James Bernoulli

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James Bernoulli (also known as Jacob I) was born in Basel, Switzerland on December 27, 1654 and lived until August 16, 1705. He is one of the eight prominent mathematicians in the Bernoulli family.

Following his father's wish, James studies 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. This included the work of Robert Boyle and Robert Hooke.

He became familiar with calculus through a correspondence with Gottfried Leibniz, then collaborated with his brother Johann on various applications, notably publishing papers on transcendental curves (1696) and isoperimetry (1700, 1701). In 1690, James became the first person to develop the technique for solving separable differential equations.

Upon returning to Basel in 1682, he founded a school for mathematics and the sciences. He was appointed professor of mathematics at the University of Basel in 1687, remaining in this position for the rest of his life.

James is best known for the work Ars Conjectandi (The Art of Conjecture), published eight years after his death in 1713 by his nephew Nicholas. In this work, he described the known results in probability theory and in enumeration, often proving alternative proofs of known results. This work also includes the application of probability theory to games of chance and his introduction of the theorem known as the law of large numbers. The terms Bernoulli trial and Bernoulli Numbers result from this work. Bernoulli crater, on the Moon, is also named after him jointly with his brother Johann.