“I had heard rumors that this was coming up, and I didn’t know exactly what to expect,” said Vesna Stojanoska, a mathematician at the University of Illinois, Urbana-Champaign who attended the conference.

It was soon clear the rumors were true. Beginning on Tuesday, and over the next three days, Levy and his co-authors — Robert Burklund, Jeremy Hahn and Tomer Schlank — explained to the crowd of some 200 mathematicians how they’d proved that the telescope conjecture was false, making it the only one of Ravenel’s original conjectures not to be true.

The disproof of the telescope conjecture has wide-ranging implications, but one of the simplest and most profound is this: It means that in very high dimensions (think of a 100-dimensional sphere), the universe of different shapes is far more complicated than mathematicians anticipated.

Mapping the Maps

To classify shapes, or topological spaces, mathematicians distinguish between differences that matter and those that don’t. Homotopy theory is a perspective from which to make those distinctions. It considers a ball and an egg to be fundamentally the same topological space, because you can bend and stretch one into the other without ripping either. In the same way, homotopy th