> For Eckmann, the new work is a showcase of how rich mathematics can be even in a field as well-trod as the study of rotations. Tlusty says that it could also have practical consequences, for instance, in nuclear magnetic resonance (NMR), which is the basis of magnetic resonance imaging (MRI). Here, researchers learn properties of materials and tissues by studying the response of quantum spins inside them to rotations imposed on them by external magnetic fields. The new proof could help develop procedures for undoing unwanted spin rotations that would interfere with the imaging process.