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{{Short description|Swiss mathematician and physicist (1700–1782)}}
{{Use dmy dates|date=January 2024}}
{{Infobox scientist
| name              = Daniel Bernoulli
| image             = Porträt des Daniel Bernoulli - edit1.jpg
| caption           = Portrait of Daniel Bernoulli, {{circa}} 1720-1725
| birth_date        = 8 February 1700
| birth_place       = [[Groningen (city)|Groningen]], [[Dutch Republic]]
| death_date        = 27 March 1782 (aged 82)
| death_place       = [[Basel]], [[Old Swiss Confederacy|Republic of the Swiss]]
| fields            = [[Mathematics]], [[physics]], [[medicine]]
| workplaces        = 
| education         = [[University of Basel]] (M.D., 1721)<br />[[Heidelberg University]]<br/ >[[University of Strasbourg]]
| thesis_title      = Dissertatio physico-medica de respiratione (Dissertation on the medical physics of respiration)
| thesis_url        = https://books.google.com/books/about/Dissertatio_inauguralis_physico_medica_d.html?id=hxVbAAAAQAAJ&redir_esc=y
| thesis_year       = 1721
| doctoral_advisor  = 
| academic_advisors = 
| doctoral_students = 
| notable_students  = 
| known_for         = [[Bernoulli's principle]]<br>[[Euler–Bernoulli beam theory]]<br>Early [[kinetic theory of gases]]<br>[[Gamma function]]<br>[[St. Petersburg paradox]]<br>[[Superposition principle]]<br>[[Thermodynamics]]
| prizes            = 
| footnotes         = 
| signature         = Daniel Bernoulli Signature.svg
}}

'''Daniel Bernoulli''' {{Post-nominals|country=GBR|FRS}} ({{IPAc-en|b|ɜr|ˈ|n|uː|l|i}} {{respell|bur|NOO|lee}}; {{IPA|de-CH|ˈdaːni̯eːl bɛrˈnʊli|lang}};<ref>Mangold, Max (1990). ''Duden — Das Aussprachewörterbuch''. 3. Auflage. Mannheim/Wien/Zürich, Dudenverlag.</ref> {{OldStyleDate|8 February|1700|29 January}} – 27 March 1782) was a [[Swiss people|Swiss]] [[mathematician]] and [[physicist]] and was one of the many prominent mathematicians in the [[Bernoulli family]] from Basel. He is particularly remembered for his applications of mathematics to mechanics, especially [[fluid mechanics]], and for his pioneering work in [[probability]] and [[statistics]].<ref>{{cite book |url=https://books.google.com/books?id=pOQy6-qnVx8C&pg=PA6 |page=6 |title=
A History of Probability and Statistics and Their Applications before 1750 |author=Anders Hald |publisher=John Wiley & Sons |year=2005|isbn=9780471725176 }}</ref> His name is commemorated in the [[Bernoulli's principle]], a particular example of the [[conservation of energy]], which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the [[carburetor]] and the aeroplane [[wing]].<ref>{{cite book |url=https://books.google.com/books?id=TQfYCwAAQBAJ&pg=SA2-PA5 |pages=2-5 – 2-6 |title=Handbook of Fluid Dynamics |author=Richard W. Johnson |publisher=CRC Press |year=2016|isbn=9781439849576 }}</ref><ref>{{cite book |url=https://books.google.com/books?id=LvsvCgAAQBAJ&pg=PA143 |page=143 |title=
Flight and Motion: The History and Science of Flying |author1=Dale Anderson |author2=Ian Graham |author3=Brian Williams |publisher=Routledge |year=2010|isbn=9781317470427 }}</ref>

==Early life==
[[File:HYDRODYNAMICA, Danielis Bernoulli.png|thumb|right|200px|Frontpage of ''[[Hydrodynamica]]'' (1738)]]
Daniel Bernoulli was born in [[Groningen (city)|Groningen]], in the Netherlands, into a [[Bernoulli family|family]] of distinguished mathematicians.<ref name=Rothbard>[[Murray Rothbard|Rothbard, Murray]]. [https://mises.org/daily/4941/Daniel-Bernoulli-and-the-Founding-of-Mathematical-Economics Daniel Bernoulli and the Founding of Mathematical Economics] {{Webarchive|url=https://web.archive.org/web/20130728151840/http://mises.org/daily/4941/Daniel-Bernoulli-and-the-Founding-of-Mathematical-Economics |date=28 July 2013 }}, ''[[Mises Institute]]'' (excerpted from ''[[An Austrian Perspective on the History of Economic Thought]]'')</ref> The Bernoulli family came originally from Antwerp, at that time in the [[Spanish Netherlands]], but emigrated to escape the Spanish persecution of the [[Protestant]]s. After a brief period in Frankfurt the family moved to Basel, in Switzerland.

Daniel was the son of [[Johann Bernoulli]] (one of the early developers of [[calculus]]) and a nephew of [[Jacob Bernoulli]] (an early researcher in [[probability theory]] and the discoverer of the mathematical constant [[E (mathematical constant)|e]]).<ref name=Rothbard/> He had two brothers, [[Nicolaus II Bernoulli|Niklaus]] and [[Johann II Bernoulli|Johann II]]. Daniel Bernoulli was described by [[W. W. Rouse Ball]] as "by far the ablest of the younger Bernoullis".<ref name="ball">{{cite book |last=Rouse Ball |first=W. W. |author-link=W. W. Rouse Ball |chapter=The Bernoullis |chapter-url=http://www.maths.tcd.ie/pub/HistMath/People/Bernoullis/RouseBall/RB_Bernoullis.html |title=A Short Account of the History of Mathematics |publisher=Dover |orig-year=1908 |year=2003 |isbn=0-486-20630-0 |edition=4th |url-access=registration |url=https://archive.org/details/shortaccountofhi0000ball }}</ref>

He is said to have had a bad relationship with his father. Both of them entered and tied for first place in a scientific contest at the [[University of Paris]]. Johann banned Daniel from his house, allegedly being unable to bear the "shame" of Daniel being considered his equal. Johann allegedly plagiarized key ideas from Daniel's book ''[[Hydrodynamica]]'' in his book ''Hydraulica'' and backdated them to before ''Hydrodynamica''.{{cn|date=April 2024}} Daniel's attempts at reconciliation with his father were unsuccessful.<ref name="mactutor">{{MacTutor Biography|id=Bernoulli_Daniel}} (1998)</ref>

When he was in school, Johann encouraged Daniel to study business citing poor financial compensation for mathematicians. Daniel initially refused but later relented and studied both business and [[medicine]] at his father's behest under the condition that his father would teach him mathematics privately.<ref name="mactutor"/> Daniel studied medicine at [[University of Basel|Basel]], [[Heidelberg University|Heidelberg]], and [[University of Strasbourg|Strasbourg]], and earned a PhD in anatomy and botany in 1721.

He was a contemporary and close friend of [[Leonhard Euler]].<ref name="andhist">{{cite book|last=Anderson, John David|title=A History of Aerodynamics and its Impact on Flying Machines|publisher=Cambridge University Press|year=1997|location=New York, NY|page=47|isbn=0-521-45435-2}}</ref><ref>{{Cite journal|last=Calinger|first=Ronald|date=1996|title=Leonhard Euler: The First St. Petersburg Years (1727–1741)|url=https://core.ac.uk/download/pdf/82068344.pdf |archive-url=https://web.archive.org/web/20190328192941/https://core.ac.uk/download/pdf/82068344.pdf |archive-date=28 March 2019 |url-status=live|journal=Historia Mathematica|volume=23|issue=2|pages=121–166|doi=10.1006/hmat.1996.0015}}</ref> He went to [[Saint Petersburg|St. Petersburg]] in 1724 as professor of mathematics, but was very unhappy there. A temporary illness<ref name="mactutor"/> together with the censorship by the [[Russian Orthodox Church]]<ref>Calinger, Ronald (1996).p.127</ref> and disagreements over his salary gave him an excuse for leaving St. Petersburg in 1733.<ref>Calinger, Ronald (1996), pp.127–128</ref> He returned to the [[University of Basel]], where he successively held the chairs of [[medicine]], [[metaphysics]], and [[natural philosophy]] until his death.<ref name="eb">[Anon.] (2001) "Daniel Bernoulli", ''[[Encyclopædia Britannica]]''</ref>

In May 1750 he was elected a [[Fellow of the Royal Society]].<ref>{{cite web|url=https://makingscience.royalsociety.org/people/na2318/daniel-bernoulli|title=Daniel Bernoulli|work=Science in the Making |publisher=Royal Society |access-date=30 April 2025 }}</ref>

==Mathematical work==
{{more citations needed|section|date=February 2018}}<!--last 3 paragraphs are not cited-->
[[File:ETH-BIB-Bernoulli, Daniel (1700-1782)-Portrait-Portr 10971.tif (cropped).jpg|thumb|Daniel Bernoulli]]
His earliest mathematical work was the ''Exercitationes'' (''Mathematical Exercises''), published in 1724 with the help of [[Christian Goldbach|Goldbach]]. Two years later he pointed out for the first time the frequent desirability of resolving a compound motion into motions of translation and motion of rotation. In 1729, he published a [[polynomial root-finding]] algorithm which became known as [[Bernoulli's method]].<ref name="chabert">{{cite book |editor1-last=Chabert |editor1-first=Jean-Luc |title=A history of algorithms : from the pebble to the microchip |date=1999 |location=Berlin; New York |publisher=Springer |isbn=978-3-540-63369-3 |pages=223–224 |url=https://archive.org/details/isbn_0116404090940/page/222/mode/2up}}</ref> His chief work is ''[[Hydrodynamica]]'', published in 1738. It resembles [[Joseph Louis Lagrange]]'s ''Mécanique Analytique'' in being arranged so that all the results are consequences of a single principle, namely, the conservation of [[vis viva]], an early version of the [[conservation of energy]]. This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler and [[Colin Maclaurin]], a prize was awarded by the [[French Academy]]: these three memoirs contain all that was done on this subject between the publication of [[Isaac Newton]]'s ''[[Philosophiae Naturalis Principia Mathematica]]'' and the investigations of [[Pierre-Simon Laplace]]. Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with [[vibrating string]]s, and the solutions given by [[Brook Taylor]] and by [[Jean le Rond d'Alembert]].<ref name="ball"/>

<gallery>
File:Hydrodynamica-2.jpg|alt=Outer spine of Bernoulli's Hydrodynamica|A 1738 copy of Bernoulli's ''Hydrodynamica''
File:Hydrodynamica-1.jpg|alt=|First page of the first section of a 1738 copy of ''Hydrodynamica''
</gallery>

==Economics and statistics==
In his 1738 book ''Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk)'',<ref>English translation in {{cite journal|journal=Econometrica|volume=22|title=Exposition of a New Theory on the Measurement of Risk|year=1954|pages=23–36|url=http://www.econ.ucsb.edu/~tedb/Courses/GraduateTheoryUCSB/Bernoulli.pdf |archive-url=https://web.archive.org/web/20080513060618/http://www.econ.ucsb.edu/~tedb/Courses/GraduateTheoryUCSB/Bernoulli.pdf |archive-date=13 May 2008 |url-status=live|jstor=1909829|doi=10.2307/1909829|last1=Bernoulli|first1=D.|issue=1 |s2cid=9165746 }}</ref> Bernoulli offered a solution to the [[St. Petersburg paradox]] as the basis of the economic theory of [[risk aversion]], [[risk premium]], and [[utility]].<ref>[[Stanford Encyclopedia of Philosophy]]: "[http://plato.stanford.edu/entries/paradox-stpetersburg/ The St. Petersburg Paradox] by R. M. Martin</ref> Bernoulli often noticed that when making decisions that involved some uncertainty, people did not always try to maximize their possible monetary gain, but rather tried to maximize "[[utility]]", an economic term encompassing their personal satisfaction and benefit. Bernoulli realized that for humans, there is a direct relationship between money gained and utility, but that it diminishes as the money gained increases. For example, to a person whose income is $10,000 per year, an additional $100 in income will provide more utility than it would to a person whose income is $50,000 per year.{{sfnp|Cooter|Ulen|2016|pp=44–45}}

One of the earliest attempts to analyze a statistical problem involving [[censoring (statistics)|censored data]] was Bernoulli's 1766 analysis of [[smallpox]] [[morbidity]] and [[Mortality rate|mortality]] data to demonstrate the efficacy of [[inoculation]].<ref>reprinted in {{cite journal|year=2004|pmid=15334536|url=http://www.semel.ucla.edu/biomedicalmodeling/pdf/Bernoulli&Blower.pdf|title=An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it|last1=Blower|first1=S|last2=Bernoulli|first2=D|volume=14|issue=5|pages=275–88|doi=10.1002/rmv.443|journal=Reviews in Medical Virology|s2cid=8169180|url-status=dead|archive-url=https://web.archive.org/web/20070927032605/http://www.semel.ucla.edu/biomedicalmodeling/pdf/Bernoulli%26Blower.pdf|archive-date=27 September 2007}}</ref>

==Physics==
In ''Hydrodynamica'' (1738) he laid the basis for the [[kinetic theory of gases]], and applied the idea to explain [[Boyle's law]].<ref name="ball"/>

He worked with Euler on [[Elasticity (physics)|elasticity]] and the development of the [[Euler–Bernoulli beam equation]].<ref>{{cite book | title=History of Strength of Materials | author-link=Stephen Timoshenko | author=Timoshenko, S. P. | orig-year=1953 | year=1983 | isbn=0-486-61187-6 | location=New York | publisher=Dover |url=https://books.google.com/books?id=tkScQmyhsb8C}}</ref> [[Bernoulli's principle]] is of critical use in [[hydrodynamics]].

According to [[Léon Brillouin]], the [[Superposition principle|principle of superposition]] was first stated by Daniel Bernoulli in 1753: "The general motion of a vibrating system is given by a superposition of its proper vibrations."<ref>[[Léon Brillouin|Brillouin, L.]] (1946). ''Wave propagation in Periodic Structures: Electric Filters and Crystal Lattices'', McGraw–Hill, New York, p. 2.</ref>

==Works==
[[File:Bernoulli, Daniel – Pieces qui ont remporté le Prix double de l'Academie royale des sciences en 1737, 1737 – BEIC 1285085.jpg|thumb|''Pieces qui ont remporté le Prix double de l'Academie royale des sciences en 1737'']]

* {{Cite book|title=Pieces qui ont remporté le Prix double de l'Academie royale des sciences en 1737|volume=|publisher=Imprimerie Royale|location=Paris|year=1737|language=fr|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=1285085}}

==Legacy==
In 2002, Bernoulli was inducted into the [[International Air & Space Hall of Fame]] at the [[San Diego Air & Space Museum]].<ref>Sprekelmeyer, Linda, editor. ''These We Honor: The International Aerospace Hall of Fame''. Donning Co. Publishers, 2006. {{ISBN|978-1-57864-397-4}}.</ref>

==See also==
* [[Hydrodynamica]]
* [[Mathematical modelling of infectious diseases]]
* [[List of second-generation Mathematicians]]

==References==
===Footnotes===
{{reflist|25em}}

===Works cited===
{{refbegin|35em}}
*(Original entry based on the [[public domain]] ''[[Rouse History of Mathematics]]'')
*{{Cite EB1911 |wstitle=Bernoulli |display= Bernoulli § V. Daniel Bernoulli |volume=3 |page=805}}
*{{cite book | author=Cardwell, D.S.L. | title=From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age | location=Heinemann | publisher=London | year=1971 | isbn=0-435-54150-1 }}
*{{cite book | first1 = Robert | last1 = Cooter | author-link = Robert Cooter | first2 = Thomas | last2 = Ulen | author-link2 = Thomas Ulen | title = Law & Economics | edition = 6th | year = 2016 | location = Berkeley | publisher = Addison-Wesley | series = Berkeley Law Books | isbn = 978-0-13-254065-0 }}
*{{cite book |first=G.K. |last=Mikhailov |chapter=Hydrodynamica |chapter-url=https://books.google.com/books?id=UdGBy8iLpocC&pg=PA131 |editor1-first=Ivor |editor1-last=Grattan-Guinness |editor1-link=Ivor Grattan-Guinness |title=Landmark Writings in Western Mathematics 1640–1940 |url=https://books.google.com/books?id=UdGBy8iLpocC |year=2005 |publisher=Elsevier |isbn=978-0-08-045744-4 |pages=131–42 }}
*{{cite journal |last1=Pacey |first1=A. J. |last2=Fisher |first2=S. J. |title=Daniel Bernoulli and the ''vis viva'' of compressed air |journal=British Journal for the History of Science |volume=3 |issue=4 |pages=388–392 |date=December 1967 |doi=10.1017/S0007087400002934 |s2cid=145513749 |url=http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2904748&fulltextType=XX&fileId=S0007087400002934 |url-access=subscription }}
* {{cite encyclopedia | last =Straub | first =Hans | title =Bernoulli, Daniel | encyclopedia = [[Dictionary of Scientific Biography]] | volume = 2 | pages =36–46  | publisher = Charles Scribner's Sons | location = New York | year = 1970 | isbn = 0-684-10114-9}}
{{refend}}

==External links==
{{Commons category}}
{{Wikiquote}}
* {{cite web | url=http://www.mathematik.ch/mathematiker/daniel_bernoulli.php | title=Bernoulli Daniel | work=Mathematik.ch | access-date=7 September 2007 | archive-date=23 October 2015 | archive-url=https://web.archive.org/web/20151023160731/http://www.mathematik.ch/mathematiker/daniel_bernoulli.php | url-status=dead }}
* [[Murray Rothbard|Rothbard, Murray]]. [https://mises.org/daily/4941/Daniel-Bernoulli-and-the-Founding-of-Mathematical-Economics Daniel Bernoulli and the Founding of Mathematical Economics] {{Webarchive|url=https://web.archive.org/web/20130728151840/http://mises.org/daily/4941/Daniel-Bernoulli-and-the-Founding-of-Mathematical-Economics |date=28 July 2013 }}, ''[[Mises Institute]]'' (excerpted from ''[[An Austrian Perspective on the History of Economic Thought]]'')
* {{ScienceWorldBiography | urlname=BernoulliDaniel | title=Bernoulli, Daniel (1700–1782)}}
* {{Gutenberg author | id=41345| name=Daniel Bernoulli}}
* {{Internet Archive author |sname=Daniel Bernoulli}}

{{Bernoulli family}}
{{Authority control}}

{{DEFAULTSORT:Bernoulli, Daniel}}
[[Category:1700 births]]
[[Category:1782 deaths]]
[[Category:Bernoulli family|Daniel]]
[[Category:Heidelberg University alumni]]
[[Category:18th-century Swiss physicists]]
[[Category:18th-century writers in Latin]]
[[Category:18th-century male writers]]
[[Category:18th-century Swiss mathematicians]]
[[Category:Swiss Calvinist and Reformed Christians]]
[[Category:Mathematical analysts]]
[[Category:Fluid dynamicists]]
[[Category:Probability theorists]]
[[Category:Fellows of the Royal Society]]
[[Category:Full members of the Saint Petersburg Academy of Sciences]]
[[Category:Swiss expatriates in the Dutch Republic]]
[[Category:Scientists from Groningen (city)]]
[[Category:Swiss expatriates in Germany]]
[[Category:People associated with the University of Basel]]