# Guillaume L’Hôpital

(1661 – 1704)

Guillaume Francois Antoine de L’Hôpital, Marquis de Sainte-Mesme, Comte d’Entremont, was born in Paris, France in 1661. His gift for mathematics was revealed when, at the age of fifteen, he solved a problem on cycloids posed by Pascal. Despite his obvious mathematical talent, the marquis opted first for a career in the military. Only after nearsightedness forced his resignation from the calvary did L’Hôpital turn to mathematics.

L’Hôpital’s attention was inevitably drawn to the newly emerging calculus, though he considered the revolutionary subject too difficult to master without assistance. At the time, the infinitesimal calculus was fully understood by only four men: Leibniz, Newton, and the Bernoulli brothers, John and James. John Bernoulli was known throughout Europe as an effective and inspiring teacher, and L’Hôpital was elated when Bernoulli agreed to tutor him in the calculus.

Bernoulli taught the marquis primarily through letters that explained the calculus and elucidated Bernoulli’s continuing mathematical research. As agreed, L’Hôpital paid Bernoulli for his services

as tutor, and also bought the rights to Bernoulli’s mathematical discoveries.

Because L’Hôpital purchased Bernoulli’s research, he had the legal right to claim his teacher’s work as his own. L’Hôpital’s *Analyse des infiniment petits*, the first calculus textbook, was comprised almost exclusively of Bernoulli’s letters. The *Analyse*, published in 1696, included a method for finding the limiting value of fractions of the type 0/0. This theorem, though the work of John Bernoulli, is known as L’Hôpital’s Rule.

L’Hôpital’s *Analyse* met with instant acclaim and was regarded throughout the seventeenth and eighteenth centuries as the standard text on infinitesimal analysis. A treatise on analytical conics, written largely by the marquis himself, enjoyed a similarly warm reception upon its publication, posthumously, in 1707. L’Hôpital died in Paris on February 2, 1704, at the age of 43.

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### References

- Ball, W. W. Rouse.
*A Short Account of the History of Mathematics*. 1908. Reprint. New York: Dover Publications, Inc., 1960. - Dunham, William.
*Journey Through Genius: The Great Theorems of Mathematics*. New York: John Wiley & Sons, Inc., 1990. - Eves, Howard.
*An Introduction to the History of Mathematics*. 6th ed. Fort Worth: Saunders College Publishing, 1992. - Gillispie, Charles Coulston, ed.
*Dictionary of Scientific Biography*. Vol. VIII. New York: Charles Scribner’s Sons, 1973. - Simmons, George F.
*Calculus Gems: Brief Lives and Memorable Mathematics*. New York: McGraw-Hill, Inc., 1992. - Struik, Dirk J.
*A Concise History of Mathematics*. New York: Dover Publications, Inc., 1987.