 Infinitesimals have a long and colorful history. They make an early appearance in the mathematics of the Greek atomist philosopher Democritus (c. 450 BCE), only to be banished by the mathematician Eudoxus (c. 350 BCE) in what was to become official “Euclidean” mathematics. Taking the somewhat obscure form of “indivisibles”, they reappear in the mathematics of the late Middle Ages and later played an important role in the development of the calculus. Their doubtful logical status led in the nineteenth century to their abandonment and replacement by the limit concept. In recent years, however, the concept of infinitesimal has been refounded on a rigorous basis.