Jacob Bernoulli
Jakob I Bernoulli (* December 27 1654jul / January 6 1655greg in Basel;. . † August 16, 1705 ) was a Swiss mathematician and physicist. The name " James I " is used to distinguish him from his great-nephew James II Bernoulli (1759-1789), see also the article on the Bernoulli family.
Importance
Jakob Bernoulli has contributed significantly to the development of probability theory (see also Bernoulli distribution ) as well as for the calculus of variations and for the study of power series. Furthermore, he and his brother Johann Bernoulli processed and disseminated the calculus of Leibniz.
Life
James I was the son of the merchant Niklaus Bernoulli and his wife Margaretha Schönau, and brother of the mathematician Johann Bernoulli. After schooling and first lessons from his father Jacob studied at his request, philosophy and theology at the University of Basel. In 1671 he reached the Master of Arts and in 1676 the licentiate lic. theol .. Against the will of the Father, and almost self-taught, he immersed himself very in mathematics and astronomy.
In the years 1676-1680 Jakob held various positions as a tutor in Geneva. During this time he also traveled several times to France. In the years 1681 to 1682, James I undertook a kind of gentleman's tour through Holland, the UK and Germany. During these trips, he learned not only know the Cartesian mathematics, but including Hudde, Boyle and Hooke. Many of his later contacts with then leading mathematicians have emerged from this period.
Back home in Basel, Jakob held in 1683 private lectures on experimental physics at the University of Basel. During this time he studied, among others the Geometry tools of René Descartes and the work of John Wallis and Isaac Barrow, whereupon he began to be interested in the calculus. In 1684 he married Judith Stupanus, with whom he had two children later. Unlike many other members of the Bernoulli family both were active either in mathematics or in physics.
From 1686 used Jakob full induction, examined important power series using the Bernoulli numbers, and founded the probability theory (see Bernoulli distribution ). In 1687 he was appointed professor of mathematics at the University of Basel and started together with his younger brother and pupil Johann Bernoulli to edit the calculus of Leibniz and apply. The two brothers used as the first this new calculus without belonging to the environment of Leibniz.
By 1689, Jacob had published important work on power series and probability theory, including the law of large numbers. In the early 1690s he worked primarily in the field of calculus of variations, where he examined important curves and differential equations. In 1697 Jacob fell out after years of rivalry with his brother Johann.
1699 was included James I as a member of the Academy of Sciences of Paris and two years later in the Berlin ( Prussian Academy of Sciences). During this time he corresponded et al Gottfried Wilhelm Leibniz and Nicolas Fatio de Duillier.
At the age of 50 years, James I. Bernoulli died on August 16, 1705 in Basel; his professorship in Basel was then taken over by his brother Johann.
Works
Bernoulli wrote in the period 1689-1704 five treatises on the theory of series, gave the Geometrica of René Descartes and wrote out new mathematical contributions for Acta Eruditorum. One of his most important works, the Ars Conjectandi was so published until 1713, eight years after his death, in Basel. The book summarized the work of other authors together in the field of probability theory and developed it further. In addition to strategies to win various games of chance, the work also includes the Bernoulli numbers.
One of Bernoulli's favorite toys was the logarithmic spiral, with whom he was very busy. The story according to Bernoulli wanted such a spiral on his grave stone. Instead, chiseled responsible Steinmetz after the death of Bernoulli's (presumably out of ignorance or in order to save work) an Archimedean spiral in the epitaph which can be seen in the cloister of the cathedral to Basel today.
Quote
" Every science requires math, the math does not need. "
Posthumous honors
In Basel in 1875 in honor of James I. Bernoulli erected a bust at the entrance of Bernoullianums.