In 1925 and 1926 two versions of quantum mechanics were born almost at once. Werner Heisenberg’s used infinite matrices; Erwin Schrödinger’s, a wave equation. Both gave the same results in experiments, but they seemed to speak of different things, and physicists used tricks that mathematicians found unacceptable, such as Dirac’s delta “function”. In Göttingen, working with Hilbert, von Neumann showed that the two were the same theory written in different coordinates, and rewrote everything in a single language. The book Mathematical Foundations of Quantum Mechanics, of 1932, is still the reference for anyone who wants the theory with full rigour.