Jacob Bernoulli 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.
Jacob Bernoulli
Image from Acta Eruditorum (1682) wherein was published the critique of Bernoulli's Conamen novi systematis cometarum
Jacob Bernoulli's tombstone in Basel Münster
De gravitate aetheris, 1683
Johann Bernoulli was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus and educating Leonhard Euler in the pupil's youth.
Johann Bernoulli (portrait by Johann Rudolf Huber, c. 1740)
Commercium philosophicum et mathematicum (1745), a collection of letters between Leibnitz and Bernoulli
Illustration from De motu corporum gravium published in Acta Eruditorum, 1713
Volumes I-IV of Bernoulli's 1742 Opera Omnia
