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Half a century ago, a brilliant young mathematician named John Horton Conway discovered, of all things, a knot. This knot wasn’t something you’d be likely to encounter in the real world. You could certainly create it out of string if you wanted to, but, generally speaking, it existed only in Conway’s calculations. There are thousands upon thousands of these kinds of conceptual tangles in a bewildering corner of mathematics known as knot theory, but even there Conway’s discovery was special — not so much for what it was, but for what it might or might not be. Yes, that is confusing, but when talking knot theory, it’s best to accept that things are going to get a little fuzzy.
In any case, the Conway knot is hardly remarkable at first glance. With just 11 crossings or places where it overlaps itself, it’s rather nondescript by the standards of higher-dimensional knot theory. But the knot has one property that made it the subject of intense mathematical scrutiny. Conway, who died recently at age 82 of complications from COVID-19, made innumerable contributions to the field of mathematics, yet it was his knot that specialists would return to again and again. And again and again, these decorated mathematicians were unable to find a solution to what became known as the Conway knot problem.
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Mathematician Lisa Piccirillo at MIT, where she is now an assistant professor.WEBB CHAPPELL
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