A knot is said to be slice if it bounds a smooth properly embedded disk in B^4. We demonstrate that the Conway knot is not slice. This completes the classification of slice knots under 13 crossings and gives the first example of a non-slice knot which is both topologically slice and a positive mutant of a slice knot.
This is not and cannot be other than the ancient myth of the extraordinarily difficult Gordian knot “solved” by Alexander the Great who drew his sword to slice it in half.
Unfortunately the full text of the article is pay-per-view. It is the jealously guarded intellectual property of the educational establishment. There is no free access for the general public to read the article let alone the educational and legal qualifications necessary to “work on” or consider such an advanced problem in pure mathematics without being arrested or detained as a threat to society or danger to national security.
There is also said to be, in the same vein, a rather mythically abstract algebraic classification of all finite simple groups, but some have called it “monstrous moonshine,” essentially likening the officially published and peer-reviewed mathematical proofs to rotgut bootleg liquor which falls short of objective standards of establishing mathematical truth from solid foundational principles or axioms.
Once again, the establishment is serving us peer-reviewed and licensed mathematical proof fait accompli, and charging us money for it, but we aren’t buying it at the elementary or open-access level.
I wouldn’t call myself a “prepper” or a backwoods survivalist, but I do feel a need to stock up and go “back to the basics” when so much faculty has so much vested interest in defending mathematical work already published on shaky foundations.