One of these problems has had mathematicians stumped for years, with legions of them having made only piecemeal progress. Few people outside physics have heard of the quantum Hall conductance problem, but it is intimately connected with experiments that get us closer than ever to harnessing the mysterious power of quantum technology. You can imagine the anticipation, then, when a newcomer named Spyridon Michalakis claimed he had the answer. Fittingly, however, his solution to this impossible problem was itself impossible to understand – or at least nearly impossible.