View source for Blaise Pascal

{{Short description|French polymath (1623–1662)}}
{{For|the Canadian singer-songwriter|Blaise Pascal (musician)}}
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{{Use dmy dates|date=May 2020}}
{{Infobox philosopher
| image              = Blaise Pascal Versailles.JPG
| caption            = Pascal {{circa|1691}}
| birth_date         = {{birth date|df=yes|1623|6|19}}
| birth_place        = [[Clermont-Ferrand]], France
| death_date         = {{death date and age|df=yes|1662|8|19|1623|6|19}}
| death_place        = Paris, France
| father             = [[Étienne Pascal]]
| relatives          = [[Marguerite Périer]] (niece) <br>[[Jacqueline Pascal]] (sister) <br /> [[Gilberte Périer]] (sister)
| region = [[Western philosophy]]
| era = [[17th-century philosophy]]
| school_tradition = {{ubl|[[Cartesianism]]|[[Jansenism]]|[[Fideism]]}}
| main_interests = {{hlist |Theology |Mathematics |Philosophy |[[Physics]]}}
| notable_ideas = {{vunblist |[[Probability theory]] | [[Negative binomial distribution|Pascal distribution]]<br>[[Pascal's wager]] |[[Pascal's triangle]] |[[Pascal's law]] |[[Pascal's rule]]|[[Pascal's theorem]] |[[Pascal's calculator]]}}
| signature = Blaise Pascal signature.svg
}}
{{Catholic philosophy}}

'''Blaise Pascal'''{{efn|name=pronounciation|{{IPAc-en|p|æ|ˈ|s|k|æ|l}} {{Respell|pass|KAL}}, {{IPAc-en|alsoUK|-|ˈ|s|k|ɑː|l|,_|'|p|ae|s|k|@l|,_|-|s|k|æ|l}} {{Respell|-|KAHL|,_|PASS|kəl|,_-|kal}}, {{IPAc-en|US|p|ɑː|ˈ|s|k|ɑː|l}} {{Respell|pahs|KAHL}};<ref>{{cite book|last=Wells|first=John|author-link=John C. Wells|title=Longman Pronunciation Dictionary|publisher=Pearson Longman|edition=3rd|date=3 April 2008|isbn=978-1-4058-8118-0}}</ref><ref>[http://dictionary.reference.com/browse/pascal "Pascal"] {{Webarchive|url=https://web.archive.org/web/20150106120015/http://dictionary.reference.com/browse/Pascal |date=6 January 2015 }}. ''[[Random House Webster's Unabridged Dictionary]]''.</ref><ref>{{Cite encyclopedia |url=http://www.lexico.com/definition/Pascal,+Blaise |archive-url=https://web.archive.org/web/20211205064720/https://www.lexico.com/definition/pascal,_blaise |url-status=dead |archive-date=2021-12-05 |title=Pascal, Blaise |dictionary=[[Lexico]] UK English Dictionary |publisher=[[Oxford University Press]]}}</ref><ref>{{cite web|url=https://www.collinsdictionary.com/dictionary/english/pascal|title=Pascal|work=[[Collins English Dictionary]]|publisher=[[HarperCollins]]|access-date=14 August 2019|archive-date=14 August 2019|archive-url=https://web.archive.org/web/20190814214044/https://www.collinsdictionary.com/dictionary/english/pascal|url-status=live}}</ref><ref>{{Cite Merriam-Webster|Pascal|access-date=14 August 2019}}</ref> {{IPA|fr|blɛz paskal|lang}}}} (19{{nbsp}}June 1623{{snd}}19{{nbsp}}August 1662) was a French mathematician, physicist, inventor, philosopher, and [[Catholic Church|Catholic]] writer.

Pascal was a [[child prodigy]] who was educated by his father [[Étienne Pascal]], a tax collector in [[Rouen]]. His earliest mathematical work was on [[projective geometry]]; he wrote a significant treatise on the subject of [[conic section]]s at the age of 16. He later corresponded with [[Pierre de Fermat]] on [[probability theory]], strongly influencing the development of modern economics and [[social sciences|social science]].{{citation needed|date=September 2025}} In 1642, he started some pioneering work on calculating machines (called [[Pascal's calculator]]s and later Pascalines), establishing him as one of the first two inventors of the [[mechanical calculator]].<ref>See [http://metastudies.net/pmwiki/pmwiki.php?n=Site.SchicardvsPascal Schickard versus Pascal: An Empty Debate?] {{Webarchive|url=https://web.archive.org/web/20140408215848/http://metastudies.net/pmwiki/pmwiki.php?n=Site.SchicardvsPascal |date=8 April 2014 }} and {{cite book|last=Marguin|first=Jean|title=Histoire des instruments et machines à calculer, trois siècles de mécanique pensante 1642–1942|publisher=Hermann|year=1994|isbn=978-2-7056-6166-3|page=48|language=fr}}</ref><ref>{{cite book|last=d'Ocagne|first=Maurice|url=https://cnum.cnam.fr/CGI/fpage.cgi?8KU54-2.5/248/150/369/363/369|title=Le calcul simplifié|publisher=Gauthier-Villars et fils|year=1893|page=245|language=fr|access-date=14 May 2010|archive-date=9 August 2018|archive-url=https://web.archive.org/web/20180809111700/http://cnum.cnam.fr/CGI/fpage.cgi?8KU54-2.5%2F248%2F150%2F369%2F363%2F369|url-status=live}}</ref>

Like his contemporary [[René Descartes]], Pascal was also a pioneer in the natural and applied sciences. Pascal wrote in defence of the [[scientific method]] and produced several controversial results.{{clarify|date=September 2025}} He made important contributions to the study of [[fluid]]s, and clarified the concepts of [[pressure]] and [[vacuum]] by generalising the work of [[Evangelista Torricelli]]. The [[International System of Units|SI]] [[Unit of measurement|unit]] for pressure is named for [[Pascal (unit)|Pascal]]. Following Torricelli and [[Galileo Galilei]], in 1647, he rebutted the likes of [[Aristotle]] and Descartes who insisted that [[Horror vacui (physics)|nature abhors a vacuum]].

He is also credited as the inventor of modern [[public transport]]ation, having established the [[carrosses à cinq sols]], the first modern public transport service, shortly before his death in 1662.<ref>{{Cite web |last=Jarrett |date=2024-12-31 |title=One of the Greatest Inventions in the History of Human Transport |url=https://humantransit.org/2024/12/one-of-the-greatest-inventions-in-the-history-of-human-transport.html#commentsC |access-date=2025-01-02 |website=Human Transit |language=en-US}}</ref>

In 1646, he and his sister Jacqueline identified with the religious movement within [[Catholicism]] known by its detractors as [[Jansenism]].<ref>{{cite encyclopedia |url=https://www.newadvent.org/cathen/11511a.htm |title=Blaise Pascal |access-date=23 February 2009 |encyclopedia=Catholic Encyclopedia |archive-date=10 March 2009 |archive-url=https://web.archive.org/web/20090310204300/https://www.newadvent.org/cathen/11511a.htm |url-status=live }}</ref> Following a religious experience in late 1654, he began writing influential works on philosophy and theology. His two most famous works date from this period: the {{lang|fr|[[Lettres provinciales]]}} and the ''[[Pensées]]'', the former set in the conflict between Jansenists and [[Jesuits]]. The latter contains [[Pascal's wager]], known in the original as the ''Discourse on the Machine'',<ref>{{Cite web |last=Grumball |first=Kevin Shaun |title=Thesis submitted to the University of Nottingham for the degree of Doctor of Philosophy |url=https://eprints.nottingham.ac.uk/14569/1/594871.pdf |archive-url=https://web.archive.org/web/20200605221151/http://eprints.nottingham.ac.uk/14569/1/594871.pdf |archive-date=2020-06-05 |url-status=live |access-date=20 October 2022 |website=University of Nottingham}}</ref><ref>{{Cite web |title=Internet History Sourcebooks |url=https://sourcebooks.fordham.edu/mod/1660pascal-pensees.asp |access-date=2022-10-20 |website=sourcebooks.fordham.edu |archive-date=19 October 2022 |archive-url=https://web.archive.org/web/20221019123402/https://sourcebooks.fordham.edu/mod/1660pascal-pensees.asp |url-status=live }}</ref> a [[Fideism|fideistic]] probabilistic argument for why one should believe in God. In that year, he also wrote an important treatise on the arithmetical triangle. Between 1658 and 1659, he wrote on the [[cycloid]] and its use in calculating the volume of solids. Following several years of illness, Pascal died in Paris at the age of 39.

==Early life and education==
[[File:Maison de Blaise Pascal (Clermont).png|thumb|left|165px|Pascal's birthplace]]

Pascal was born in [[Clermont-Ferrand]], which is in France's [[Auvergne (region)|Auvergne region]], by the [[Massif Central]]. He lost his mother, Antoinette Begon, at the age of three.{{sfn|Devlin|p=20}} His father, [[Étienne Pascal]], also an amateur mathematician, was a local judge and member of the "[[Nobles of the Robe|Noblesse de Robe]]". Pascal had two sisters, the younger [[Jacqueline Pascal|Jacqueline]] and the elder [[Gilberte Périer|Gilberte]].

=== Move to Paris ===
In 1631, five years after the death of his wife,<ref name="MCS">{{cite web |last1=O'Connor |first1=J.J. |last2=Robertson |first2=E.F. |author-link1=John J. O'Connor (mathematician) |author-link2=Edmund F. Robertson |title=Étienne Pascal |url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Pascal_Etienne.html |date=August 2006 |publisher=[[University of St Andrews|University of St. Andrews, Scotland]] |access-date=5 February 2010 |archive-date=19 April 2010 |archive-url=https://web.archive.org/web/20100419181846/http://www-history.mcs.st-andrews.ac.uk/Biographies/Pascal_Etienne.html |url-status=live }}</ref> Étienne Pascal moved with his children to Paris. The newly arrived family soon hired Louise Delfault, a maid who eventually became a key member of the family.{{citation needed|date=September 2025}} Étienne, who never remarried, decided that he alone would educate his children.
[[File:Leroux--scene de la jeunesse de blaise pascal--Cherbourg.jpg|thumb|200px|A scene from Pascal's youth]]
The young Pascal showed an extraordinary intellectual ability, with an amazing aptitude for mathematics and science.<ref>{{Cite web |date=2024-04-08 |title=Blaise Pascal {{!}} Biography, Facts, & Inventions {{!}} Britannica |url=https://www.britannica.com/biography/Blaise-Pascal |access-date=2024-04-19 |website=www.britannica.com |language=en}}</ref> Etienne had tried to keep his son from learning mathematics; but by the age of 12, Pascal had rediscovered, on his own, using charcoal on a tile floor, [[Euclid]]’s first thirty-two geometric propositions, and was thus given a copy of Euclid's [[Euclid's Elements|''Elements'']].<ref>Cole, J. R. (1995). Pascal : the man and his two loves. United Kingdom: NYU Press. p. 40</ref>

==== ''Essay on Conics'' ====
Particularly of interest to Pascal was a work of [[Gérard Desargues|Desargues]] on [[conic section]]s. Following Desargues' thinking, the 16-year-old Pascal produced, as a means of proof, a short treatise on what was called the ''Mystic [[Hexagram]]'', ''Essai pour les coniques'' (''Essay on Conics'') and sent it — his first serious work of mathematics — to [[Marin Mersenne|Père Mersenne]] in Paris; it is known still today as [[Pascal's theorem]]. It states that if a [[hexagon]] is inscribed in a circle (or conic), then the three intersection points of opposite sides lie on a line (called the Pascal line).

Pascal's work was so precocious that [[René Descartes]] was convinced that Pascal's father had written it. When assured by Mersenne that it was, indeed, the product of the son and not the father, Descartes replied: "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," adding, "but other matters related to this subject can be proposed that would scarcely occur to a 16-year-old child."<ref>''[[The Story of Civilization]]: Volume 8, "The Age of Louis XIV"'' by [[Will Durant|Will & Ariel Durant]]; chapter II, subsection 4.1 p. 56</ref>

===Leaving Paris===
In France at that time, offices and positions could be—and were—bought and sold. In 1631, Étienne sold his position as second president of the ''[[Cour des Aides]]'' for 65,665 [[Livre tournois|livres]].<ref>Connor, James A., ''Pascal's wager: the man who played dice with God'' (HarperCollins, NY, 2006) {{isbn|0-06-076691-3}} p. 42</ref> The money was invested in a [[government bond]] which provided, if not a lavish, then certainly a comfortable income which allowed the Pascal family to move to, and enjoy, Paris, but in 1638 [[Cardinal Richelieu]], desperate for money to carry on the [[Thirty Years' War]], defaulted on the government's bonds. Suddenly, Étienne Pascal's worth had dropped from nearly 66,000 livres to less than 7,300.{{citation needed|date=May 2023}}

Like so many others, Étienne was eventually forced to flee Paris because of his opposition to the fiscal policies of Richelieu, leaving his three children in the care of his neighbour Madame Sainctot, a great beauty with an infamous past who kept one of the most glittering and intellectual salons in all of France. It was only when Jacqueline performed well in a children's play with Richelieu in attendance that Étienne was pardoned. In time, Étienne was back in good graces with the Cardinal and in 1639 had been appointed the king's commissioner of taxes in the city of [[Rouen]]—a city whose tax records, thanks to uprisings, were in utter chaos.

===Pascaline===
[[File:Pascaline-CnAM 823-1-IMG 1506-black.jpg|thumb|An early [[Pascaline]] on display at the [[Musée des Arts et Métiers]], Paris|alt=]]
In 1642, in an effort to ease his father's endless, exhausting calculations and recalculations of taxes owed and paid (into which work the young Pascal had been recruited), Pascal, not yet 19, constructed a mechanical calculator capable of addition and subtraction, called ''[[Pascal's calculator]]'' or the ''Pascaline''. Of the eight Pascalines known to have survived, four are held by the [[Musée des Arts et Métiers]] in Paris and one more by the [[Zwinger museum]] in [[Dresden]], Germany, which exhibit two of his original mechanical calculators.<ref>A complete list of known Pascalines and also a review of contemporary replicas can be found at [http://metastudies.net/pmwiki/pmwiki.php?n=Site.SurvivingPascalines Surviving Pascalines] {{Webarchive|url=https://web.archive.org/web/20211105180308/http://metastudies.net/pmwiki/pmwiki.php?n=Site.SurvivingPascalines |date=5 November 2021 }} and [http://metastudies.net/pmwiki/pmwiki.php?n=Site.ReplicaPascalines Replica Pascalines] {{Webarchive|url=https://web.archive.org/web/20211105181911/http://metastudies.net/pmwiki/pmwiki.php?n=Site.ReplicaPascalines |date=5 November 2021 }} at http://things-that-count.net {{Webarchive|url=https://web.archive.org/web/20181215022135/http://things-that-count.net/ |date=15 December 2018 }}</ref>

Although these machines are pioneering forerunners to a further 400 years of development of mechanical methods of calculation, and in a sense to the later field of [[computer engineering]], the calculator failed to be a great commercial success. Partly because it was still quite cumbersome to use in practice, but probably primarily because it was extraordinarily expensive, the Pascaline became little more than a toy, and a [[status symbol]], for the very rich both in France and elsewhere in Europe. He also presented the first mechanical calculator to [[Christina, Queen of Sweden]] in 1632.<ref>{{cite journal | last1=Zirpolo | first1=Lilian H. | title=Christina of Sweden's Patronage of Bernini: The Mirror of Truth Revealed by Time | journal=Woman's Art Journal | date=2005 | volume=26 | issue=1 | pages=38–43 | doi=10.2307/3566533 | jstor=3566533 | url=https://www.jstor.org/stable/3566533?searchText=christina%20sweden&searchUri=%2Faction%2FdoBasicSearch%3FQuery%3Dchristina%2Bsweden%26so%3Drel&ab_segments=0%2Fspellcheck_basic_search%2Fcontrol&refreqid=fastly-default%3A31c0955fd8d8615cd04a976542bfc78c | url-access=subscription }}</ref> Pascal continued to make improvements to his design through the next decade, and he refers to some 50 machines that were built to his design.<ref>[http://fr.wikisource.org/wiki/La_Machine_d%E2%80%99arithm%C3%A9tique (fr) La Machine d'arithmétique, Blaise Pascal] {{Webarchive|url=https://web.archive.org/web/20110515015452/http://fr.wikisource.org/wiki/La_Machine_d%E2%80%99arithm%C3%A9tique |date=15 May 2011 }}, Wikisource</ref> He built 20 finished machines over the following 10 years.<ref>{{cite book|last=Mourlevat|first=Guy|title=Les machines arithmétiques de Blaise Pascal|publisher=La Française d'Édition et d'Imprimerie|year=1988|location=Clermont-Ferrand|page=12|language=fr}}</ref>

==Mathematics==
===Probability===
In 1654, prompted by his friend the [[Chevalier de Méré]], Pascal corresponded with [[Pierre de Fermat]] on the subject of gambling problems, and from that collaboration was born the mathematical theory of [[probability]].{{sfn|Devlin|p=24}} The specific problem was that of two players who want to finish a game early and, given the current circumstances of the game, want to [[division of the stakes|divide the stakes fairly]], based on the chance each has of winning the game from that point. The notion of [[expected value]] evolved from this discussion. John Ross writes, "Probability theory and the discoveries following it changed the way we regard uncertainty, risk, decision-making, and an individual's and society's ability to influence the course of future events."<ref>{{cite journal|last1=Ross|first1=John F.|year=2004|title=Pascal's legacy|journal=EMBO Reports|volume=5|issue=Suppl 1|pages=S7–S10|doi=10.1038/sj.embor.7400229|pmc=1299210|pmid=15459727}}</ref> Pascal, in the ''[[Pensées]]'', used a probabilistic argument, [[Pascal's wager]], to justify belief in God and a virtuous life. However, Pascal and Fermat, though doing important early work in probability theory, did not develop the field very far. [[Christiaan Huygens]], learning of the subject from the correspondence of Pascal and Fermat, wrote the first book on the subject. Later figures who continued the development of the theory include [[Abraham de Moivre]] and [[Pierre-Simon Laplace]]. The work done by Fermat and Pascal on the calculus of probabilities laid important groundwork for [[Gottfried Wilhelm Leibniz|Leibniz]]'s formulation of the [[calculus]].<ref>{{cite web|title=The Mathematical Leibniz|url=http://www.math.rutgers.edu/courses/436/Honors02/leibniz.html|access-date=16 August 2009|publisher=Math.rutgers.edu|archive-date=3 February 2017|archive-url=https://web.archive.org/web/20170203084344/http://www.math.rutgers.edu/courses/436/Honors02/leibniz.html|url-status=live}}</ref>

===''Treatise on the Arithmetical Triangle''===
{{Main|Pascal's triangle}}

[[File:PascalTriangleAnimated2.gif|thumb|Pascal's triangle. Each number is the sum of the two directly above it. The triangle demonstrates many mathematical properties in addition to showing binomial coefficients.]]
Pascal's ''Traité du triangle arithmétique'', written in 1654 but published posthumously in 1665, described a convenient tabular presentation for [[binomial coefficient]]s which he called the arithmetical triangle, but is now called [[Pascal's triangle]].<ref name=":1">{{Cite book|last=Katz|first=Victor|author-link=Victor J. Katz|title=A History of Mathematics: An Introduction|publisher=Addison-Wesley|year=2009|isbn=978-0-321-38700-4|pages=491|chapter=14.3: Elementary Probability}}</ref><ref>{{cite book| url = http://www.bookrags.com/research/pascals-triangle-wom/| title = Pascal's triangle {{!}} World of Mathematics Summary| access-date = 4 December 2020| archive-date = 4 March 2016| archive-url = https://web.archive.org/web/20160304065153/http://www.bookrags.com/research/pascals-triangle-wom/| url-status = live}}</ref> The triangle can also be represented:
{| class="wikitable"
|-
! style="width:20px;" |
! style="width:20px;" |0
! style="width:20px;" |1
! style="width:20px;" |2
! style="width:20px;" |3
! style="width:20px;" |4
! style="width:20px;" |5
! style="width:20px;" |6
|-
|'''0'''|| 1|| 1|| 1|| 1||1||1||1
|-
|'''1'''|| 1 ||2 || 3 || 4 || 5 || 6 ||
|-
|'''2'''||1|| 3 || 6 || 10 || 15 ||  ||
|-
|'''3'''|| 1||4 || 10 || 20 ||  ||  ||
|-
|'''4'''|| 1||5 || 15 ||  ||  ||  ||
|-
|'''5'''|| 1||6 ||  ||  ||  ||  ||
|-
|'''6'''|| 1 ||  ||  ||  ||  ||  ||
|}

He defined the numbers in the triangle by [[recursion]]: Call the number in the (''m''&nbsp;+&nbsp;1)th row and (''n''&nbsp;+&nbsp;1)th column ''t''<sub>''mn''</sub>. Then ''t''<sub>''mn''</sub>&nbsp;=&nbsp;''t''<sub>''m''−1,''n''</sub>&nbsp;+&nbsp;''t''<sub>''m'',''n''−1</sub>, for ''m''&nbsp;=&nbsp;0,&nbsp;1,&nbsp;2,&nbsp;... and ''n''&nbsp;=&nbsp;0,&nbsp;1,&nbsp;2,&nbsp;... The boundary conditions are ''t''<sub>''m'',−1</sub>&nbsp;=&nbsp;0, ''t''<sub>−1,''n''</sub>&nbsp;=&nbsp;0 for ''m''&nbsp;=&nbsp;1,&nbsp;2,&nbsp;3,&nbsp;... and ''n''&nbsp;=&nbsp;1,&nbsp;2,&nbsp;3,&nbsp;... The generator ''t''<sub>00</sub>&nbsp;=&nbsp;1. Pascal concluded with the proof,
:<math>t_{mn} = \frac{(m+n)(m+n-1)\cdots(m+1)}{n(n-1)\cdots 1}.</math>

In the same treatise, Pascal gave an explicit statement of the principle of [[mathematical induction]].<ref name=":1" /> In 1654, he proved [[Faulhaber's formula|''Pascal's identity'']] relating the sums of the ''p''-th powers of the first ''n'' positive integers for ''p'' = 0, 1, 2, ..., ''k''.<ref>{{cite journal|author=Kieren MacMillan, Jonathan Sondow|title=Proofs of power sum and binomial coefficient congruences via Pascal's identity |journal=[[American Mathematical Monthly]] |year=2011 |volume=118 |issue=6 |pages=549–551 |doi=10.4169/amer.math.monthly.118.06.549|arxiv=1011.0076|s2cid=207521003 }}</ref>

That same year, Pascal had a religious experience, and he mostly gave up work in mathematics.
{{Clear}}

===Cycloid===
[[File:Pascal Pajou Louvre RF2981.jpg|thumb|upright|Pascal studying the [[cycloid]], by [[Augustin Pajou]], 1785, [[Louvre]]|alt=]]

In 1658, Pascal, while suffering from a toothache, began considering several problems concerning the cycloid. His toothache disappeared, and he took this as a heavenly sign to proceed with his research. Eight days later he had completed his essay<ref name="Ball_1960">{{cite book |last=Ball |first= W. W. Rouse |date=2010-09-16 |title=A Short Account of the History of Mathematics |url=https://www.gutenberg.org/files/31246/31246-pdf.pdf |location=New York, NY, USA |publisher=Dover Publications, Inc |page=234 |isbn=978-0486206301}}</ref> and, to publicize the results, proposed a contest.<ref name="Ferroli_1935">{{cite journal |last1=Ferroli |first1=D. |date=April 1935 |title=A Note on Blaise Pascal (1623-1662). A Forerunner of Leibnitz and Newton in the Discovery of the Calculus |url=https://www.jstor.org/stable/24221628 |journal=Current Science |volume=3 |issue=10 |pages=459–461 |jstor=24221628 |access-date=2024-03-02}}</ref>

Pascal proposed three questions relating to the [[Center of mass| centre of gravity]], area and volume of the cycloid, with the winner or winners to receive prizes of 20 and 40 Spanish [[doubloon]]s. Pascal, [[Gilles de Roberval]] and [[Pierre de Carcavi]] were the judges, and neither of the two submissions (by [[John Wallis]] and [[Antoine de Lalouvère]]) were judged to be adequate.<ref>{{citation
| last=Conner
| first=James A.
| title=Pascal's Wager: The Man Who Played Dice with God
| pages=[https://archive.org/details/pascalswagermanw00conn/page/224 224]
| isbn=9780060766917
| edition=1st
| year=2006
| publisher=HarperCollins
| url-access=registration
| url=https://archive.org/details/pascalswagermanw00conn/page/224
}}</ref> While the contest was ongoing, [[Christopher Wren]] sent Pascal a proposal for a proof of the [[arc length|rectification]] of the cycloid; Roberval claimed promptly that he had known of the proof for years. Wallis published Wren's proof (crediting Wren) in Wallis's ''Tractus Duo'', giving Wren priority for the first published proof.
{{Clear}}

==Physics==
[[File:Pascal's Barrel.png|thumb|An illustration of the (apocryphal) [[Pascal's barrel]] experiment]]

Pascal contributed to several fields in physics, most notably the fields of fluid mechanics and pressure. In honour of his scientific contributions, the name ''Pascal'' has been given to the [[pascal (unit)|SI unit of pressure]] and [[Pascal's law]] (an important principle of hydrostatics). He introduced a primitive form of [[roulette]] and the roulette wheel in his search for a [[perpetual motion]] machine.<ref>
[[Massachusetts Institute of Technology|MIT]], [https://web.archive.org/web/20030827232844/http://web.mit.edu/invent/iow/pascal.html "Inventor of the Week Archive: Pascal : Mechanical Calculator"], May 2003. "Pascal worked on many versions of the devices, leading to his attempt to create a perpetual motion machine. He has been credited with introducing the roulette machine, which was a by-product of these experiments."</ref> [[Blaise Pascal Chair]]s are given to outstanding international scientists to conduct their research in the [[Île-de-France (region)|Ile de France]] region.<ref>{{cite web|title=Chaires Blaise Pascal|url=http://www.chaires-blaise-pascal.org/uk/index.html|url-status=dead|archive-url=https://web.archive.org/web/20090613064029/http://www.chaires-blaise-pascal.org/uk/index.html|archive-date=13 June 2009|access-date=16 August 2009|publisher=Chaires Blaise Pascal}}</ref>

===Fluid dynamics===
His work in the fields of [[hydrodynamics]] and [[hydrostatics]] centred on the principles of [[hydraulic fluid]]s. His inventions include the [[hydraulic press]] (using hydraulic pressure to multiply force) and the [[syringe]]. He proved that hydrostatic pressure depends not on the weight of the fluid but on the elevation difference. He allegedly demonstrated this principle by attaching a thin tube to a barrel full of water and filling the tube with water up to the level of the third floor of a building. This caused the barrel to leak, in what became known as [[Pascal's barrel]] experiment.

===Vacuum===
By 1647, Pascal had learned of [[Evangelista Torricelli]]'s experimentation with [[barometer]]s. Having replicated an experiment that involved placing a tube filled with mercury upside down in a bowl of mercury, Pascal questioned what force kept some mercury in the tube and what filled the space above the mercury in the tube. At the time, most scientists, including [[Descartes]], believed in a plenum, i.e. some invisible matter filled all of space, rather than a [[vacuum]] ("[[Nature abhors a vacuum]])." This was based on the Aristotelian notion that everything in motion was a substance, moved by another substance.<ref>Aristotle, ''Physics'', VII, 1.</ref> Furthermore, light passed through the glass tube, suggesting a substance such as [[Luminiferous aether|aether]] rather than a vacuum filled the space.

Following more experimentation in this vein, in 1647 Pascal produced ''Experiences nouvelles touchant le vide'' ("New experiments with the vacuum"), which detailed basic rules describing to what degree various liquids could be supported by [[air pressure]]. It also provided reasons why it was indeed a vacuum above the column of liquid in a barometer tube. This work was followed by ''Récit de la grande expérience de l'équilibre des liqueurs'' ("Account of the great experiment on equilibrium in liquids") published in 1648.

==== First atmospheric pressure vs. altitude experiment ====
[[File:Puy de Dôme near Clermont-Ferrand in Auvergne in France.jpg|thumb|Puy de Dôme]]
[[File:Florin Périer measuring the mercury level in a Torricelli barometer near the top of the Puy de Dôme.jpg|alt=Florin Périer measuring the mercury level in a Torricelli barometer near the top of the Puy de Dôme|thumb|Florin Périer on the Puy de Dôme]]

The [[Torricellian vacuum]] found that air pressure is equal to the weight of 30 inches of mercury. If air has a finite weight, Earth's atmosphere must have a maximum height. Pascal reasoned that if true, air pressure on a high mountain must be less than at a lower altitude. He lived near the [[Puy de Dôme]] mountain, {{convert|4790|ft}} tall, but his health was poor, so he could not climb it.<ref name="ley196606">{{Cite magazine
 |last=Ley
 |first=Willy
 |date=June 1966
 |title=The Re-Designed Solar System
 |department=For Your Information
 |url=https://archive.org/stream/Galaxy_v24n05_1966-06#page/n93/mode/2up
 |magazine=Galaxy Science Fiction
 |pages=94–106
}}</ref> On 19 September 1648, after many months of Pascal's friendly but insistent prodding, [[Florin Périer]], husband of Pascal's elder sister Gilberte, was finally able to carry out the fact-finding mission vital to Pascal's theory. The account, written by Périer, reads:

{{blockquote|The weather was chancy last Saturday...[but] around five o'clock that morning...the Puy-de-Dôme was visible...so I decided to give it a try. Several important people of the city of [[Clermont-Ferrand|Clermont]] had asked me to let them know when I would make the ascent...I was delighted to have them with me in this great work...

...at eight o'clock we met in the gardens of the Minim Fathers, which has the lowest elevation in town....First I poured 16 pounds of [[Mercury (element)|quicksilver]]...into a vessel...then took several glass tubes...each four feet long and [[Hermetic seal|hermetically sealed]] at one end and opened at the other...then placed them in the vessel [of quicksilver]...I found the quick silver stood at 26" and {{frac|3|1|2}} lines above the quicksilver in the vessel...I repeated the experiment two more times while standing in the same spot...[they] produced the same result each time...

I attached one of the tubes to the vessel and marked the height of the quicksilver and...asked Father Chastin, one of the Minim Brothers...to watch if any changes should occur through the day...Taking the other tube and a portion of the quick silver...I walked to the top of Puy-de-Dôme, about 500 [[fathoms]] higher than the monastery, where upon experiment...found that the quicksilver reached a height of only 23" and 2 lines...I repeated the experiment five times with care...each at different points on the summit...found the same height of quicksilver...in each case...<ref>Périer to Pascal, 22 September 1648, Pascal, Blaise. ''Oeuvres complètes''. (Paris: Seuil, 1960), 2:682.</ref>}}

Pascal replicated the experiment in Paris by carrying a barometer up to the top of the bell tower at the church of [[Saint-Jacques Tower|Saint-Jacques-de-la-Boucherie]], a height of about 50 metres. The mercury dropped two lines. He found with both experiments that an ascent of 7 fathoms lowers the mercury by half a line.{{efn|1=1 ligne = 2.256 mm, and 1 toise = 1.949 m. Mercury density is 13.534 g/cm3. So by Pascal's numbers, the density of air is about 1.1 kg/m<sup>3</sup>.}} Note: Pascal used [[Units of measurement in France before the French Revolution#Length|''pouce'' and ''ligne'']] for "inch" and "line", and ''[[toise]]'' for "fathom".<ref>{{Cite journal |last=Rougier |first=Louis |date=2010-10-01 |title=– Chapitre XI – La Grande expérience de l'équilibre des liqueurs |journal=Philosophia Scientiæ. Travaux d'histoire et de philosophie des sciences |volume=14-2 |language=fr |issue=14–2 |pages=196–206 |doi=10.4000/philosophiascientiae.189 |issn=1281-2463 |doi-access=free }}</ref>

In a reply to [[Étienne Noël]], who believed in the plenum, Pascal wrote, echoing contemporary notions of science and [[falsifiability]]: "In order to show that a hypothesis is evident, it does not suffice that all the phenomena follow from it; instead, if it leads to something contrary to a single one of the phenomena, that suffices to establish its falsity."<ref>''Pour faire qu'une hypothèse soit évidente, il ne suffit pas que tous les phénomènes s'en ensuivent, au lieu que, s'il s'ensuit quelque chose de contraire à un seul des phénomènes, cela suffit pour assurer de sa fausseté'', in ''Les Lettres de Blaise Pascal: Accompagnées de Lettres de ses Correspondants Publiées'', ed. Maurice Beaufreton, 6th edition (Paris: G. Crès, 1922), 25–26, available at http://gallica.bnf.fr {{Webarchive|url=https://web.archive.org/web/20161218172021/http://gallica.bnf.fr/ |date=18 December 2016 }} and translated in Saul Fisher, ''Pierre Gassendi's Philosophy and Science: Atomism for Empiricists'' Brill's Studies in Intellectual History 131 (Leiden: E. J. Brill, 2005), 126 n.7</ref>

==Adult life: religion, literature, and philosophy==
=== Religious conversion ===
[[File:Blaise Pascal 2.jpg|thumb|Portrait of Pascal]]

In the winter of 1646, Pascal's 58-year-old father broke his hip when he slipped and fell on an icy street of Rouen; given the man's age and the state of medicine in the 17th century, a [[Hip fracture|broken hip]] could be a very serious condition, perhaps even fatal. Rouen was home to two of the finest doctors in France, Deslandes and de la Bouteillerie. The elder Pascal "would not let anyone other than these men attend him...It was a good choice, for the old man survived and was able to walk again..."<ref>Connor, James A., ''Pascal's wager: the man who played dice with God'' (HarperCollins, NY, 2006) {{isbn|0-06-076691-3}} p. 70</ref> However treatment and rehabilitation took three months, during which time La Bouteillerie and Deslandes had become regular visitors.

Both men were followers of [[Jean Guillebert]], a proponent of a splinter group from Catholic teaching known as [[Jansenism]]. This still fairly small sect was making surprising inroads into the French Catholic community at that time. It espoused rigorous [[Augustinism]]. Blaise spoke with the doctors frequently, and after their successful treatment of his father, borrowed from them works by Jansenist authors. In this period, Pascal experienced a sort of "first conversion" and began to write on theological subjects in the course of the following year.

Pascal fell away from this initial religious engagement and experienced a few years of what some biographers have called his "worldly period" (1648–54). His father died in 1651 and left his inheritance to Pascal and his sister Jacqueline, for whom Pascal acted as conservator. Jacqueline announced that she would soon become a [[postulant]] in the Jansenist convent of [[Port-Royal-des-Champs|Port-Royal]]. Pascal was deeply affected and very sad, not because of her choice, but because of his chronic poor health; he needed her just as she had needed him.

{{blockquote|Suddenly there was war in the Pascal household. Blaise pleaded with Jacqueline not to leave, but she was adamant. He commanded her to stay, but that didn't work, either. At the heart of this was...Blaise's fear of abandonment...if Jacqueline entered Port-Royal, she would have to leave her inheritance behind...[but] nothing would change her mind.<ref>Miel, Jan. ''Pascal and Theology''. (Baltimore: Johns Hopkins University Press, 1969), p. 122</ref>}}

By the end of October in 1651, a truce had been reached between brother and sister. In return for a healthy annual stipend, Jacqueline signed over her part of the inheritance to her brother. Gilberte had already been given her inheritance in the form of a dowry. In early January, Jacqueline left for Port-Royal. On that day, according to Gilberte concerning her brother, "He retired very sadly to his rooms without seeing Jacqueline, who was waiting in the little parlor..."<ref>Jacqueline Pascal, ''"Memoir"'' p. 87</ref> In early June 1653, after what must have seemed like endless badgering from Jacqueline, Pascal formally signed over the whole of his sister's inheritance to Port-Royal, which, to him, "had begun to smell like a cult".<ref>Miel, Jan. ''Pascal and Theology''. (Baltimore: Johns Hopkins University Press, 1969), p. 124</ref> With two-thirds of his father's estate now gone, the 29-year-old Pascal was now consigned to genteel poverty.

For a while, Pascal pursued the life of a bachelor. During visits to his sister at Port-Royal in 1654, he displayed contempt for affairs of the world but was not drawn to God.<ref name="ep52">Richard H. Popkin, Paul Edwards (ed.), ''Encyclopedia of Philosophy'', 1967 edition, s.v. "Pascal, Blaise.", vol. 6, p. 52–55, New York: Macmillan</ref>

====''Memorial''====
On 23 November, 1654, between 10:30 and 12:30 at night, Pascal had an [[Christian mysticism|intense religious experience]] and immediately wrote a brief note to himself which began: "Fire. God of Abraham, God of Isaac, God of Jacob, not of the philosophers and the scholars..." and concluded by quoting Psalm 119:16: "I will not forget thy word. Amen." He seems to have carefully sewn this document into his coat and always transferred it when he changed clothes; a servant discovered it only by chance after his death.<ref name="oc618">Pascal, Blaise. ''Oeuvres complètes''. (Paris: Seuil, 1960), p. 618</ref> This piece is now known as the ''Memorial''. The story of a carriage accident as having led to the experience described in the ''Memorial'' is disputed by some scholars.<ref>MathPages, [https://www.mathpages.com/home/kmath558/kmath558.htm Hold Your Horses.] {{Webarchive|url=https://web.archive.org/web/20240229162655/https://www.mathpages.com/home/kmath558/kmath558.htm |date=29 February 2024 }} For the sources on which the hypothesis of a link between a carriage accident and Pascal's second conversion is based, and for a sage weighing of the evidence for and against, see Henri Gouhier, ''Blaise Pascal: Commentaires'', Vrin, 1984, pp. 379ff.</ref> His belief and religious commitment revitalized, Pascal visited the older of two convents at [[Port-Royal-des-Champs|Port-Royal]] for a two-week retreat in January 1655. For the next four years, he regularly travelled between Port-Royal and Paris. It was at this point, immediately after his conversion, that he began writing his first major literary work on religion, the ''Provincial Letters''.

== Literature ==
[[File:Blaise pascal.jpg|thumb|Pascal]]

In literature, Pascal is regarded as one of the most important authors of the French Classical Period and is read today as one of the greatest masters of French prose. [[Seymour Eaton]] called him "the greatest of all French thinkers".<ref>Eaton, S. (1916). Three Centuries of French Literature. (n.p.): American College Society. p. 76</ref> His use of satire and wit influenced later [[polemic]]ists.

=== The ''Provincial Letters'' ===
{{Main|Lettres provinciales}}

Beginning in 1656–57, Pascal published his memorable attack on [[casuistry]], a popular [[Ethics|ethical]] method used by [[Catholic Church|Catholic]] thinkers in the early modern period (especially the [[Jesuits]], and in particular [[Antonio Escobar y Mendoza|Antonio Escobar]]). Pascal denounced casuistry as the mere use of complex reasoning to justify moral laxity and all sorts of [[sin]]s. The 18-letter series was published between 1656 and 1657 under the pseudonym '''Louis de Montalte''' and incensed [[Louis XIV]]. The king ordered that the book be [[book burning|shredded and burnt]] in 1660. In 1661, in the midst of the [[formulary controversy]], the Jansenist school at Port-Royal was condemned and closed down; those involved with the school had to sign a 1656 [[papal bull]] condemning the teachings of Jansen as heretical. The final letter from Pascal, in 1657, had defied [[Alexander VII]] himself. Even Pope Alexander, while publicly opposing them, was nonetheless persuaded by Pascal's arguments.

Aside from their religious influence, the ''Provincial Letters'' were popular as a literary work. Pascal's use of humour, mockery, and vicious satire in his arguments made the letters ripe for public consumption and influenced the prose of later French writers like [[Voltaire]] and [[Jean-Jacques Rousseau]].

It is in the ''Provincial Letters'' that Pascal made his oft-quoted apology for writing a long letter, as he had not had time to write a shorter one.
From Letter XVI, as translated by Thomas M'Crie:
'Reverend fathers, my letters were not wont either to be so prolix, or to follow so closely on
one another. Want of time must plead my excuse for both of these faults. The present letter is
a very long one, simply because I had no leisure to make it shorter.'

Charles Perrault wrote of the ''Letters'': "Everything is there—purity of language, nobility of thought, solidity in reasoning, finesse in raillery, and throughout an ''agrément'' not to be found anywhere else."<ref>Charles Perrault, ''Parallèle des Anciens et des Modernes'' (Paris, 1693), Vol. I, p. 296.</ref>

=== Philosophy ===
[[Émile Faguet]] called Pascal "one of the greatest of French philosophers".<ref>Faguet, É. (1907). A Literary History of France. United Kingdom: C. Scribner's sons. p. 396</ref> Pascal was a [[Dualism|dualist]] and scientist following [[René Descartes]].<ref name=":2">Ariew, Roger (2007). Descartes and Pascal. ''Perspectives on Science'' 15 (4):397-409.</ref><ref>The Historians' History of the World: France, 843-1715. (1904). United States: Outlook Company. p. 640</ref> 

==== Philosophy of religion ====
[[File:Scène représentant Pascal en compagnie de Désargues et du Père Mersenne, place Royale, en 1643.jpg|thumb|280px|A scene of Desargues, Mersenne, Pascal, and Descartes]]
However, Pascal cared most of all about the [[philosophy of religion]], writing that Descartes' philosophy was "useless and uncertain".<ref name=":2" /> He further wrote: "I cannot forgive Descartes. In all his philosophy he would have been quite willing to dispense with God, but he couldn't avoid letting him put the world in motion; afterwards he didn't need God anymore".<ref>{{cite book |title=Mathematics and the Divine A Historical Study |date=2004 |publisher=Elsevier |editor1-last=Bergmans |editor1-first=Luc |page=402 |editor2-last=Koetsier |editor2-first=T.}}</ref>

Pascal opposed both the [[rationalism]] of the likes of Descartes, stating "reason can decide nothing here",<ref name=":3">{{cite book |title=Fundamentals of Philosophy |date=2004 |publisher=Taylor & Francis |editor1-last=Shand |editor1-first=John |page=391}}</ref> and the main countervailing epistemology, [[empiricism]], preferring [[fideism]]. For Pascal, the nature of God was such that proofs cannot reveal Him. Humans "are in darkness and estranged from God" because "he has hidden Himself from their knowledge".<ref name=":4">{{cite book |title=A Companion to Phenomenology and Existentialism |date=2009 |publisher=Wiley |page=140}}</ref>  Pascalian theology has grown out of his perspective that humans are, according to Wood, "born into a duplicitous world that shapes us into duplicitous subjects and so we find it easy to reject God continually and deceive ourselves about our own sinfulness".<ref name=":0">{{Cite book |url=https://global.oup.com/academic/product/blaise-pascal-on-duplicity-sin-and-the-fall-9780199656363?cc=gb&lang=en& |title=Blaise Pascal on Duplicity, Sin, and the Fall |date=4 July 2013 |publisher=Oxford University Press |isbn=9780199656363 |series=Changing Paradigms in Historical and Systematic Theology |access-date=24 March 2016 |archive-url=https://web.archive.org/web/20180809115036/https://global.oup.com/academic/product/blaise-pascal-on-duplicity-sin-and-the-fall-9780199656363?cc=gb&lang=en& |archive-date=9 August 2018 |url-status=live}}</ref>

=====Pensées=====
{{blockquote|text=Man is only a reed, the weakest in nature, but he is a thinking reed.|author=Blaise Pascal|title={{lang|fr|Pensées}}|source=No. 200}}

Pascal's most influential theological work, referred to posthumously as the ''[[Pensées]]'' ("Thoughts"), is widely considered to be a masterpiece and a landmark in French prose. When commenting on one particular section (Thought #72), [[Charles Augustin Sainte-Beuve|Sainte-Beuve]] praised it as the finest pages in the [[French language]].<ref name="finest">Sainte-Beuve, [https://books.google.com/books?id=I0P0A8XK29QC&pg=PA167 ''Seventeenth Century''] {{isbn|1-113-16675-4}} p. 174 (2009 reprint).</ref> [[Will Durant]] hailed the Pensées as "the most eloquent book in French prose".<ref name="eloquent">''[[The Story of Civilization]]: Volume 8, "The Age of Louis XIV"'' by [[Will Durant|Will & Ariel Durant]], chapter II, Subsection 4.4, p. 66 {{isbn|1-56731-019-2}}</ref>

The ''Pensées'' was not completed before his death. It was to have been a sustained and coherent examination and defence of the [[Christian faith]], with the original title ''Apologie de la religion Chrétienne'' ("Defence of the Christian Religion"). The first version of the numerous scraps of paper found after his death appeared in print as a book in 1669 titled ''Pensées de M. Pascal sur la religion, et sur quelques autres sujets'' ("Thoughts of M. Pascal on religion, and on some other subjects") and soon thereafter became a classic.

One of the ''Apologie''{{'}}s main strategies was to use the contradictory philosophies of [[Pyrrhonism]] and [[Stoicism]], personalized by [[Michel de Montaigne|Montaigne]] on one hand, and [[Epictetus]] on the other, in order to bring the unbeliever to such despair and confusion that he would embrace God.

====Philosophy of mathematics====
[[File:Port-Royal-des-Champs Vergers.JPG|thumb|180px|The orchards of Port-Royal]]
Pascal's major contribution to the [[philosophy of mathematics]] came with his ''De l'Esprit géométrique'' ("Of the Geometrical Spirit"), originally written as a preface to a geometry textbook for one of the famous [[Petites écoles de Port-Royal]] ("Little Schools of Port-Royal"). The work was unpublished until over a century after his death. Here, Pascal looked into the issue of discovering truths, arguing that the ideal of such a method would be to found all propositions on already established truths. At the same time, however, he claimed this was impossible because such established truths would require other truths to back them up—first principles, therefore, cannot be reached. Based on this, Pascal argued that the procedure used in geometry was as perfect as possible, with certain principles assumed and other propositions developed from them. Nevertheless, there was no way to know whether the assumed principles were true.

Pascal also used ''De l'Esprit géométrique'' to develop a theory of [[definition]]. He distinguished between definitions which are conventional labels defined by the writer and definitions which are within the language and understood by everyone because they naturally designate their referent. The second type would be characteristic of the philosophy of [[essentialism]]. Pascal claimed that only definitions of the first type were important to science and mathematics, arguing that those fields should adopt the philosophy of [[Formalism (philosophy)|formalism]] as formulated by Descartes.

In ''De l'Art de persuader'' ("On the Art of Persuasion"), Pascal looked deeper into geometry's [[axiomatic method]], specifically the question of how people come to be convinced of the [[axioms]] upon which later conclusions are based. Pascal agreed with [[Montaigne]] that achieving certainty in these axioms and conclusions through human methods is impossible. He asserted that these principles can be grasped only through intuition, and that this fact underscored the necessity for submission to God in searching out truths.

==Last works and death==
[[File:001Paskal.JPG|thumb|200px|[[Death mask]] of Blaise Pascal|alt=]]

[[T. S. Eliot]] described him during this phase of his life as "a man of the world among ascetics, and an ascetic among men of the world." Pascal's ascetic lifestyle derived from a belief that it was natural and necessary for a person to suffer. In 1659, Pascal fell seriously ill. During his last years, he frequently tried to reject the ministrations of his doctors, saying, "Don't pity me, sickness is the natural state of Christians, because in it we are, as we should always be, in the suffering of evils, in the deprivation of all the goods and pleasures of the senses, free from all the passions that work throughout the course of life, without ambition, without avarice, in the continual expectation of death."<ref name="m104-">Muir, Jane. [https://books.google.com/books?id=uV3rJkmnQhsC ''Of Men and Numbers''] {{Webarchive|url=https://web.archive.org/web/20230411061236/https://books.google.com/books?id=uV3rJkmnQhsC |date=11 April 2023 }}. (New York: Dover Publications, Inc, 1996). {{isbn|0-486-28973-7}}, p. 104.</ref><ref>{{Cite web |last=Périer |first=Gilberte |date=1845 |title=Lettres, opuscules et mémoires de madame Périer et de Jacqueline, sœurs de Pascal, et de Marguerite Périer, sa nièce |url=https://gallica.bnf.fr/ark:/12148/bpt6k294479/f69.item.zoom# |website=BnF Galica |pages=41–42}}</ref> Desiring to imitate Jesus’ poverty of spirit, in his spirit of zeal and charity, Pascal said if God allowed him to recover from his illness, he would be resolved to "have no other employment or occupation for the rest of my life than the service of the poor."<ref>{{Cite web |last=Périer |first=Gilberte |date=1845 |title=Lettres, opuscules et mémoires de madame Périer et de Jacqueline, sœurs de Pascal, et de Marguerite Périer, sa nièce |url=https://gallica.bnf.fr/ark:/12148/bpt6k294479/f69.item.zoom# |website=BnF Galica |pages=44}}</ref>

Louis XIV suppressed the Jansenist movement at Port-Royal in 1661. In response, Pascal wrote one of his final works, ''Écrit sur la signature du formulaire'' ("Writ on the Signing of the Form"), exhorting the Jansenists not to give in. Later that year, his sister Jacqueline died, which convinced Pascal to cease his [[polemics]] on [[Jansenism]].

=== Inventor of public transportation ===
[[File:Les carrosses à cinq sols - network map.jpg|thumb|280px|Route map of the carrosses à cinq sols in central Paris]]
Pascal's last major achievement, returning to his mechanical genius, was inaugurating one of the first land-based [[public transport]] services, the [[carrosses à cinq sols]], a network of horse-drawn multi-seat carriages that carried passengers on five fixed routes. Pascal also designated the operation principles which were later used to plan public transportation; the carriages had a fixed route, fixed price (five [[French sol|sols]], hence the name), and left even if there were no passengers.<ref>{{cite news |last1=Blinkin |first1=Mikhail |title=Это в моде: почему в мире возрождается общественный транспорт |url=https://postnauka.ru/longreads/156572 |work=Post-Nauka |date=20 August 2021 |language=ru |access-date=15 September 2021 |archive-date=15 September 2021 |archive-url=https://web.archive.org/web/20210915184104/https://postnauka.ru/longreads/156572 |url-status=live }}</ref> The lines were not commercially successful, and the last one closed by 1675.<ref>{{cite news |last1=Alfred |first1=Randy |title=March 18, 1662: The Bus Starts Here ... in Paris |url=https://www.wired.com/2008/03/march-18-1662-the-bus-starts-here-in-paris/ |magazine=[[Wired (magazine)|Wired]] |date=17 March 2008 |access-date=15 September 2021 |archive-date=14 October 2021 |archive-url=https://web.archive.org/web/20211014221608/https://www.wired.com/2008/03/march-18-1662-the-bus-starts-here-in-paris/ |url-status=live }}</ref> Nonetheless, he has been described as the inventor of public transportation.<ref>{{Cite web |date=2024-12-27 |title=The Inventor of Transit |url=https://www.straphanger.blog/the-inventor-of-transit/?ref=straphanger-newsletter |access-date=2025-01-02 |website=Straphanger}}</ref>

=== Illness and death ===
In 1662, Pascal's illness became more violent, and his emotional condition had severely worsened since his sister's death. Aware that his health was fading quickly, he sought a move to the hospital for incurable diseases, but his doctors declared that he was too unstable to be carried. In Paris on 18 August 1662, Pascal went into convulsions and received [[extreme unction]]. He died the next morning, his last words being "May God never abandon me," and was buried in the cemetery of [[Saint-Étienne-du-Mont]].<ref name="m104-" />

An [[autopsy]] performed after his death revealed grave problems with his stomach and other organs of his abdomen, along with [[brain damage|damage to his brain]]. Despite the autopsy, the cause of his poor health was never precisely determined, though speculation focuses on [[tuberculosis]], [[stomach cancer]], or a combination of the two.<ref name="m103">Muir, Jane. [https://books.google.com/books?id=uV3rJkmnQhsC ''Of Men and Numbers''] {{Webarchive|url=https://web.archive.org/web/20230411061236/https://books.google.com/books?id=uV3rJkmnQhsC |date=11 April 2023 }}. (New York: Dover Publications, Inc, 1996). {{isbn|0-486-28973-7}}, p. 103.</ref> The headaches which affected Pascal are generally attributed to his brain [[lesion]].<ref>{{Cite journal |last1=Zanello |first1=Marc |last2=Arnaud |first2=Eric |last3=Di Rocco |first3=Federico |date=2015-04-01 |title=The mysteries of Blaise Pascal's sutures |url=https://doi.org/10.1007/s00381-015-2622-9 |journal=Child's Nervous System |language=en |volume=31 |issue=4 |pages=503–506 |doi=10.1007/s00381-015-2622-9 |pmid=25697145 |issn=1433-0350}}</ref>

==Legacy ==
[[File:Epitaph Blaise Pascal Saint-Etienne.jpg|thumb|Pascal's epitaph in [[Saint-Étienne-du-Mont]], where he was buried]]

One of the Universities of [[Clermont-Ferrand]], France{{Mdash}}[[Université Blaise Pascal]]{{Mdash}}is named after him. [[Établissement scolaire français Blaise-Pascal]] in [[Lubumbashi]], Democratic Republic of the Congo, is named after Pascal.

The 1969 [[Eric Rohmer]] film ''[[My Night at Maud's]]'' is based on the work of Pascal. [[Roberto Rossellini]] directed a filmed biopic, ''Blaise Pascal'', which originally aired on Italian television in 1971.<ref>{{TCMDb title|488698}}</ref> Pascal was a subject of the first edition of the 1984 [[BBC Two]] documentary, ''[[Sea of Faith (TV series)|Sea of Faith]]'', presented by [[Don Cupitt]]. The chameleon in the animated film ''[[Tangled]]'' is named for [[Pascal and Maximus|Pascal]].

A [[Pascal (programming language)|programming language]] is named for Pascal. In 2014, [[Nvidia]] announced its new [[Pascal microarchitecture]], which is named for Pascal. The first [[graphics cards]] featuring Pascal were released in 2016.

The 2017 game ''[[Nier: Automata]]'' has multiple characters named after famous philosophers; one of these is a sentient pacifistic machine named Pascal, who serves as a major supporting character. Pascal creates a village for machines to live peacefully with the androids they are at war with and acts as a parental figure for other machines trying to adapt to their newly-found individuality.

The otter in the [[Animal Crossing|''Animal Crossing'' series]] is named for Pascal.<ref>{{cite web| url = https://www.nintendolife.com/news/2020/07/animal_crossing_new_horizons_pascal_-_spawn_times_locations_and_mermaid_clothing_rewards | title = Animal Crossing: New Horizons: Pascal - Spawn Times, Locations And Mermaid Clothing Rewards| date = 8 November 2021| access-date = 4 October 2020| archive-date = 8 October 2020| archive-url = https://web.archive.org/web/20201008080021/https://www.nintendolife.com/news/2020/07/animal_crossing_new_horizons_pascal_-_spawn_times_locations_and_mermaid_clothing_rewards | url-status = live}}</ref>

The [[minor planet]] [[4500 Pascal]] is named in his honor.<ref>{{cite book |last1=Schmadel |first1=Lutz D. |title=Dictionary of Minor Planet Names Addendum to 6th Edition: 2012-2014 |date=2015 |publisher=Springer International Publishing |page=363|bibcode=2015dmpn.book.....S }}</ref>

[[Pope Paul VI]], in [[encyclical]] ''[[Populorum progressio]]'', issued in 1967, quotes Pascal's ''Pensées'':

{{blockquote|True [[humanism]] points the way toward God and acknowledges the task to which we are called, the task which offers us the real meaning of human life. Man is not the ultimate measure of man. Man becomes truly man only by passing beyond himself. In the words of Pascal: "Man infinitely surpasses man.<ref>{{Cite web |title=Populorum Progressio (March 26, 1967) {{!}} Paul VI |url=https://www.vatican.va/content/paul-vi/en/encyclicals/documents/hf_p-vi_enc_26031967_populorum.html |access-date=2022-10-20 |website=The Holy See |archive-date=15 October 2022 |archive-url=https://web.archive.org/web/20221015074543/https://www.vatican.va/content/paul-vi/en/encyclicals/documents/hf_p-vi_enc_26031967_populorum.html |url-status=live }}</ref>}}

In 2023, [[Pope Francis]] released an [[Ecclesiastical letter#Letters of the popes in modern times|apostolic letter]], ''Sublimitas et miseria hominis'', dedicated to Blaise Pascal, in commemoration of the fourth centenary of his birth.

Pascal influenced both French sociologist [[Pierre Bourdieu]], who named his ''Pascalian Meditations'' (1997) after him,<ref>{{cite book |last1=Luke |first1=Allan |last2=Albright |first2=James |title=Pierre Bourdieu and Literacy Education |date=2010 |publisher=Taylor & Francis |page=37}}</ref> and French philosopher [[Louis Althusser]].<ref>{{cite book |last1=Sotiris |first1=Panagiotis |title=A Philosophy for Communism: Rethinking Althusser |publisher=Brill |page=126}}</ref>

==Works==
* ''Essai pour les coniques'' [Essay on conics] (1639)
* ''Experiences nouvelles touchant le vide'' [New experiments with the vacuum] (1647)
* ''Récit de la grande expérience de l'équilibre des liqueurs'' [Account of the great experiment on equilibrium in liquids] (1648)
* ''Traité du triangle arithmétique'' [Treatise on the arithmetical triangle] (written {{Circa|1654}};<ref>{{Cite web |url=https://www.math.nmsu.edu/hist_projects/pascalII.pdf |title=David Pengelley - "Pascal's Treatise on the Arithmetical Triangle" |access-date=27 March 2017 |archive-url=https://web.archive.org/web/20170328195055/https://www.math.nmsu.edu/hist_projects/pascalII.pdf |archive-date=28 March 2017 |url-status=dead }}</ref> publ. 1665)
* {{Lang|fr|[[Lettres provinciales]]}} [The Provincial Letters] (1656–57)
* ''De l'Esprit géométrique'' [On the Geometrical Spirit] (1657 or 1658)
* ''Écrit sur la signature du formulaire'' (1661)
* ''[[Pensées]]'' [Thoughts] (incomplete at death; publ. 1670)
* ''[[Discours sur les passions de l'amour]]'' [Discourse on the Passion of Love] (possible forgery)
* ''[[s:Blaise Pascal/On the Conversion of the Sinner|On the Conversion of the Sinner]]''
* ''Ecrits sur la grace'' [Writings on Grace]

==See also==
* [[Expected value]]
* [[Gambler's ruin]]
* [[List of pioneers in computer science]]
* [[List of works by Eugène Guillaume]]
* [[Negative binomial distribution|Pascal distribution]]
* [[Pascal's mugging]]
* [[Pascal's pyramid]]
* [[Pascal's simplex]]
* [[Problem of points]]
* [[Scientific Revolution]]

==Notes==
{{reflist|group=lower-alpha}}

==References==
{{Reflist}}{{reflist|group=note}}

==Further reading==
{{refbegin}}
* [[Donald Adamson|Adamson, Donald]]. ''Blaise Pascal: Mathematician, Physicist, and Thinker about God'' (1995) {{isbn|0-333-55036-6}}
* Adamson, Donald. [https://books.google.com/books?id=AMOQZfrZq-EC&pg=PA405 "Pascal's Views on Mathematics and the Divine,"] {{Webarchive|url=https://web.archive.org/web/20230207083333/https://books.google.com/books?id=AMOQZfrZq-EC&pg=PA405 |date=7 February 2023 }} ''Mathematics and the Divine: A Historical Study'' (eds. T. Koetsier and L. Bergmans. Amsterdam: Elsevier 2005), pp.&nbsp;407–21.
* Broome, J.H. ''Pascal''. London: E. Arnold, 1965. {{isbn|0-7131-5021-1}}
* [[Antoine Compagnon|Compagnon, Antoine]]. ''A Summer with Pascal''. Cambridge, Massachusetts: Belknap Press, 2024.
* [[Rüdiger Campe|Campe, Rüdiger]], "Numbers and Calculation in Context: The Game of Decision - Pascal" in The ''Game of Probability. Literature and Calculation from Pascal and Kleist'', Stanford University Press, 2012
* Davidson, Hugh M. ''Blaise Pascal''. Boston: Twayne Publishers, 1983.
* {{cite book | last1 = Devlin | first1 = Keith | author-link = Keith Devlin | year = 2008 | title = The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern | location = New York | publisher = Basic Books | isbn = 978-0-465-00910-7 | ref = {{sfnRef|Devlin}} }}
* Farrell, John. "Pascal and Power". Chapter seven of ''Paranoia and Modernity: Cervantes to Rousseau'' (Cornell UP, 2006).
* [[Lucien Goldmann|Goldmann, Lucien]], ''The hidden God; a study of tragic vision in the Pensees of Pascal and the tragedies of Racine'' (original ed. 1955, Trans. [[Philip Thody]]. London: Routledge, 1964).
* [[Douglas Groothuis|Groothuis, Douglas]]. ''On Pascal''. (Belmont: Wadsworth, 2002). {{isbn|978-0534583910}}
* Jordan, Jeff. ''Pascal's Wager: Pragmatic Arguments and Belief in God''. Oxford: Clarendon Press, 2006.
* Landkildehus, Søren. "Kierkegaard and Pascal as kindred spirits in the Fight against Christendom" in ''Kierkegaard and the Renaissance and Modern Traditions'' (ed. Jon Stewart. Farnham: Ashgate Publishing, 2009).
* Mackie, John Leslie. ''The Miracle of Theism: Arguments for and against the Existence of God''. (Oxford: Oxford University Press, 1982).
* [[Stafford Harry Northcote, Viscount Saint Cyres]], ''Pascal'' (London: Smith, Elder & Company, 1909; New York: E. P. Dutton)
* Pugh, Anthony R. ''The Composition of Pascal's Apologia'', (University of Toronto Press, 1984).
* {{Cite EB1911|wstitle= Pascal, Blaise | volume= 20 |last1= Saintsbury |first1= George |author1-link= George Saintsbury ||last2= Chrystal |first2= George |author2-link= George Chrystal | pages = 878&ndash;881 |short=1}}
* {{cite journal |last1=Saka |first1=Paul |year=2001 |title=Pascal's Wager and the Many Gods Objection |journal=Religious Studies |volume=37 |issue=3 |pages=321–41 |doi=10.1017/S0034412501005686|s2cid=170266714 }}
* {{cite book |last=Stephen |first=Leslie |author-link=Leslie Stephen|title=Studies of a Biographer |volume=2 |publisher=Duckworth and Co. |location=London |pages=241–284 |chapter=[[s:en:Studies of a Biographer/Pascal|Pascal]]}}
* Tobin, Paul. "The Rejection of Pascal's Wager: A Skeptic's Guide to the Bible and the Historical Jesus". authorsonline.co.uk, 2009.
* {{cite book |last1=Tomlin |first1=Graham |title=Blaise Pascal: The Man Who Made the Modern World |date=2025 |publisher=Hodder & Stoughton |edition=1}}
{{refend}}

==External links==
{{Sister project links|voy=no}}
* [https://babel.hathitrust.org/cgi/pt?id=ucm.5325890510;view=1up;seq=15 Oeuvres complètes, volume 2] (1858) Paris: Libraire de L Hachette et Cie, link from [[HathiTrust]].
* {{Gutenberg author |id=7913| name=Blaise Pascal}}
* {{Internet Archive author |sname=Blaise Pascal}}
* {{Librivox author | id=4890}}
* [http://emlo.bodleian.ox.ac.uk/blog/?catalogue=blaise-pascal The Correspondence of Blaise Pascal] in [http://emlo.bodleian.ox.ac.uk/home EMLO]
* {{cite IEP |url-id=pascal-b |title="Blaise Pascal" |last=Simpson |first=David}}
* {{cite SEP |url-id=pascal |title=Blaise Pascal |last=Clarke |first=Desmond}}
* {{MathGenealogy|id=126406}}
* ''Pensées de Blaise Pascal''. Renouard, Paris 1812 (2 vols.) ({{ULBDD|urn:nbn:de:hbz:061:1-484828}})
* [https://web.archive.org/web/20211103201931/http://metastudies.net/pmwiki/pmwiki.php?n=Site.TheModernEpochAndTheEmergenceOfTheModernCalculator#pascaline Discussion of the Pascaline, its history, mechanism, surviving examples, and modern replicas at http://things-that-count.net]
* [https://web.archive.org/web/20100217023133/http://www.users.csbsju.edu/~eknuth/pascal.html Pascal's Memorial] in orig. French/Latin and modern English, trans. Elizabeth T. Knuth.
* [https://web.archive.org/web/20060114173522/http://www.biblioweb.org/-PASCAL-Blaise-.html Biography, Bibliography.] (in French)
* {{OL author}}
* [https://www.bbc.co.uk/programmes/b03b2v6m BBC Radio 4. In Our Time: Pascal.]
* [http://www-personal.umich.edu/~jbourj/money5.htm Blaise Pascal featured on the 500 French Franc banknote in 1977.] {{Webarchive|url=https://web.archive.org/web/20090416151301/http://www-personal.umich.edu/~jbourj/money5.htm |date=16 April 2009 }}
* [http://www.intratext.com/Catalogo/Autori/Aut852.htm Blaise Pascal's works]: text, concordances and frequency lists
* {{Cite CE1913|wstitle=Blaise Pascal |short=x}}
* Etext of Pascal's ''[https://www.ccel.org/ccel/pascal/pensees.html Pensées]'' (English, in various formats)
* Etext of Pascal's ''[https://web.archive.org/web/20050428180845/http://oregonstate.edu/instruct/phl302/texts/pascal/letters-a.html Lettres Provinciales]'' (English)
* Etext of a number of Pascal's [https://www.bartleby.com/48/3/ minor works] (English translation) including, ''De l'Esprit géométrique'' and ''De l'Art de persuader''.
* {{MacTutor Biography|id=Pascal}}

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