Johann Bernoulli

• 1. Introduction

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  Johann Bernoulli arrived at the University of Basel not to study mathematics, but medicine. His father, a Basel apothecary named Nicolaus Bernoulli, had originally wanted his son to take over the family spice trade. Johann pushed back, and medicine was the compromise. Yet what consumed him during those university years was something else entirely: the brand-new language of infinitesimal calculus, which he studied on the side with his older brother Jacob. What does it mean that one of the most consequential mathematical minds of his era came to the discipline through a series of family arguments and quiet rebellions? And what happens when a man who is brilliant enough to teach Leonhard Euler is also bitter enough to steal credit from his own son?

• 2. The Calculus Brothers

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  Basel University in the late seventeenth century was where Johann and Jacob Bernoulli quietly positioned themselves at the frontier of mathematics. The infinitesimal calculus they were absorbing had only recently been articulated, and the Bernoulli brothers were among the first mathematicians anywhere not merely to understand it but to put it to work on real problems. Johann's medicine dissertation in 1690, reviewed by Gottfried Leibniz himself, was titled De Motu musculorum et de effervescentia et fermentatione. That Leibniz reviewed it is telling: even as a medical student, Johann was already orbiting the people who mattered most in European mathematics. After graduating, he moved into teaching differential equations, and in 1694 he married Dorothea Falkner, the daughter of a Basel alderman, before accepting the professorship of mathematics at the University of Groningen.

• 3. Taking Leibniz's Side

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  In 1713, the long-simmering dispute over who deserved credit for inventing calculus broke into open conflict, and Johann Bernoulli chose Leibniz over Newton without hesitation. His argument was concrete: he demonstrated that Leibniz's methods had solved certain problems that Newton's methods had failed to crack. Beyond calculus priority, Bernoulli also championed Descartes' vortex theory of motion against Newton's account of gravitation. The practical consequence of his influence was significant: acceptance of Newton's gravitational theory was delayed across continental Europe. In 1724, he entered a competition run by the French Academie Royale des Sciences, which asked competitors to explain the laws governing the collision of perfectly hard bodies. Defending a position associated with Leibniz, Bernoulli found himself arguing for an infinite external force to make a body elastic, which led directly to his disqualification. The prize that year went to Maclaurin. Two years later, in 1726, a related competition on elastic bodies saw the prize go to Pierre Maziere, while Bernoulli received an honourable mention in both rounds.

• 4. The l'Hopital Arrangement

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  Guillaume de l'Hopital hired Bernoulli as a private mathematics tutor, and the two men formalized their relationship in a contract. Under its terms, l'Hopital was free to use Bernoulli's mathematical discoveries however he chose. In 1696, l'Hopital published Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes, the first textbook ever written on infinitesimal calculus. Much of it was Bernoulli's work, including the result that would come to carry l'Hopital's name: l'Hopital's rule. The book's preface acknowledged the debt, with l'Hopital writing that he recognized he owed much to the insights of the Bernoullis, especially "to those of the younger (John), currently a professor in Groningen," and that he had "unceremoniously used their discoveries." Despite that admission, Bernoulli was not satisfied. In letters to Leibniz, Pierre Varignon, and others, he complained persistently that he had not received enough credit for what he contributed.

• 5. Jealousy and Rivalry

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  While the Bernoulli brothers collaborated through much of their time at Basel, a jealous and competitive streak emerged between them once Johann graduated. Johann resented Jacob's professional standing, and the two repeatedly tried to outdo each other. Their fiercest clash centred on the brachistochrone curve: the equation for the fastest path a particle under gravity alone can travel between two points. Johann posed the problem publicly in 1696 and offered a reward for its solution. He proposed the cycloid as the answer, noting its connection to the path light takes through layers of varying density. Jacob arrived at the same solution, but Johann's derivation was wrong. He then presented Jacob's correct derivation as his own. Jacob died of tuberculosis in 1705. Johann had been travelling back to Basel at his father-in-law's urging when he learned of his brother's death along the way. He had expected to become professor of Greek at Basel University on his return; instead, he stepped into Jacob's old chair in mathematics. After Jacob was gone, the competitive jealousy did not disappear. It shifted toward Johann's own son Daniel.

• 6. A Father Against His Son

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  Daniel Bernoulli published Hydrodynamica in 1738, a landmark work in the science of fluid motion. Johann responded with his own book on the same subject, Hydraulica, which appeared in 1743. To claim priority over his son, Johann falsely predated Hydraulica by six years, placing its claimed composition before Daniel's work. The fraud was deliberate. The man who had complained for years about receiving insufficient credit was willing to manufacture credit against his own child. Johann had tutored Leonhard Euler during the young mathematician's early years, a relationship that left a lasting mark on one of the most productive mathematicians in history. That generosity toward a student stood in sharp contrast to the calculation he applied to his own son.