View source for John Pell (mathematician)

{{Short description|British mathematician (1611–1685)}}
{{about|the mathematician|his son, the American landowner|John Pell (landowner)}}
{{Use British English|date=February 2020}}
{{Use dmy dates|date=February 2020}}
{{Infobox scientist
| name              = John Pell
| image             = John_Pell.jpg
| image_size        = 230px
| caption           = 
| birth_date        = {{Birth date|1611|03|01|df=y}}
| birth_place       = [[Southwick, West Sussex|Southwick]], [[Sussex]], [[Kingdom of England|England]]
| death_date        = {{Death date and age|1685|12|12|1611|03|01|df=y}}
| death_place       = [[Westminster]], [[Middlesex]], England
| citizenship       =
| nationality       = English
| ethnicity         = 
| field             = [[Mathematician]] and [[linguist]]
| work_institutions = [[University of Amsterdam]]
| alma_mater        = [[Trinity College, Cambridge]]
| doctoral_advisor  = 
| doctoral_students = [[William Brereton, 3rd Baron Brereton|William Brereton]]
| known_for         = [[Pell's equation]]<br />[[Pell number]]
| author_abbrev_bot = 
| author_abbrev_zoo = 
| prizes            = 
| signature         =  
}}
'''John Pell''' (1 March 1611 – 12 December 1685) was an English [[mathematician]] and political agent abroad. He was made Royal Chair of Mathematics at [[Orange College of Breda|Orange College]] by the [[Frederick Henry, Prince of Orange|Prince of Orange]], and was under the patronage of [[Sir Charles Cavendish]]. He was also a compeer and correspondent of [[René Descartes]] and [[Thomas Hobbes]].

==Early life==
He was born at [[Southwick, West Sussex|Southwick]] in [[West Sussex]], [[England]]. His father, also named John Pell, was from Southwick, and his mother was Mary Holland, from [[Halden]] in Kent. The second of two sons, Pell's older brother was [[Thomas Pell]]. By the time he was six, they were orphans, their father dying in 1616 and their mother the following year. John Pell the elder had a fine library, which proved valuable to the young Pell as he grew up. He was educated at [[Steyning Grammar School]] and entered [[Trinity College, Cambridge]], at the age of 13.<ref>{{acad|id=PL624J|name=Pell, John}}</ref> 

During his university career he became an accomplished linguist; even before taking a B.A. degree in 1629, he corresponded with [[Henry Briggs (mathematician)|Henry Briggs]] and other mathematicians. He was promoted by seniority to M.A. in 1630 and taught in the short-lived Chichester Academy set up by [[Samuel Hartlib]].<ref>Malcolm and Stedall, p. 29.</ref><ref name = MacTutor>{{Cite web|url=http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Pell.html|title = John Pell - Biography}}</ref> On 3 July 1632 he married Ithamaria Reginald (also rendered as Ithamara or Ithumaria, with the surname Reginolles), sister of the writer and polymath [[Bathsua Makin]].<ref>Malcolm and Stedall, p. 69.</ref> They had four sons and four daughters. Ithumaria died in 1661. Some time before 1669 Pell remarried.

Pell spent much of the 1630s working under Hartlib's influence, on topics in the area of [[pedagogy]], encyclopedism and [[pansophy]], [[combinatorics]], and the legacy of [[Trithemius]]. By 1638 he had formulated a proposal for a [[universal language]].<ref>Malcolm and Stedall, p. 55.</ref> In mathematics, he concentrated on expanding the scope of algebra in the [[theory of equations]], and on [[mathematical table]]s.<ref name="Malcolm and Stedall, p. 57">Malcolm and Stedall, p. 57.</ref> As part of a joint lobbying effort with Hartlib to find himself support to continue as a researcher, he had his short ''Idea of Mathematics'' printed in October 1638.<ref name="Malcolm and Stedall, p. 57"/> It brought interested responses from [[Johann Moriaen]] and [[Marin Mersenne]].<ref>Malcolm and Stedall, pp. 73–74.</ref>

==Academic and diplomat==
His reputation and the influence of Sir [[William Boswell]], the English resident, with the States-General procured his election in 1644 to the chair of mathematics in [[Amsterdam]], after an earlier attempt immediately after [[Martin van den Hove]] left for Leiden had failed.<ref>Malcolm and Stedall, pp. 77.</ref> From 1644 he worked on a polemical work, against [[Longomontanus]]. For this he put in a large effort soliciting help and testimonials: from [[Bonaventura Cavalieri]], his patron [[Sir Charles Cavendish]], [[René Descartes]], [[Thomas Hobbes]], Mersenne, [[Claude Mydorge]], and [[Gilles de Roberval]].<ref>[https://ia800908.us.archive.org/15/items/pellianapellofpe00unse_0/pellianapellofpe00unse_0.pdf Pelliana : Pell of Pelham : Sir John Pell, second Lord of the Manor of Pelham], New Series, Vol I, No. II, October 1963, p. 7-13-14-16</ref><ref>[https://books.google.com/books?id=D6BcAAAAMAAJ&q=pell Descartes Correspondance], René Descartes, Volume 4, F. Alcan, 1947, p. 30-387-402</ref><ref>[https://plato.stanford.edu/entries/descartes-mathematics/ Descartes’ Early Mathematical Researches (ca. 1616–1629)], Descartes’ Mathematics, First published Mon Nov 28, 2011; substantive revision Wed Apr 28, 2021</ref> It finally appeared as ''Controversy with Longomontanus concerning the Quadrature of the Circle'' (1647).<ref>Aloysius Martinich, ''Hobbes: A Biography'' (1999), p. 278.</ref><ref name = Pyle>[[Andrew Pyle (philosopher)|Andrew Pyle]] (editor), ''Dictionary of Seventeenth-Century British Philosophers'' (2000), article ''Pell, John'', pp. 638–641.</ref>

In 1646, on the invitation of [[Frederick Henry, Prince of Orange]], Pell accepted a professorship at the new [[Orange College of Breda|Orange College]] at [[Breda]], where he taught until 1652. He realised that war between the English and the Dutch was imminent and that he would be in an extremely difficult position in Breda, so returned to England before the outbreak of the [[First Anglo-Dutch War]] in July 1652. After his return, [[Oliver Cromwell]] appointed Pell to a post teaching mathematics in London.

From 1654 to 1658 Pell acted as Cromwell's political agent in [[Zürich]] to the [[Protestant]] [[cantons of Switzerland]]; he cooperated with [[Samuel Morland]], the English resident at [[Geneva]].<ref>{{Cite web|url=http://www.berkshirehistory.com/bios/smorland.html|title = RBH Biography: Sir Samuel Morland (1625-1695)}}</ref> Pell was described in Zürich by the English traveller [[Sir John Reresby, 2nd Baronet|Sir John Reresby]] in about 1656 as "a strange unknown person, not unsuiting the people he was sent to, nor the master [Cromwell] he came from. They are here so strict in their religion, they suffer not the Venetian ambassador to hear mass in his own house."<ref>Albert Ivatt, M. A., ed: ''The Memoir and Travels of Sir John Reresby, Bart.'' (London: Kegan Paul, Trench, Trubner, 1904), p. 42.</ref> Cromwell wanted to split the Protestant cantons of Switzerland off to join a Protestant League, with England at its head. However Pell's negotiations were long drawn out and he returned to England to deliver his report only shortly before Cromwell's death. He was unable to report as he waited in vain for an audience with the ailing Cromwell.
 
A mathematical pupil and disciple in Switzerland, from 1657, was [[Johann Heinrich Rahn]], known as Rhonius.<ref>Malcolm and Stedall p. 77.</ref> Rahn is credited with the invention of the [[division sign]] ({{code|÷}}) from one of the classic symbols for [[Obelus]]; it has also been attributed to Pell, who taught Rahn a three-column spreadsheet-style technique of tabulation of calculations, and acted as editor for Rahn's 1659 book ''Teutsche Algebra'' in which it appeared. This book by Rahn also contained what would become known as the "Pell equation".<ref>[[Florian Cajori]], ''A History of Mathematical Notations: Two Volumes Bound as One'' (1993 edition), p. 271.</ref><ref>{{cite web |url=http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Rahn.html |title=Rahn biography |access-date=9 January 2009 |url-status=dead |archive-url=https://web.archive.org/web/20080612120226/http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Rahn.html |archive-date=12 June 2008 }}</ref> [[Diophantine equation]]s was a favourite subject with Pell; he lectured on them at Amsterdam. He is now best remembered, if perhaps erroneously, for the indeterminate equation

:<math>ax^2+1=y^2,</math>

which is known as ''[[Pell's equation]]''. This problem was in fact proposed by [[Pierre de Fermat]] first to [[Bernard Frénicle de Bessy]], and in 1657 to all mathematicians. Pell's connection with the problem is through Rahn. It consisted of publication of the solutions of [[John Wallis]] and [[Lord Brouncker]] in his edition of [[Thomas Branker]]'s ''Translation of Rhonius's Algebra'' (1668); added to his earlier editorial contributions, whatever they were, to the 1659 algebra book written by Rahn (i.e. Rhonius).<ref name=pell>{{citation | last1 = O'Connor | first1 = J. J. | last2 = Robertson | first2 = E. F. | title=John Pell | url=http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Pell.html| year=2005}}</ref> This new edition by Pell of what was essentially Rahn's work included a great deal of additional material on [[number theory]], amounting to a reply to the 1657 book ''Exercitationes mathematicae'' by [[Frans van Schooten]]. It is also notable for its inclusion of a ''Table of Incomposits'', an early large [[factor table]].<ref>{{cite web|url=http://www.kuttaka.org/FactorTables.pdf |title=Archived copy |access-date=9 January 2009 |url-status=dead |archive-url=https://web.archive.org/web/20090326043035/http://www.kuttaka.org/FactorTables.pdf |archive-date=26 March 2009 }}</ref>

==After the Restoration==
After his return to England, Pell took orders and in 1661 became rector of [[Fobbing]] in [[Essex]]. In 1663 he was given an honorary D. D. ([[Lambeth degree]]) and was also elected a [[Fellow of the Royal Society]]. At the same time he was presented by Bishop [[Gilbert Sheldon]] to the rectory of [[Laindon]], Essex; Sheldon expected him to treat the positions as sinecures.<ref name = Pyle/><ref>''Concise Dictionary of National Biography''</ref> He spent time visiting [[William Brereton, 3rd Baron Brereton]], at [[Brereton Hall]] in [[Cheshire]], having taught him mathematics at Breda, and after Brereton died in 1680 [[John Aubrey]] reported a very close friendship between the two men.<ref>[[John Aubrey]], ed. Oliver Lawson Dick, ''Aubrey's Brief Lives'' (Random House, 2016), p. 232</ref>

In 1673 Pell met [[Gottfried Wilhelm Leibniz|Leibniz]] in London, and was able to inform him that some of his mathematical work had been anticipated by François Regnaud and [[Gabriel Mouton]].<ref>{{Cite web |url=http://www.math.rutgers.edu/courses/436/Honors02/leibniz.html |title=Archived copy |access-date=9 January 2009 |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=dead }}</ref><ref>Nicholas Jolley, ''Leibniz'' (2005), p. 17.</ref> His devotion to mathematics seems to have interfered with his advancement in the Church and with his private life. For a time he was confined as a [[debtor]] in the [[King's Bench Prison]]. He lived, on the invitation of Dr [[Daniel Whistler]], for a short time in 1682 at the [[College of Physicians]], but died at the house of Mr Cothorne, reader of the church of [[St Giles in the Fields|St Giles-in-the Fields]].

==Works==
Many of Pell's manuscripts fell into the hands of [[Richard Busby]], master of [[Westminster School]], and afterwards came into the possession of the [[Royal Society]]; they are still preserved in nearly forty folio volumes in the [[British Library]], which contain, not only Pell's own memoirs, but much of his correspondence with the mathematicians of his time.

His chief works are:
*''Astronomical History of Observations of Heavenly Motions and Appearances'' (1634)
*''Ecliptica prognostica'' (1634)
*''An Idea of Mathematicks'' (1638)
*''Controversy with Longomontanus concerning the Quadrature of the Circle'' (1646?)
*''A Table of Ten Thousand Square Numbers'' (fol.; 1672).

The ''Idea'' was a short manifesto. It made three suggestions: a mathematical encyclopedia and bibliography; a complete mathematics research library and collection of instruments, with state sponsorship; and a three-volume comprehensive set of mathematical textbooks, able to convey the state of the art to any scholar.<ref>John T. Young (1998), ''Faith, Alchemy and Natural Philosophy: Johann Moriaen, Reformed Intelligencer, and the Hartlib Circle.'' Aldershot: Ashgate. {{isbn|1-84014-282-0}}, p. 115.</ref>

==Family==
John Pell's brother, [[Thomas Pell]] (1612/3–1669), was a physician who emigrated to [[New England]] in the 1630s. In 1654,<ref>Sources variously give the date of the transaction as 27 June 11 November, or 14 November 1654.</ref> Thomas Pell signed a treaty with [[Chief Wampage]] and other [[Siwanoy]] Indian tribal members that granted him {{convert|50000|acre}} of tribal land, including all or part of [[the Bronx]] and land to the west along [[Long Island Sound]] in what is now Westchester County, extending west to the [[Hutchinson River]] and north to [[Mamaroneck, New York|Mamaroneck]]. Having no children, he left his estate to his nephew [[Sir John Pell]] (1643–1702), one of the mathematician's four sons, who travelled from England to New York and took up residence there as the first [[Lord of the Manor]] of [[Pelham (village), New York|Pelham]]. His descendants have continued to be prominent in American polity, including Ambassador and U.S. Representative [[Herbert Pell]] and U.S. Senator [[Claiborne Pell]]. Philip Pell II built [[Pelhamdale]] at [[Pelham Manor, New York]] about 1750,<ref name="nrhpinv_ny">{{cite web| url=http://www.oprhp.state.ny.us/hpimaging/hp_view.asp?GroupView=10657| title=National Register of Historic Places Registration: Pelhamdale| date=August 1982| access-date=24 December 2010| author=Austin N. O'Brien| publisher=[[New York State Office of Parks, Recreation and Historic Preservation]]| url-status=dead| archive-url=https://web.archive.org/web/20121018081540/http://www.oprhp.state.ny.us/hpimaging/hp_view.asp?GroupView=10657| archive-date=18 October 2012| df=dmy-all}}</ref> and another descendant, [[Stephen Hyatt Pell]], restored [[Fort Ticonderoga]], New York in 1909 and formally opened it to the public. ([[William Ferris Pell]] had bought the Fort and surrounding lands in 1820, and used the property as a summer retreat.<ref>{{cite news |last1=Times |first1=Enid Nemy Special to The New York |title=Pell Clan: 'A Nice Little Thing to Belong to' |url=https://www.nytimes.com/1979/08/13/archives/pell-clan-a-nice-little-thing-to-belong-to-several-score-of-pells.html |access-date=13 March 2022 |work=The New York Times |date=13 August 1979}}</ref>)

Yet another of John Pell's American descendants, [[Morris Birkbeck Pell]], graduated as [[senior wrangler]] in mathematics at [[Cambridge University]] in 1849 and emigrated to Australia in 1852 to become the first professor of mathematics and [[natural philosophy]] at the newly inaugurated [[University of Sydney]].

==See also==

* {{Annotated link |Obelus}}
* {{Annotated link |Claiborne Pell}}

==Notes==
{{Reflist|30em}}

==References==
*{{EB1911|wstitle = Pell, John|volume=21}}
*{{cite ODNB|first=Christoph J.|last= Scriba|title =Pell, John (1611–1685)|id=21802}}
*The most recent study of Pell is by [[Noel Malcolm]] and Jacqueline Stedall, ''John Pell (1611–1685) and His Correspondence with Sir Charles Cavendish: The Mental World of an Early Modern Mathematician'' (Oxford: Oxford University Press, 2005). {{isbn|0-19-856484-8}}

==External links==
*{{MacTutor Biography|id=Pell}}
*[http://galileo.rice.edu/Catalog/NewFiles/pell.html Galileo Project page]
*https://web.archive.org/web/20060615060236/http://www.townofpelham.com/townhistorian/index.html

{{Authority control}}

{{DEFAULTSORT:Pell, John}}
[[Category:1611 births]]
[[Category:1685 deaths]]
[[Category:17th-century English mathematicians]]
[[Category:Doctors of Divinity]]
[[Category:Original fellows of the Royal Society]]
[[Category:Number theorists]]
[[Category:People educated at Steyning Grammar School]]
[[Category:People educated at Westminster School, London]]
[[Category:Alumni of Trinity College, Cambridge]]
[[Category:People from Fobbing]]
[[Category:People from Southwick, West Sussex]]
[[Category:People imprisoned for debt]]
[[Category:Pell family]]