Untangling Knots: The Unknotting Number and a 2025 Breakthrough
About this episode
A friendly dive into knot theory and the unknotting number—the minimum number of crossing switches needed to untie a knot. We ride from simple knots like the trefoil and the figure-eight to complex families like twist and torus knots, explain why the unknotting number gives a deep glimpse into a knot's structure, and celebrate the 2025 result showing that unknotting numbers are not always additive when you connect a knot with its mirror. Plus a peek at other invariants that round out the knot-theory toolkit.
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