The Unknotting Number of a Knot - A Historical Perspective and Modern Developments

Explore a mathematics lecture that delves into the fascinating concept of unknotting numbers in knot theory, presented by Cameron Gordon from UT Austin as part of the CMSA/Tsinghua Math-Science Literature series. Learn about one of the oldest knot invariants, which measures the minimum number of self-intersections required to transform a knot into an unknot. Discover the historical progression of this concept from its introduction by Tait nearly 150 years ago to modern developments, including its connections to 4-dimensional topology. Examine the computational challenges surrounding unknotting numbers, including the intriguing case of an 8-crossing knot whose unknotting number remains undetermined. Gain insights into both the historical advances and current open questions in this fundamental area of knot theory.