Heisenberg’s purely mathematical approach to the structure of the atom — based on a difficult set of matrix calculations — yielded results that matched the bewildering array of new observations physicists were making about the properties of simple atoms. But for a chemist like Pauling, trained to view atoms and molecules as real things with particular sizes and shapes, pure mathematics was unsatisfactory.

He preferred Schrödinger’s theory. The old picture of electrons circling the atomic nucleus like little planets did not fit the new data physicists were gathering. But unlike Heisenberg’s purely mathematical approach, Schrödinger proposed a new theory that replaced orbiting electrons with an image more like standing waves around the nucleus — waves like those found in a plucked guitar string or the head of a beaten drum. By applying an existing mathematics of wave functions to atomic questions, Schrödinger was able to create equations that matched the properties of simple atoms.

It became clear during the months of Pauling’s stay in Europe that Schrödinger’s and Heisenberg’s ideas were not two different realities but two different mathematical methods for arriving at the same atomic reality. Ultimately they became joined under a new name: quantum mechanics. Researchers, it seemed, could pick whichever method was easiest to use for a particular problem.

Pauling preferred the wave approach not only because the mathematics was somewhat easier for him but also, he said, because it contained "at least a trace of physical picture behind the mathematics."