Mathematicians know that math is a work in progress. The diverse and illustrious history of mathematics demonstrates the impressive fertility of the discipline. The innovations sometimes arise from the perception of new orders within mathematics itself, new possibilities for expressing new meanings, as in the development of infinitesimals and complex numbers. In the sciences, formal mathematics has often been ahead of the curve of application. For example, in the 1960s, Murray Gell-Mann and George Zweig, wrestling with how to understand particle physics, proposed the existence of a new type of subatomic particle called a “quark” as the fundamental building block of protons and neutrons. Gell-Mann, striving for a theory of how quarks behave under the strong nuclear force, turned to existing group theory, a branch of algebra, to describe their symmetries. Group theory had been developed, mostly in the nineteenth century, as a theory of algebraic structures, including numbers. The mathematics was already at hand when the particle physicists needed it.