665875 external_news 1676578494 1676578494 Over 60 years ago, Ralph Fox posed a problem about knots that haunts mathematicians to this day. His question is now often formulated as the “slice-ribbon conjecture,” which posits that two seemingly distinct groups of mathematical knots are actually the same. With its suggestion of elegant simplicity within the world of knots, it’s become one of the most high-profile problems in knot theory. For decades, one particular knot was suspected to be a possible route to settling the conjecture. Yet in a paper posted last summer, five mathematicians found that this knot isn’t going to work after all. While the arguments they introduced will provide new insights into a broader class of knots, the work as a whole leaves mathematicians uncertain about the conjecture. Jen Hom, associate professor in the School of Mathematics, has previously collaborated with two of the new paper's authors, and she weighs in on the results. 

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