Jacob (Jacques) Bernoulli

Jacob (Jacques) Bernoulli

Born: 27 Dec 1654 in Basel, Switzerland

Died: 16 Aug 1705 in Basel, Switzerland

Jacob Bernoulli's father, Nicolaus Bernoulli (1623-1708) inherited the spice business in Basel that had been set up by his own father, first in Amsterdam and then in Basel. The family, of Belgium origin, were refugees fleeing from persecution by the Spanish rulers of the Netherlands. Philip, the King of Spain, had sent the Duke of Alba to the Netherlands in 1567 with a large army to punish those opposed to Spanish rule, to enforce adherence to Roman Catholicism, and to re-establish Philip's authority. Alba set up the Council of Troubles which was a court that condemned over 12000 people but most, like the Bernoulli family who were of the Protestant faith, fled the country.

Nicolaus Bernoulli was an important citizen of Basel, being a member of the town council and a magistrate. Jacob Bernoulli's mother also came from an important Basel family of bankers and local councillors. Jacob Bernoulli was the brother of Johann Bernoulli and the uncle of Daniel Bernoulli. He was compelled to study philosophy and theology by his parents, which he greatly resented, and he graduated from the University of Basel with a master's degree in philosophy in 1671 and a licentiate in theology in 1676.

During the time that Jacob Bernoulli was taking his university degrees he was studying mathematics and astronomy against the wishes of his parents. It is worth remarking that this was a typical pattern for many of the Bernoulli family who made a study of mathematics despite pressure to make a career in other areas. However Jacob Bernoulli was the first to go down this road so for him it was rather different in that there was no tradition of mathematics in the family before Jacob Bernoulli. Later members of the family must have been much influenced by the tradition of studying mathematics and mathematical physics.

In 1676, after taking his theology degree, Bernoulli moved to Geneva where he worked as a tutor. He then travelled to France spending two years studying with the followers of Descartes who were led at this time by Malebranche. In 1681 Bernoulli travelled to the Netherlands where he met many mathematicians including Hudde. Continuing his studies with the leading mathematicians and scientists of Europe he went to England where, among others, he met Boyle and Hooke. At this time he was deeply interested in astronomy and produced a work giving an incorrect theory of comets. As a result of his travels, Bernoulli began a correspondence with many mathematicians which he carried on over many years.

Jacob Bernoulli returned to Switzerland and taught mechanics at the University in Basel from 1683, giving a series of important lectures on the mechanics of solids and liquids. Since his degree was in theology it would have been natural for him to turn to the Church, but although he was offered an appointment in the Church he turned it down. Bernoulli's real love was for mathematics and theoretical physics and it was in these topics that he taught and researched. During this period he studied the leading mathematical works of his time including Descartes's Géométrie and van Schooten's additional material in the Latin edition. Jacob Bernoulli also studied the work of Wallis and Barrow and through these he became interested in infinitesimal geometry. Jacob began publishing in the journal Acta Eruditorum which was established in Leipzig in 1682.

In 1684 Jacob Bernoulli married Judith Stupanus. They were to have two children, a son who was given his grandfather's name of Nicolaus and a daughter. These children, unlike many members of the Bernoulli family, did not go on to become mathematicians or physicists.

One of the most significant events concerning the mathematical studies of Jacob Bernoulli occurred when his younger brother, Johann Bernoulli, began to work on mathematical topics. Johann Bernoulli was told by his father to study medicine but while he was studying that topic he asked his brother Jacob Bernoulli to teach him mathematics. Jacob Bernoulli was appointed professor of mathematics in Basel in 1687 and the two brothers began to study the calculus as presented by Leibniz in his 1684 paper on the differential calculus in Nova Methodus pro Maximis et Minimis, itemque Tangentibus... published in Acta Eruditorum. They also studied the publications of von Tschirnhaus. It must be understood that Leibniz's publications on the calculus were very obscure to mathematicians of that time and the Bernoullis were the first to try to understand and apply Leibniz's theories.Although Jacob and Johann Bernoulli both worked on similar problems their relationship was soon to change from one of collaborators to one of rivals. Johann Bernoulli's boasts were the first cause of Jacob's attacks on him and Jacob wrote that Johann was his pupil whose only achievements were to repeat what his teacher had taught him. Of course this was a grossly unfair statement. Jacob Bernoulli continued to attack his brother in print in a disgraceful and unnecessary fashion, particularly after 1697. However he did not reserve public criticism for his brother. He was critical of the university authorities at Basel and again he was very public in making critical statements that, as one would expect, left him in a difficult situation at the university. Jacob probably felt that Johann was the more powerful mathematician of the two and, this hurt since Jacob's nature meant that he always had to feel that he was winning praise from all sides. Hofmann writes in:-

Sensitivity, irritability, a mutual passion for criticism, and an exaggerated need for recognition alienated the brothers, of whom Jacob had the slower but deeper intellect.

As suggested by this quote the brothers were equally at fault in their quarrel. Johann Bernoulli would have liked the chair of mathematics at Basel which Jacob held and he certainly resented having to move to Holland in 1695. This was another factor in the complete breakdown of relations in 1697.

Of course the dispute between the brothers over who could obtain the greatest recognition was a particularly stupid one in the sense that both made contributions to mathematics of the very greatest importance. Whether the rivalry spurred them on to greater things or whether they might have achieved more had they continued their initial collaboration, it is impossible to say. We shall now examine some of the major contributions made by Jacob Bernoulli at an important stage in the development of mathematics following Leibniz's work on the calculus.

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.