Measure Knots Has Come Unraveled
5 hours ago
- #unknotting number
- #knot theory
- #mathematics
- Peter Guthrie Tait introduced the concept of 'beknottedness' in 1876 to measure and differentiate knots, now known as the 'unknotting number'.
- The unknotting number represents the minimum crossing changes needed to transform a knot into an unknotted circle, but it's often hard to compute.
- A 1937 conjecture by Hilmar Wendt suggested that the unknotting number of combined knots (connect sum) is the sum of their individual unknotting numbers.
- Mark Brittenham and Susan Hermiller disproved the additivity conjecture in 2024 by finding a pair of knots whose combined unknotting number was less than the sum of their parts.
- Their discovery, using computational methods and a database of knots, revealed that the unknotting number is more chaotic and unpredictable than previously thought.
- The result opens new questions in knot theory, highlighting the complexity of understanding knot behavior and the unknotting number's role in measuring it.