Jacob Bernoulli

Jacob Bernoulli[lower-alpha 1] (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 sided with Gottfried Wilhelm 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.[4]

Jacob Bernoulli
Born(1655-01-06)6 January 1655
Died16 August 1705(1705-08-16) (aged 50)
EducationUniversity of Basel
(D.Th., 1676; Dr. phil. hab., 1684)
Known forBernoulli 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
FieldsMathematics, mechanics
InstitutionsUniversity of Basel
  • Primi et Secundi Adami Collatio (1676)
  • Solutionem tergemini problematis arithmetici, geometrici et astronomici (Solutions to a triple problem in arithmetics, geometry and astronomy) (1684)
Doctoral advisorPeter Werenfels
(1676 thesis advisor)
Other academic advisorsGottfried Wilhelm Leibniz (epistolary correspondent)
Doctoral studentsJacob Hermann
Nicolaus I Bernoulli
Other notable studentsJohann Bernoulli
InfluencesNicolas Malebranche[1]
Brother of Johann Bernoulli

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