Swiss mathematician (also known as Jean I or John I) who was the father of Daniel Bernoulli) and brother of Jakob Bernoulli. With his brother Jakob, Johann Bernoulli is considered the most important founder of calculus (with the exception of Newton and Leibniz). Nonetheless, Johann and Jakob two had bitter arguments about the quality of each other's work. Johann instructed l'Hospital, who later incorporated one of his Johann's results in a textbook he wrote, so that it has come to be known as l'Hospital's rule. Johann filled the mathematics chair at Basel left vacant by his brother's death. He drove his son Daniel away from home after he won a prize of the Paris Academy of Sciences for which Johann had competed.

Johann Bernoulli proposed the brachistochrone problem, which asks what shape a wire must be for a bead to slide from one end to the other in the shortest possible time, as a challenge to other mathematicians in June 1696. For this, he is regarded as one of the founders of the calculus of variations. The brachistochrone problem was solved by himself, Newton, Leibniz, l'Hospital, and his older brother Jakob and turned out to be a segment of a cycloid. At first, Johann found an incorrect proof and tried to substitute Jakob's proof for his own. However, he then realized that the solution was the same as that for a light ray in a medium with index of refraction given by

Bernoulli (Daniel), Bernoulli (Jakob), Bernoulli (Nicholas)

Additional biographies: MacTutor (St. Andrews), Dublin Trinity College, Bonn