  $B$ 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.
