Jacob Bernoulli (also known as James or Jacques) (27 December 1654/6 January 1655 – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.
He became familiar with calculus through a correspondence with Gottfried Leibniz, then collaborated with his brother Johann on various applications, notably publishing papers ontranscendental curves (1696) and isoperimetry(1700, 1701). In 1690, Jacob Bernoulli 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 theUniversity of Basel in 1687, remaining in this position for the rest of his life.
Jacob Bernoulli 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 providing 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. The lunar crater Bernoulli is also named after him jointly with his brother Johann.
John Craig (1663 – October 11, 1731) was a Scottish mathematician theologist.
Born in Dumfries and educated at the University of Edinburgh, he moved to England and became a vicar in the Church of England.
A friend of Isaac Newton, he wrote several minor works about the new calculus. He is mainly known for his book Theologiae Christianae Principia Mathematica (Mathematical Principles of Christian Theology), published in 1698.
René Descartes (French: [ʁəne dekaʁt]; Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and