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.

He traveled throughout Europe from 1676 to 1682, learning about the latest discoveries in mathematics and the sciences under leading figures of the time.

His travels allowed him to establish correspondence with many leading mathematicians and scientists of his era, which he maintained throughout his life.

During this time, he studied the new discoveries in mathematics, including Christiaan Huygens's De ratiociniis in aleae ludo, Descartes' La Géométrie and Frans van Schooten's supplements of it.

People believe he was appointed professor of mathematics at the University of Basel in 1687, remaining in this position for the rest of his life.

Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra published in 1685, work on probability in 1685 and geometry in 1687.

His geometry result gave a construction to divide any triangle into four equal parts with two perpendicular lines.

In May 1690, in a paper published in Acta Eruditorum, Jacob Bernoulli showed that the problem of determining the isochrone is equivalent to solving a first-order nonlinear differential equation.

Bernoulli's most original work was Ars Conjectandi, published in Basel in 1713, eight years after his death.

The book also covers other related subjects, including a review of combinatorics, in particular the work of van Schooten, Leibniz, and Prestet, as well as the use of Bernoulli numbers in a discussion of the exponential series.

Inspired by Huygens' work, Bernoulli also gives many examples on how much one would expect to win playing various games of chance.

Astuteness and elegance are seldom found in his method of presentation and expression, but there is a maximum of integrity.

Bernoulli wanted a logarithmic spiral and the motto Eadem mutata resurgo ('Although changed, I rise again the same') engraved on his tombstone.

He wrote that the self-similar spiral "may be used as a symbol, either of fortitude and constancy in adversity, or of the human body, which after all its changes, even after death, will be restored to its exact and perfect self".