The unknotting number for a torus knot is . This 40-year-old conjecture was proved (Adams 1994) by Kronheimer and Mrowka (1993, 1995).
Milnor's Conjecture
See also
Torus Knot, Unknotting NumberExplore with Wolfram|Alpha
References
Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, p. 113, 1994.Kronheimer, P. B. and Mrowka, T. S. "Gauge Theory for Embedded Surfaces. I." Topology 32, 773-826, 1993.Kronheimer, P. B. and Mrowka, T. S. "Gauge Theory for Embedded Surfaces. II." Topology 34, 37-97, 1995.Referenced on Wolfram|Alpha
Milnor's ConjectureCite this as:
Weisstein, Eric W. "Milnor's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MilnorsConjecture.html