From TFA: “Whenever a new invariant comes along, we try to test it against the Conway knot,” Greene said. “It’s just this one stubborn example that, it seems,

From TFA: “Whenever a new invariant comes along, we try to test it against the Conway knot,” Greene said. “It’s just this one stubborn example that, it seems, no matter what invariant you come up with, it won’t tell you whether or not the thing is slice.” The Conway knot “sits at the intersection of the blind spots” of these different tools, Piccirillo said. One mathematician, Mark Hughes of Brigham Young University, created a neural network that uses knot invariants and other information to make predictions about features such as sliceness. For most knots, the network makes clear predictions. But its guess about whether the Conway knot is smoothly slice? Fifty-fifty. “Over time it stood out as the knot that we couldn’t handle,” Livingston said. Not my area, but if the article is to be believed, pretty much every new related technique gets thrown at this knot as a matter of course. That's what I mean by "fresh eyes."