Bernoulli, Jakob (or Jacques or Jacob or James) (1655–1705) and his brother Jean were pioneers of Leibniz calculus. Jakob reformulated the problem of calculating an expectation into probability calculus. He also formulated the weak law of large numbers, upon which modern probability and statistics are based. Bernoulli, Jakob was nominated maître ès lettres in 1671. During his studies in theology, which he terminated in 1676, he studied mathematics and astronomy, contrary to the will of his father (Nikolaus Bernoulli).
In 1682, Leibniz published (in Acta Eruditorium) a method that could be used to determine the integrals of algebraic functions, a brief discourse on differential calculus in an algorithmic scheme, and some remarks on the fundamental idea of integral calculus. This paper attracted the attention of Jakob and his brother, and they considerably improved upon the work already done by Leibniz. Leibniz himself recognized that infinitesimal calculus was mostly founded by...
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© 2008 Springer-Verlag
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(2008). Bernoulli, Jakob. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_26
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