**Jacques Bernoulli** (or Jakob Bernoulli) was a Swiss mathematician. He and his brother Jean Bernoulli were 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.

Jacques Bernoulli was born in Basel on December 27, 1654 and died in the same city on August 16, 1705 at the age of 50. He studied theology only to fulfill his father's wish, since from an early age he expressed an extraordinary vocation for mathematics. He visited France in 1676 and shortly thereafter was in the Netherlands, where he lived with mathematicians at the universities of Amsterdam and Leiden.

His first works are from 1682, with original hypotheses, which, however, did not elaborate. In that year, he founded in Basel the *Collegium Experimentale Physicomechanicum*, where he began reading Leibniz's works, published in the Acta Eruditorum.

He was the first mathematician to develop infinitesimal calculus beyond what Newton and Leibniz had done, applying it to new problems.

Published the first integration of a differential equation; It solved the problem of isoperimeters, which paved the way for calculating the variations of Euler and Lagrange and extended its main applications to calculating probabilities. It is considered the father of exponential calculus. He was a mathematics teacher in Basel, and his contribution to analytical geometry, probability theory and the calculus of variations was very important.

In 1713, after his death, his great treatise on probability theory was published. *Ars Conjectandi* (The art of conjecture), which still offers practical interest in the application of probability theory to insurance and statistics.