After studying at the Ecole Normale Supérieure, he completed his agrégation in 1943, being received premier ex aequo alongside Tran Duc Thao.

A student of French historical epistemologists Gaston Bachelard and Jean Cavaillès, he was however at first influenced by phenomenology and existentialism, before shifting towards study of logics and science.

In 1962, he published a book titled The Philosophy of Algebra, dedicated to mathematician Pierre Samuel (a member of the Bourbaki group), René Thom, physicist Raymond Siestrunck,[6] and linguist Georges Vallet.

[7] Vuillemin thought that renewals of methods in mathematics have influenced philosophy, thus relating the discovery of irrational numbers to Platonism, algebraic geometry to Cartesianism, infinitesimal calculus to Gottfried Wilhelm Leibniz.

[8] He was one of the main French commentators on the philosophy and works of Bertrand Russell, Ludwig Wittgenstein, Rudolf Carnap and Willard Van Orman Quine.