L'Hôpital, a Parisian by birth, began his career as a cavalry officer. However, he was forced to resign because of his short-sightedness and devoted the rest of his life to mathematical study and research. To this end he invited the German mathematician Jean Bernoulli to his château in 1691 to teach him the details of his newly-worked-out differential calculus. Shortly afterward L'Hôpital published his Analyse des infiniment petits pour l'intelligence des lignes courbes (Analysis of Infinitely Small Quantities for the Understanding of Curved Lines) (1696), the first calculus textbook ever to appear. L'Hôpital's basic assumption was that “…a quantity, which is increased or decreased only by an infinitely smaller quantity, may be considered as remaining the same.” It was in this work that he first formulated the rule for finding the limiting value of a fraction with a numerator and denominator simultaneously tending to zero (0/0), since known to mathematicians as L'Hôpital's rule.

Bernoulli appeared none too pleased with L'Hôpital's book considering it to be largely his own work, a belief supported by the discovery in 1921 of Die Differentialrechnung, a manuscript of Bernoulli, on which L'Hôpital had clearly based his own text.