Quanta Reimann Surfaces — Myriam Wares for Quanta Magazine

Surfaces Beyond Imagination Are Discovered After Decades-Long Search

"Last July, two mathematicians from Durham University, Will Hide and Michael Magee, confirmed the existence of a much sought-after sequence of surfaces: each more complicated than the last, ultimately becoming so intricately connected with themselves that they nearly reach the limits of what’s possible.

At first, it wasn’t obvious these surfaces existed at all. But since the question of their existence first arose in the 1980s, mathematicians have come to realize that these surfaces may actually be commonplace, even if they’re exceedingly difficult to pinpoint — a perfect example of how mathematics can subvert human intuition. The new work is a step forward in a quest to move beyond intuition to understand the myriad ways surfaces can manifest.

'It’s a brilliant piece of mathematics,' said Peter Sarnak, a mathematician at the Institute for Advanced Study in Princeton, New Jersey."