Guillaume de l'Hôpital

Lore & Background

L'Hôpital was born into a military family. His father was Anne-Alexandre de l'Hôpital, a Lieutenant-General of the King's army, and his mother was Elisabeth Gobelin. He abandoned a military career due to poor eyesight and pursued mathematics. Among his accomplishments were the determination of the arc length of the logarithmic graph, one of the solutions to the brachistochrone problem, and the discovery of a turning point singularity on the involute of a plane curve near an inflection point. The history leading to its publication became a subject of protracted controversy. After l'Hôpital's death, Bernoulli publicly revealed their agreement and claimed credit for statements and portions of the text. L'Hôpital married Marie-Charlotte de Romilley de La Chesnelaye, also a mathematician and a member of the nobility, and inheritor of large estates in Brittany. Together they had one son and three daughters. L'Hôpital died at the age of 42; the exact cause of his death is not widely recorded.

Reader's Guide

This book presented the ideas of differential calculus and their applications to differential geometry of curves in a lucid form with numerous figures, though it did not consider integration. Several editions and translations to other languages were published, and it became a model for subsequent treatments of calculus. His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞, although the rule did not originate with him—it appeared in print for the first time in his treatise. L'Hôpital's legacy is thus intertwined with both his influential textbook and the disputed origins of its material. His other mathematical contributions include work on the arc length of the logarithmic graph, the brachistochrone problem, and a turning point singularity on the involute of a plane curve.

Did You Know?

• L'Hôpital abandoned a military career due to poor eyesight.