Jean Bernoulli (or Johann Bernoulli) was a Swiss mathematician. He and his brother Jacques Bernoulli were important disciples of Leibniz. No family in human history has produced as many mathematicians as the Bernoulli family, twelve in all, who have contributed unparalleled in the creation and development of differential and integral calculus.
It was the Bernoulli who first used the word integral (1669), and shortly afterwards Leibniz would agree that Calculus Integralis would be a better name than Calculus Sommatorius. The Bernoulli family originated in the Netherlands in the city of Antwerp, fleeing to Switzerland for being Protestants. Jean Bernoulli was born in the city of Basel, Switzerland, on August 7, 1667. Son of Nicholas Bernoulli, also the father of two other mathematicians: Jacques and Nicholas. Although Mr Nicholas had provided his children with a great deal of mathematical knowledge, he did not intend them to devote themselves to it. He hoped his children were religious ministers or doctors. At first, Jean follows her father's path, even writing a doctoral dissertation on fermentation at the age of 23.
From 1691, Jean became passionate about the theory of differential and integral calculus, writing two books on calculus. In 1692, Jean was in Paris and, to earn a living, became a private tutor to a young man, Guilherme François L'Hospital, Marquis de St Mesme, With which he made a pact: In exchange for a monthly salary given by the Marquis, Jean would agree to pass on his mathematical discoveries to be used as the Marquis desired.
The result of this agreement was that one of Jean Bernoulli's most important contributions, dating from 1694, to the resolution of indefinite limits, became known worldwide as the rule of L'Hospital, Analysis des Infinites Petits, published in Paris in 1699. The publication is considered to be the first book of differential calculus and Integral published in the world, whose importance was enormous for the spread of calculus among the scholars of the eighteenth century. In this book, L'Hospital proves to be an excellent writer by orderly exposing, through his pedagogical skills, all the evolution of the main supporting ideas of integrals and derivatives. This book was so successful that for two centuries it was published with print runs of thousands of copies. In the preface, L'Hospital especially thanks Jean Bernoulli and Leibniz.
In 1694, he married Marie Euler, niece of the great Euler, with whom he had three sons, all geniuses: Nicholas I, Daniel I and Jean II. These would do great work in physics and mathematics and it would be no less, for in their veins flowed the blood of two large families: the Euler and the Bernoulli.
In 1695 Bernoulli was invited to become a professor at the University of Groningen, and in 1696 he became interested in what would be variant calculus. At this time, he proposed, in Acta Eruditorium magazine, the famous problem of the minimum descent time of a body under the action of the gravitational field, a problem solved by Euler and several mathematicians, including Jean himself.
In 1704, after the death of L'Hospital, he accuses him to other mathematicians of having plagiarized several of his results, which was considered unfounded by his contemporaries. However, years later, when the correspondence between him and L'Hospital became public, mathematicians realized that all the great ideas of the latter were given by the former.
In 1711, Jean Bernoulli was known throughout the world for his important work in mathematics, physics and engineering, especially for his studies of catenary properties, being honored several times by kings and queens. Legend has it around his name that when he performed where he was not known, people would reply: if you are Bernoulli, then we are Newton.
In 1712, he shows clear signs of madness by expelling his son Daniel from home for winning a prize from the Paris Academy of Sciences, which Jean also applied for. The fact that his son was better than him provoked him to envy that lasted until the end of his life. He refused to talk to the people around him, and if they knew math he claimed they were thieves of his ideas. All of these symptoms of paranoia would become acute over the years. In the year 1747, he is practically alone in the world, abandoned even by his own family.
Jean Bernoulli died of madness in the city of Basel on January 3, 1748, at the age of 81.