Sylvestre Lacroix's parents were poor and he was fortunate to be a student of Monge who was influential in his career. Through Monge's influence he was appointed Professor of Mathematics at the École Gardes de Marine at Rochefort in 1782.
From Rochefort Lacroix went to a chair at the École Normale, then he moved to the École Centrale des Quatre Nations. He was appointed professor of mathematics at the École Polytechnique from 1799 where he held the chair of analysis. In the same year he became a member of the Institute. He also became professor at Faculté des Sciences in 1810.
In 1815 he left the École Polytechnique to take up a chair at the Sorbonne and a chair at the Collège de France.
Lacroix was the writer of important textbooks in mathematics and through these he made a major contribution to the teaching of mathematics throughout France. He published a three volume text Traité de Calcul differéntiel et intégral (1797-1800). During the same period he was publishing a 10 volume work Cours de Mathématique (1797-1799).
These texts had an influence beyond France for it was through English translations of the texts that the 'new continental mathematics' entered universities in Britain.
Lacroix held the view that algebra and geometry
should be treated separately, as far apart as they can be; and that the results in each should serve for mutual clarification, corresponding, so to speak, to the text of a book and its translation.