The Strange History of B Functions or How Theoretical Chemists and Mathematicians Do (not) Interact

B functions are a class of relatively complicated exponentially decaying basis functions. Since the molecular multicenter integrals of the much simpler Slater-type functions are notoriously difficult, it is not at all obvious why B functions should offer any advantages. However, B functions have Fourier transforms of exceptional simplicity, which greatly simplifies many of their molecular multicenter integrals. This article discusses the historical development of B functions from the perspective of the interaction between mathematics and theoretical chemistry, which traditionally has not been very good. Nevertheless, future progress in theoretical chemistry depends very much on a fertile interaction with neighboring disciplines.