Joseph Serret graduated from the École Polytechnique in Paris in 1840. He became an entrance examiner for the École Polytechnique in 1848. In 1861 he became professor of celestial mechanics at Collège de France, then two years later he was appointed to the chair of differential and integral calculus at the Sorbonne. Serret joined the Bureau des Longitudes in 1873.
Serret did important work in differential geometry. Together with Bonnet and Bertrand he made major advances in this topic. The fundamental formulas in the theory of space curves are the Frenet-Serret formulas.
In 1860 Serret succeeded Poinsot in the Académie des Sciences. In 1871 he retired to Versailles as his health began to deteriorate.
Serret also worked in number theory, calculus and
mechanics. He edited the works of Lagrange
which were published in 14 volumes between 1867 and 1892. He also edited the 5th
edition of Monge
in 1850.