So great was the reputation of the Bernoulli family, and so numerous its members—a condition not unlike that of their German contemporaries the Bachs—that historians often have a hard time sorting out the various personalities. Thus Johann Bernoulli was also known as Jean, while his equally famous older brother Jakob (1654-1705) has been variously identified as Jacques, James, or Jakob I to distinguish him from other Bernoullis of that name. Another abiding characteristic of the Bernoulli family was a tendency toward rivalries, conflicts that always seemed to center around Johann—who struggled first with his brother, and later with his son Daniel (1700-1782), most notable among a prominent line.
Johann originally studied medicine, but from the beginning of his academic career, his passion was mathematics. Thus his doctoral dissertation was a mathematical treatise presented as a study of muscle contractions. By 1691, when he was 24, Bernoulli had travelled from the family's home in Switzerland to Paris, where he became associated with some of the leading scientists and philosophers of the day. Of these, none was more significant than Gottfried Wilhelm von Leibniz (1646-1716), whose friend, correspondent, and loyalist Bernoulli would remain for the rest of his life.
Hired by the young Marquis de L'Hospital (1661-1704) as the latter's tutor in 1692, Bernoulli eventually "sold" a number of his mathematical discoveries to the wealthy young man. Thus L'Hospital's Rule, which enabled mathematicians to determine the limiting value of a fraction in which both numerator and denominator tend toward zero, was actually a discovery of Bernoulli. L'Hospital was, however, a talented thinker in his own right as well. Thus some years later, when Bernoulli presented his famous brachistochrone problem, Leibniz correctly posited that only five people would solve it: Leibniz himself, the two Bernoulli brothers, Sir Isaac Newton (1642-1727), and L'Hospital.
The brachistochrone problem, which concerned the curve marking the quickest descent of an object between two points at different altitudes (but not along a vertical line), was but one of several points of contention for the Bernoullis. Jakob claimed to have found the solution first, and in the case of the isoperimetric problem—involving the comparison of different polygons with equal perimeters—there is no doubt that Jakob was first, though Johann did improve on his brother's findings.
This rivalry was a driving force in Johann's career: in 1695, he took a position at the University of Gröningen in the Netherlands, knowing that Jakob would keep him off the faculty at his own University of Basel. Following Jakob's death in 1705, however, Johann took his place as professor of mathematics at Basel, where his stature as a leading figure in the European intellectual world would grow during the four subsequent decades. Soon he had a new rival within the family, however: his brilliant son Daniel, whose famous law concerning fluid pressure (Bernoulli's principle) he attempted to present as his own.
Despite his apparent disloyalty to blood kin, Johann proved a loyal supporter of Leibniz throughout his career. In early years, he defended the German mathematician as the founder of calculus against supporters of Newton, who had simultaneously developed his own calculus. Late in life, Bernoulli made a name for himself in the realm of mechanics, supporting Leibniz's views on what became known as the conservation of energy. Thanks in part to Bernoulli's efforts, the Leibnizian concept of "living force" would gain acceptance over countervailing (but not entirely inaccurate) ideas presented by René Descartes (1596-1650). Today living force is known as kinetic energy, and Bernoulli as credited as the one of the first thinkers to recognize the principle of conservation.