L'Hôpital's rule was really Bernoulli's, sold under a tutoring contract
Calculus students learn l'Hôpital's rule for tricky limits. The marquis de l'Hôpital did not discover it. He paid Johann Bernoulli to tutor him, under a contract letting him use Bernoulli's findings however he liked, then published the first calculus textbook in 1696, built largely from his tutor's work.
L'Hôpital was at least candid about it. His preface admitted he had freely used the discoveries of the Bernoulli brothers, especially the younger one then teaching at Groningen, and invited them to claim whatever credit they wished. Johann nonetheless spent years complaining in letters to Leibniz, Varignon and others that he had been shortchanged.
Rivalry ran through his life. Born in Basel in 1667 to an apothecary father who wanted him in the family spice business, Johann talked his way into medicine and studied the brand-new calculus on the side with his older brother Jacob. The two were among the first to put it to work on real problems. Collaboration soon soured into competition. In 1696 Johann posed the brachistochrone challenge: find the curve down which a ball rolling under gravity alone travels between two points fastest. Both brothers answered with the cycloid, the curve traced by a point on a rolling wheel, but Johann's derivation was wrong and he passed off Jacob's as his own.
When Jacob died of tuberculosis in 1705, Johann took over his professorship in Basel. His jealousy then turned on his own son Daniel. After Daniel published Hydrodynamica in 1738, Johann released Hydraulica and deliberately backdated it six years to claim priority. He also backed Leibniz in the fight with Newton over who invented calculus and promoted Descartes' vortex theory over Newtonian gravity, slowing the acceptance of Newton's ideas on the Continent.
A 1724 Paris Academy prize went wrong when his argument for perfectly hard bodies required an infinite force; he was disqualified and Maclaurin won. His greatest legacy may be a student: he helped educate the young Leonhard Euler. He died on New Year's Day 1748.
Source: Johann Bernoulli
