Heisenberg set himself the task of finding the new quantum mechanics upon returning to Göttingen from Copenhagen in April 1925. Inspired by Bohr and his assistant, H.A. Kramers, in Copenhagen, Pauli in Hamburg, and Born in Göttingen, Heisenberg’s intensive struggle over the following months to achieve his goal has been well documented by historians. Since the electron orbits in atoms could not be observed, Heisenberg tried to develop a quantum mechanics without them.

He relied instead on what can be observed, namely the light emitted and absorbed by the atoms. By July 1925 Heisenberg had an answer, but the mathematics was so unfamiliar that he was not sure if it made any sense. Heisenberg handed a paper on the derivation to his mentor, Max Born, before leaving on a month-long lecture trip to Holland and England and a camping trip to Scandinavia with his youth-movement group. After puzzling over the derivation, Born finally recognized that the unfamiliar mathematics was related to the mathematics of arrays of numbers known as “matrices.” Born sent Heisenberg’s paper off for publication. It was the breakthrough to quantum mechanics.