Guillaume François Antoine, Marquis de l'Hôpital (1661 - February 2, 1704) was a French mathematician. He is perhaps best known for the rule which bears his name for calculating the limiting value of a fraction whose numerator and denominator approach zero.
L'Hôpital is commonly spelled as both "L'Hospital" and "L'Hôpital" since the Marquis spelt his name with an 's'. However, the French language has since dropped the 's' (it was silent anyway) and replaced its preceding vowel with a circumflex.
L'Hospital was born in Paris, France. He initially had planned a military career, but poor eyesight caused him to switch to mathematics. He solved the brachistochrone problem, independently of other contemporary mathematicians, such as Isaac Newton.
He is also the author of the first known book on differential calculus, L'Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes. Published in 1696, the text includes the lectures of his teacher, Johann Bernoulli, in which Bernoulli discusses the indeterminate form 0/0.
He died in Paris.
His name is also spelled l'Hospital. The circumflex in "l'Hôpital" is an anachronism; it was not in use at the time l'Hôpital was alive.