  A century ago Srinivasa Ramanujan - the great self-taught Indian genius of
mathematics - died, shortly after returning from Cambridge, UK, where he had
collaborated with Godfrey Hardy. Ramanujan contributed numerous outstanding
results to different branches of mathematics, like analysis and number theory,
with a focus on special functions and series. Here we refer to apparently weird
values which he assigned to two simple divergent series, $\sum_{n \geq 1} n$
and $\sum_{n \geq 1} n^{3}$. These values are sensible, however, as analytic
continuations, which correspond to Riemann's $\zeta$-function. Moreover, they
have applications in physics: we discuss the vacuum energy of the photon field,
from which one can derive the Casimir force, which has been experimentally
measured. We also discuss its interpretation, which remains controversial. This
is a simple way to illustrate the concept of renormalization, which is vital in
quantum field theory.
