Claude Gaspar Bachet de Méziriac

Template:Short description Template:Use dmy dates Template:Infobox person 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 {{#invoke:Lang|lang}},<ref name=":0" group="note">Template:Langnf</ref> {{#invoke:Lang|lang}},<ref name=":1" group="note">Template:Langnf</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

Title page of the 1621 edition of Diophantus' Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac.

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. 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">Template:MacTutor Biography (retrieved 9 April 2021; {{#invoke:citation/CS1|citation |CitationClass=web }})</ref><ref name="Rouse Ball">W. W. Rouse Ball: A Short Account of the History of Mathematics (4th Edition, 1908) as quoted at [1] </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.Template:How 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), 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: Zahlentheorie [[[:Template:Webarchive]]]. 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"/>

Further reading

• Template:Cite encyclopedia
• 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, {{#invoke:CS1 identifiers|main|_template=doi}}.
• Problèmes plaisans et délectables, qui se font par les nombres – digital copy at the Library of Congress