We may earn commission if you buy from a link. So here’s how the intersecting relationships break down: Piccirillo found that trace sibling after all, and fast, and she was able to use the analogy method to show that the Conway knot can’t be smoothly slice. University of Texas at Austin mathematician Lisa Piccirillo learned about the Conway knot—a knot with 11 crossings, so named for the late mathematician John Horton Conway—from a colleague’s talk during a conference. An “unknot” loop is considered one dimensional, the way a geometry point or line is one dimension. (It’s not.). With just 12 pieces but 200 total challenges, Kanoodle will stump both kids and adults with 2-D and 3-D puzzles. The Conway Knot is one of the more notorious problems in knot theory, with a line that overlaps in 11 different places. [2], It is related by mutation to the Kinoshita–Terasaka knot,[3] with which it shares the same Jones polynomial. Lisa Piccirillo’s solution to the Conway knot problem helped her land a tenure-track position at the Massachusetts Institute of … America's Aircraft Are Barely Ready for War, Intelligent Life Can't Exist Anywhere Else, Read This: How to Solve the Legendary Puzzle. University of Texas at Austin mathematician Lisa Piccirillo learned about the Conway knot —a knot with 11 crossings, so named for the late mathematician John Horton Conway —from a … In mathematics, in particular in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway. Conway's Knot Conway's knot is the prime knot on 11 crossings withbraid word The Jones polynomial of Conway's knot is which is the same as for the Kinoshita-Terasakaknot. In knot theory, Conway notation, invented by John Horton Conway, is a way of describing knots that makes many of their properties clear. Escher. To be “smoothly” slice, the knot must also be a slice of the four-dimensional rubber ball: still knotted and complex, but not “crumpled.” Now you’re up to speed. It is related by mutation to the Kinoshita–Terasaka knot, with which it shares the same Jones polynomial. The problem had to do with proving whether Conway’s knot was something called “slice,” an important concept in knot theory that we’ll get to a little later. The results of these twisting math knots are one part Cat’s Cradle and one part M.C. Both knots also have the curious property of having the same Alexander polynomial and Conway polynomial as the unknot. The Jones polynomial of Conway's knot is t^(-4)(-1+2t-2t^2+2t^3+t^6-2t^7+2t^8-2t^9+t^(10)), which is the . Illustration: 5W Infographics/Quanta Magazine Looking at two knots that each have, say, 11 crossings—the Conway knot in this case, and a closely related “mutant” knot called the Kinoshita-Terasaka—knot theorists must try to answer a couple of key questions. This grad student from Maine solved it in days", "Graduate Student Solves Decades-Old Conway Knot Problem", "In a Single Measure, Invariants Capture the Essence of Math Objects", https://en.wikipedia.org/w/index.php?title=Conway_knot&oldid=976219537, Short description is different from Wikidata, Articles with dead external links from August 2020, Creative Commons Attribution-ShareAlike License, This page was last edited on 1 September 2020, at 20:27. It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway. Mathematicians learned in the ‘80s that the Conway knot is topologically slice, but they couldn’t prove one way or the other if it’s smoothly slice. The plain loop is called the unknot, and all true knots must pass a test of whether they can be untangled into an unknot. Namely, the Conway knot has a sort of sibling—what’s known as a mutant. People said he was the only mathematician who could do things with his own bare hands,” said Stephen Miller, a mathematician at Rutgers University. Think about taking the cross section of a solid foam rubber ball versus an ornate string cheese, then imagine it in extradimensional space.