After many years of research, it has been possible for the first time to find a concrete case that shows that even with closed, donut-like surfaces, local measurement data does not necessarily determine a single global shape. Credit: Astrid Eckert / TUM For more than 150 years, a guiding idea in geometry has shaped how mathematicians think about surfaces. Originating with the French mathematician Pierre Ossian Bonnet, the principle states that if you know two key properties of a compact surface