Jacob Bernoulli
Swiss mathematician (1655–1705) / From Wikipedia, the free encyclopedia
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Jacob Bernoulli^{[loweralpha 1]} (also known as James in English or Jacques in French; 6 January 1655 [O.S. 27 December 1654] – 16 August 1705) was one of the many prominent mathematicians in the Swiss Bernoulli family. He sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy and was an early proponent of Leibnizian calculus, which he made numerous contributions to; along with his brother Johann, he 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.^{[3]}
Jacob Bernoulli  

Born  (16550106)6 January 1655 
Died  16 August 1705(17050816) (aged 50) Basel, Switzerland 
Education  University of Basel (D.Th., 1676; Dr. phil. hab., 1684) 
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 
Scientific career  
Fields  Mathematics, mechanics 
Institutions  University of Basel 
Theses 

Doctoral advisor  Peter Werenfels (1676 thesis advisor) 
Other academic advisors  Gottfried Wilhelm Leibniz (epistolary correspondent) 
Doctoral students  Jacob Hermann Nicolaus I Bernoulli 
Other notable students  Johann Bernoulli 
Notes  
Brother of Johann Bernoulli 