Editing Jacob Bernoulli (section)

==Biography==
Jacob Bernoulli was born in [[Basel]] in the [[Old Swiss Confederacy|Swiss Confederation]],<ref>{{cite book|last1=Sensenbaugh |first1=Robert|date=13 September 2013|chapter=THE BERNOULLI FAMILY|chapter-url=https://books.google.co.uk/books?hl=en&lr=&id=HaHdAAAAQBAJ&oi=fnd&pg=PA122&dq=Jacob+Bernoulli+was+born+in+%5B%5BBasel%5D%5D+in+the+%5B%5BOld+Swiss+Confederacy&ots=f3r6a8MFSv&sig=Yoyxfg9FcSla_ItyvClK26A67Bw&redir_esc=y#v=onepage&q&f=false|editor-last1= Magill|editor-first1=Frank N.|title=The 17th and 18th Centuries: Dictionary of World Biography, Volume 4,|page=122|url=https://books.google.co.uk/books?id=HaHdAAAAQBAJ&dq=Jacob+Bernoulli+was+born+in+%5B%5BBasel%5D%5D+in+the+%5B%5BOld+Swiss+Confederacy&lr=&source=gbs_navlinks_s |publication-place=Oxon|publisher=Routledge|publication-date=13 September 2013|isbn=1135924147|via=[[Google Scholar]]}}</ref> the son and grandson of [[Protestant]]<ref>{{Cite journal|last1=Peiffer|first1=Jeanne|date=June 2006 |url=https://ftp.gwdg.de/pub/misc/EMIS/journals/JEHPS/Novembre2006/Peifferanglais3.pdf|title=Jacob Bernoulli, teacher and rival of his brother Johann|journal=Electronic Journal for History of Probability and Statistics|volume=2|issue=1|pages=3}}</ref> spice merchants on his fathers side, his mother was born into a family engaged in banking and city governing.<ref>{{cite book|last1=Suzuki|first1=J|date=2007|veditors=Hockey  T ''et al''|title=The Biographical Encyclopedia of Astronomers.|url=https://link.springer.com/referenceworkentry/10.1007/978-0-387-30400-7_141|publication-place=New York, NY.|publisher=Springer|doi=10.1007/978-0-387-30400-7_141|access-date=1 March 2025|isbn=978-0-387-30400-7|via=[[Qwant]]}}</ref>

Following his father's wish, he studied [[theology]] and entered the ministry. But contrary to the desires of his parents,<ref name =HLS>{{cite web |url=http://www.hls-dhs-dss.ch/textes/d/D23988.php |title=Bernoulli, Jacob |last=Nagel |first=Fritz |date=11 June 2004 |publisher=Historisches Lexikon der Schweiz |access-date=20 May 2016}}</ref> he also studied [[mathematics]] and [[astronomy]]. He traveled throughout [[Europe]] from 1676 to 1682, learning about the latest discoveries in mathematics and the sciences under leading figures of the time. This included the work of [[Johannes Hudde]], [[Robert Boyle]], and [[Robert Hooke]]. During this time he also produced an incorrect theory of [[comet]]s.
[[File:Acta Eruditorum - X astronomia, 1682 – BEIC 13349171.jpg|thumb|Image from ''[[Acta Eruditorum]]'' (1682) wherein was published the critique of Bernoulli's ''Conamen novi systematis cometarum'']]

Bernoulli returned to Switzerland, and began teaching mechanics at the [[University of Basel]] from 1683. His doctoral dissertation ''Solutionem tergemini problematis'' was submitted in 1684.<ref>{{cite book |last1=Kruit |first1=Pieter C. van der |title=Jan Hendrik Oort: Master of the Galactic System |date=2019 |publisher=Springer |isbn=978-3-030-17801-7 |page=639 |url=https://books.google.com/books?id=XwSjDwAAQBAJ&pg=PA639 |language=en}}</ref> It appeared in print in 1687.<ref>{{cite book |last1=Bernoulli |first1=Jakob |title=Die Werke von Jakob Bernoulli: Bd. 2: Elementarmathematik |date=2006 |publisher=Springer Science & Business Media |isbn=978-3-7643-1891-8 |page=92 |url=https://books.google.com/books?id=CYvAH41605QC&pg=PA92 |language=it}}</ref>

In 1684, Bernoulli married Judith Stupanus; they had two children. During this decade, he also began a fertile research career. 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. He also studied [[Isaac Barrow]] and [[John Wallis]], leading to his interest in infinitesimal geometry. Apart from these, it was between 1684 and 1689 that many of the results that were to make up ''[[Ars Conjectandi]]'' were discovered.

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. By that time, he had begun tutoring his brother [[Johann Bernoulli]] on mathematical topics. 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]]" published in ''[[Acta Eruditorum]]''. They also studied the publications of [[Ehrenfried Walther von Tschirnhaus|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 among the first to try to understand and apply Leibniz's theories.

Jacob collaborated with his brother on various applications of calculus. However the atmosphere of collaboration between the two brothers turned into rivalry as Johann's own mathematical genius began to mature, with both of them attacking each other in print, and posing difficult mathematical challenges to test each other's skills.<ref>{{cite web |url=http://www.jehps.net/Novembre2006/Peifferanglais3.pdf |title=Jacob Bernoulli |last= Pfeiffer |first=Jeanne |date=November 2006 |publisher=Journal Électronique d'Histoire des Probabilités et de la Statistique |access-date=20 May 2016}}</ref> By 1697, the relationship had completely broken down.

The lunar crater [[Bernoulli (crater)|Bernoulli]] is also named after him jointly with his brother Johann.