Varignon gained his first exposure to mathematics by reading Euclid and then Descartes' La Géométrie.

He became professor of mathematics at the Collège Mazarin in Paris in 1688 and was elected to the Académie Royale des Sciences in the same year.

Except for l'Hôpital, Varignon was the earliest and strongest French advocate of infinitesimal calculus, and exposed the errors in Michel Rolle's critique thereof.

He recognized the importance of a test for the convergence of series, but analytical difficulties prevented his success.

Among Varignon's other works was a 1699 publication concerning the application of differential calculus to fluid flow and to water clocks.