Infinitesimals have seen ups and downs in their tumultuous history. In the 18th century, d'Alembert set the tone by describing infinitesimals as chimeras. Some adversaries of infinitesimals, including Moigno and Connes, picked up on the term. We highlight the work of Cauchy, Noël, Poisson and Riemann. We also chronicle reactions by Moigno, Lamarle and Cantor, and signal the start of a revival with Peano.

17 pages. To appear in British Journal for the History of Mathematics