The simplest shape traced out by a spinning needle (orange) is a circle, butshapes with a smaller area are possible, such as the deltoid (right), createdbyspinning a needle while its central point traces out a circleMathematicians have solved a decades-old problem related to spinning a needle, in what has been hailed as one of the most important mathematical results in recent times. Once seen as impossible, the solution should now unlock answers to a slew of other difficult problems that had seemed completely out of reach. The paper is perhaps the biggest breakthrough in mathematics of