William of the Hospital
Guillaume François Antoine, Markies de l'Hôpital (Paris, 1661 - February 2, 1704) was a French mathematician. He is probably the best known because of the rule of l'Hôpital for calculating limits. In old French the writing was also called 'l'Hospital'. biography
L'Hôpital was born in Paris. He wanted to follow a military career, but a lack of sight required him to move to mathematics. Following a challenge by Johan Bernoulli, he solved the brachist crown problem in 1696, independent of other mathematicians such as Isaac Newton, Jakob Bernoulli (Johann's brother) and Gottfried Leibniz.
He is the author of the first book on differential accounts, L'Analyse des infiniment petits pour l'intelligence des lignes courbes. This book, published in 1696, contains the lectures of his teacher Johann Bernoulli, in which Bernoulli discusses indefinite forms, such as 0/0. The method of resolving this kind of indefinite forms by repeatedly differentiating was called him the rule of l'Hôpital.
Afterwards, it became known that in 1694 he concluded a deal with Johann Bernoulli. The agreement was that l'Hôpital would pay 300 Francs a year to Bernoulli, a half-professor's salary, to solve his mathematical questions in writing. After the death of l'Hôpital in 1704 Bernoulli came with this story and claimed to be the source of the analysis but was not widely believed. In 1922, other notes of Bernoulli's lessons were found, supporting Bernoulli's story.
By various sources it is pointed out that l'Hôpital was also a good mathematician in itself and that, in some respects, he has improved Bernoulli errors, for example that the integral of 1 / x would be a finite number.
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