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Jakob Bernoulli

Jacob Bernoulli
Jakob Bernoulli.jpg
Jacob Bernoulli
Born (1654-12-27)27 December 1654
Basel, Switzerland
Died 16 August 1705(1705-08-16) (aged 50)
Basel, Switzerland
Residence Switzerland
Fields Mathematics, mechanics
Institutions University of Basel
Alma mater University of Basel
(D.Th., 1676; Dr.phil.hab., 1684)
Theses
Doctoral advisor Peter Werenfels
(1676 thesis adv.)
Other academic advisors Gottfried Leibniz
Doctoral students Johann Bernoulli
Jacob Hermann
Nicolaus I Bernoulli
Known for Bernoulli differential equation
Bernoulli numbers
Bernoulli's formula
Bernoulli polynomials
Bernoulli map
Bernoulli trial
Bernoulli process
Bernoulli scheme
Bernoulli operator
Hidden Bernoulli model
Bernoulli sampling
Bernoulli distribution
Bernoulli random variable
Bernoulli's Golden Theorem
Bernoulli's inequality
Lemniscate of Bernoulli
Influences Nicolas Malebranche
Notes
Brother of Johann Bernoulli

Jacob Bernoulli (also known as James or Jacques; 6 January 1655 [O.S. 27 December 1654] – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and had sided with Leibniz during the Leibniz–Newton calculus controversy. He is known for his numerous contributions to calculus, and along with his brother Johann, was one of the founders of the calculus of variations. He also discovered the fundamental mathematical constant e. However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work Ars Conjectandi.

Jacob Bernoulli was born in Basel, Switzerland. Following his father's wish, he studied theology and entered the ministry. But contrary to the desires of his parents, he also studied mathematics and astronomy. He traveled throughout Europe from 1676 to 1682, learning about the latest discoveries in mathematics and the sciences under leading figures of the time. This included the work of Johannes Hudde, Robert Boyle, and Robert Hooke. During this time he also produced an incorrect theory of comets.

Bernoulli returned to Switzerland and began teaching mechanics at the University in Basel from 1683. In 1684 he married Judith Stupanus; and they had two children. During this decade, he also began a fertile research career. His travels allowed him to establish correspondence with many leading mathematicians and scientists of his era, which he maintained throughout his life. During this time, he studied the new discoveries in mathematics, including Christiaan Huygens's De ratiociniis in aleae ludo, Descartes' Geometrie and Frans van Schooten's supplements of it. He also studied Isaac Barrow and John Wallis, leading to his interest in infinitesimal geometry. Apart from these, it was between 1684 and 1689 that many of the results that were to make up Ars Conjectandi were discovered.


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