Jakob I Bernoulli

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Jakob Bernoulli (1654–1705) mathematician and physicist
Jakob Bernoulli

Jakob I Bernoulli (* December 27, 1654 July / January 6,  1655 reg. In Basel ; † August 16, 1705 ibid) was a Swiss mathematician and physicist. The name "Jakob I" is used to distinguish it from his great-nephew Jakob II Bernoulli (1759–1789), see also the article on the Bernoulli family . Jakob Bernoulli played an essential role in the development of probability theory (see also Bernoulli distribution ) as well as in the calculus of variations and in the investigation of power seriescontributed. He has also, together with his younger brother Johann I Bernoulli the calculus of Leibniz processed and disseminated.


Jakob I was the son of the businessman Niklaus Bernoulli and his wife Margaretha Schönauer and the eldest brother of the mathematician Johann I Bernoulli . After attending school and receiving first lessons from his father, Jakob studied philosophy and theology at the University of Basel at his father's request . 1671 he reached the Master of Arts and in 1676 the licentiate lic. theol. Against the will of his father and almost autodidactically, he immersed himself in mathematics and astronomy .

From 1676 to 1680 Jakob held various positions as private tutor in Geneva . During this time he also traveled to France several times. From 1681 to 1682, Jakob I undertook a kind of cavalier tour through Holland, Great Britain and Germany. During these trips he not only got to know Cartesian mathematics, but also Hudde , Boyle and Hooke , among others . Many of his later contacts with leading mathematicians at the time emerged from this time.

Back at home in Basel, Jakob gave private lectures on experimental physics at the University of Basel from 1683 . During this time he studied a. a. the geometry of René Descartes and the work of John Wallis and Isaac Barrow, whereupon he began to be interested in calculus . In 1684 he married Judith Stupanus, with whom he later had two children. In contrast to many other members of the Bernoulli family, neither of the children was active in mathematics or physics.

Johann Jakob Keller : Epitaph for Jakob Bernoulli, in the cloister of the Basel Minster

From 1686 Jakob used complete induction , examined important power series with the help of Bernoulli numbers , and founded the theory of probability with (see Bernoulli distribution ). In 1687 he was appointed professor of mathematics at the University of Basel and began, together with his younger brother and student Johann I Bernoulli , to work on and use Leibniz's infinitesimal calculus . The two brothers were the first to use this new calculus without belonging to Leibniz's environment.

By 1689 Jakob had published important works on power series and the calculation of probability, including the law of large numbers . He formulated Bernoulli's law of large numbers , which is considered the first weak law of large numbers . In the early 1690s he worked mainly in the field of the calculus of variations , where he examined important curves and differential equations . In 1697 Jakob fell out with his brother Johann after years of rivalry.

In 1699 Jakob I was accepted as a member of the Academy of Sciences in Paris and in 1702 in that of Berlin ( Prussian Academy of Sciences ). During this time he corresponded a. a. with Gottfried Wilhelm Leibniz and Nicolas Fatio de Duillier .

Jakob I Bernoulli died on August 16, 1705 in Basel at the age of 50; his professorship in Basel was then taken over by his brother Johann.


Ars conjectandi , 1713 (Milano, Fondazione Mansutti )
Ars Conjectandi , Basel, 1713

Bernoulli wrote five treatises on series theory between 1689 and 1704, re-edited the Geometria by René Descartes and wrote mathematical articles for the Acta Eruditorum . One of his most important works, the Ars Conjectandi , was only published in Basel in 1713, eight years after his death. The book summarized the work of other authors in the field of probability theory and developed it further. In addition to strategies for winning various games of chance, the work also contains the Bernoulli numbers .

One of Bernoulli's favorite toys was the logarithmic spiral , which he dealt with extensively. According to the story, Bernoulli wanted such a spiral on his tombstone. Instead, after Bernoulli's death, the responsible stonemason chiseled an Archimedean spiral into the epitaph , which can now be viewed in the cloister of Basel Minster (presumably out of ignorance or to save work) .


"Every science needs mathematics, mathematics does not need any."

Later honors

In Basel, in 1875, a bust was erected in honor of Jakob I Bernoulli at the entrance to the Bernoullianum .

In 1985 the lunar crater Bernoulli was named after him and his brother Johann.

See also


De gravitate aetheris , 1683
  • Conamen novi systematis cometarum . Henricus Wetstein, Amsterdam 1682 (Latin, hathitrust.org ).
  • De gravitate aetheris . Henricus Wetstein, Amsterdam 1683 (Latin, Digitale-sammlungen.de ).
  • The works of Jakob Bernoulli. 5 volumes. Birkhäuser, Basel 1969–1999.
  • Probability calculation. Ars conjectandi (1713). (= Ostwald's classic. Translated and edited by R. Haussner) Verlag Wilhelm Engelmann, Leipzig 1899 (part 1, 2 - archive.org , part 3, 4 - archive.org ).
  • The art of conjecturing together with letter to a friend on sets in court tennis. The Johns Hopkins University Press, 2006 (Editor and translator Edith Dudley Sylla.)
  • David Speiser, André Weil (ed.): The correspondence from Jacob Bernoulli. Birkhäuser, Basel 1993.
  • Jacob and Johann Bernoulli. The polemics. Calculus of variations. Birkhäuser, Basel 1991.


Web links

Commons : Jakob Bernoulli  - Collection of images, videos and audio files

Individual evidence

  1. ^ Members of the previous academies. Jakob (I.) Bernoulli. Berlin-Brandenburg Academy of Sciences and Humanities , accessed on February 21, 2015 .
  2. ^ Gustaf Adolf Wanner : All about Basel's monuments. Basel 1975, p. 40 ff.