{{Short description|French mathematician (1581–1638)}} {{Use dmy dates|date=October 2023}} {{Infobox person | name = Claude Gaspar Bachet de Méziriac | image = Claude Gaspard Bachet de Méziriac - Versailles MV 2893.jpg | caption = | birth_date = {{Birth date|1581|10|9|df=yes}} | birth_place = Bourg-en-Bresse, Duchy of Savoy | death_date = {{Death date and age|1638|2|26|1581|10|9|df=yes}} | death_place = Bourg-en-Bresse, Duchy of Savoy | nationality = | occupation = Mathematician | notable_works = {{flatlist| * {{lang|fr|Problèmes plaisans et délectables qui se font par les nombres}} * {{lang|fr|Les éléments arithmétiques}} }} }} '''Claude Gaspar Bachet Sieur de Méziriac<ref name=":0" />''' (9 October 1581 – 26 February 1638) was a French mathematician and poet born in Bourg-en-Bresse, at that time belonging to Duchy of Savoy.<ref name="mactutor" /> He wrote {{lang|fr|Problèmes plaisans et délectables qui se font par les nombres}},<ref name=":0" group="note">{{langnf|fr||Pleasant and delectable problems that are done by numbers|links=no}}</ref> {{lang|fr|Les éléments arithmétiques}},<ref name=":1" group="note">{{langnf|fr||Arithmetical elements|links=no}}</ref> and a Latin translation of the ''Arithmetica'' of Diophantus (the very translation where Fermat wrote a margin note about Fermat's Last Theorem). He also discovered means of solving indeterminate equations using continued fractions, a method of constructing magic squares, and a proof of Bézout's identity.
== Biography == [[File:Diophantus-cover.png|thumb|upright|Title page of the 1621 edition of Diophantus' ''Arithmetica'', translated into Latin by Claude Gaspard Bachet de Méziriac.|left]]Claude Gaspar Bachet de Méziriac was born in Bourg-en-Bresse on 9 October 1581. By the time he reached the age of six, both his mother (Marie de Chavanes) and his father (Jean Bachet) had died. He was then looked after by the Jesuit Order. For a year in 1601, Bachet was a member of the Jesuit Order (he left due to an illness).<ref name="mactutor" />
Bachet lived a comfortable life in Bourg-en-Bresse. He married Philiberte de Chabeu in 1620 and had seven children.<ref name="mactutor" />
Bachet was a pupil of the Jesuit mathematician Jacques de Billy at the Jesuit College in Rheims. They became close friends.<ref name="Mollin">Richard A. Mollin: ''Fundamental Number Theory with Applications''. CRC Press, 2008, ISBN 9781420066616, p. [https://books.google.com/books?id=u3IBcdhfaeEC&pg=PA279 279] </ref>
Bachet wrote the ''Problèmes plaisans et délectables qui se font par les nombres''<ref name=":0" group="note" /> of which the first edition was issued in 1612, a second and enlarged edition was brought out in 1624; this contains an interesting collection of arithmetical tricks and questions, many of which are quoted in W. W. Rouse Ball's ''Mathematical Recreations and Essays''.<ref name="mactutor">{{MacTutor Biography|id=Bachet}} (retrieved 9 April 2021; {{Cite web |url=https://mathshistory.st-andrews.ac.uk/Biographies/Bachet/ |title=Claude Gaspar Bachet (1581–1638) – Biography – MacTutor History of Mathematics |access-date=25 November 2021 |archive-date=3 July 2020 |archive-url=https://web.archive.org/web/20200703024231/https://mathshistory.st-andrews.ac.uk/Biographies/Bachet/ |url-status=bot: unknown}})</ref><ref name="Rouse Ball">W. W. Rouse Ball: ''A Short Account of the History of Mathematics'' (4th Edition, 1908) as quoted at [http://www.maths.tcd.ie/pub/HistMath/People/17thCentury/RouseBall/RB_Math17C.html#Bachet] </ref>
He also wrote ''Les éléments arithmétiques'',<ref name=":1" group="note" /> which exists in manuscript; and a translation, from Greek to Latin, of the ''Arithmetica'' of Diophantus (1621). It was this very translation in which Fermat wrote his famous margin note claiming that he had a proof of Fermat's Last Theorem. The same text renders Diophantus' term παρισὀτης as ''adaequalitat'', which became Fermat's technique of adequality, a pioneering method of infinitesimal calculus.<ref name="Singh">Simon Singh: ''Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem''. Walker, New York, 1997, ISBN 0-8027-1331-9, pp. 56–57, 61–63</ref>
Bachet was the earliest writer who discussed the solution of indeterminate equations by means of continued fractions.{{How|date=November 2021|title=How exactly can one solve an indeterminate equation using continued fractions?}} He also did work in number theory and found a method of constructing magic squares.<ref name="Rouse Ball"/> In the second edition of his ''Problèmes plaisants'' (1624) he gives a proof of Bézout's identity (as proposition XVIII) 142 years before it got published by Bézout.<ref>Claude Gaspard Bachet, sieur de Méziriac, ''Problèmes plaisants et délectables''… , 2nd ed. (Lyon, France: Pierre Rigaud & Associates, 1624), [http://www.bsb-muenchen-digital.de/~web/web1008/bsb10081407/images/index.html?digID=bsb10081407&pimage=38&v=100&nav=0&l=de pp. 18–33]. On these pages, Bachet proves (without equations) "Proposition XVIII. Deux nombres premiers entre eux estant donnez, treuver le moindre multiple de chascun d'iceux, surpassant de l'unité un multiple de l'autre." (Given two numbers [which are] relatively prime, find the lowest multiple of each of them [such that] one multiple exceeds the other by unity (1).) This problem (namely, ax – by = 1) is a special case of Bézout's equation and was used by Bachet to solve the problems appearing on pages 199 ff.</ref><ref name=":0">Wolfgang K. Seiler: [http://hilbert.math.uni-mannheim.de/~seiler/ZT18/zahlen18.pdf Zahlentheorie] [{{Webarchive|url=https://web.archive.org/web/20210105194548/http://hilbert.math.uni-mannheim.de/~seiler/ZT18/zahlen18.pdf|date=5 January 2021}}]. Lecture notes, University of Mannheim, 2018 (German, retrieved 9 April 2021)</ref>
He was elected member of the Académie française in 1635.<ref name="mactutor"/>
== Notes == {{Reflist|group=note}}
==References== {{reflist}}
==Further reading== * {{cite encyclopedia | last = Schaaf | first = William | title = Bachet de Méziriac, Claude-Gaspar | encyclopedia = Dictionary of Scientific Biography | volume = 1 | pages = 367–368 | publisher = Charles Scribner's Sons | location = New York | year = 1970 | isbn = 0-684-10114-9 }} * Ad Meskens (2010), ''Travelling Mathematics: The Fate of Diophantos' Arithmetic'' (Science Networks. Historical Studies Book 41).
== External links == * Diophantus Alexandrinus, Pierre de Fermat, Claude Gaspard Bachet de Meziriac, ''Diophanti Alexandrini Arithmeticorum libri 6, et De numeris multangulis liber unus''. Cum comm. C(laude) G(aspar) Bacheti et observationibus P(ierre) de Fermat. Acc. doctrinae analyticae inventum novum, coll. ex variis eiu. Tolosae 1670, {{doi|10.3931/e-rara-9423}}. *[http://hdl.loc.gov/loc.rbc/general.48833.1 ''Problèmes plaisans et délectables, qui se font par les nombres''] – digital copy at the Library of Congress
{{Académie française Seat 13}} {{Authority control}}
{{DEFAULTSORT:Bachet De Meziriac, Claude Gaspard}} Category:1581 births Category:1638 deaths Category:Writers from Bourg-en-Bresse Category:16th-century French Jesuits Category:French mathematicians Category:17th-century French mathematicians Category:Members of the Académie Française Category:French number theorists Category:Magic squares Category:Greek–Latin translators Category:17th-century French translators Category:17th-century French male writers Category:17th-century French poets Category:Writers from the Savoyard state