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A century ago, Srinivasa Ramanujan -- the great self-taught Indian genius ofmathematics -- died, shortly after returning from Cambridge, UK, where he hadcollaborated with Godfrey Hardy. Ramanujan contributed numerous outstandingresults to different branches of mathematics, like analysis and number theory,with a focus on special functions and series. Here we refer to apparently weirdvalues 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 analyticcontinuations, which correspond to Riemann's $\zeta$-function. Moreover, theyhave applications in physics: we discuss the vacuum energy of the photon field,from which one can derive the Casimir force, which has been experimentallymeasured. We further discuss its interpretation, which remains controversial.This is a simple way to illustrate the concept of renormalization, which isvital in quantum field theory.

From Ramanujan to renormalization: the art of doing away with divergences and arriving at physical results