Guillaume de l'Hôpital

Guillaume de l'Hôpital, Marquis de l'Hôpital, who lived from 1661 to 1704, was a French mathematician whose name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms. Born into a military family, the son of a lieutenant-general of the king's army, he abandoned a military career because of poor eyesight and pursued the mathematics that had interested him since childhood. He was a member of Nicolas Malebranche's circle in Paris, where in 1691 he met the young Johann Bernoulli, who agreed to supplement his Paris talks on infinitesimal calculus with private lectures at l'Hôpital's estate at Oucques. He was elected to the French Academy of Sciences in 1693 and served twice as its vice-president, and he corresponded with Leibniz, Huygens and both Bernoulli brothers. His 1696 treatise Analyse des Infiniment Petits was the first textbook on infinitesimal calculus and a model for later treatments, although the rule that carries his name did not originate with him, and the history of the book became the subject of a protracted controversy. His analytic treatise on conic sections was published after his death, in 1707.