Pierre Laurent Wantzel (5 June 1814 in Paris – 21 May 1848 in Paris) was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge.[1]
The solution to these problems had been sought for thousands of years, particularly by the ancient Greeks. However, Wantzel's work was neglected by his contemporaries and essentially forgotten. Indeed, it was only 50 years after its publication that Wantzel's article was mentioned either in a journal article[3] or in a textbook.[4] Before that, it seems to have been mentioned only once, by Julius Petersen, in his doctoral thesis of 1871. It was probably due to an article published about Wantzel by Florian Cajori more than 80 years after the publication of Wantzel's article[1] that his name started to be well known among mathematicians.[5]
Wantzel was also the first person to prove, in 1843,[6] that if a cubic polynomial with rational coefficients has three real roots but is irreducible in Q[x] (the so-called casus irreducibilis), then the roots cannot be expressed from the coefficients using real radicals alone; that is, complex non-real numbers must be involved if one expresses the roots from the coefficients using radicals. This theorem would be rediscovered decades later by (and sometimes attributed to) Vincenzo Mollame and Otto Hölder.
Ordinarily he worked evenings, not lying down until late; then he read, and took only a few hours of troubled sleep, making alternately wrong use of coffee and opium, and taking his meals at irregular hours until he was married. He put unlimited trust in his constitution, very strong by nature, which he taunted at pleasure by all sorts of abuse. He brought sadness to those who mourn his premature death.
Wantzel is often overlooked for his contributions to mathematics.[7] In fact, for over a century there was great confusion as to who proved the impossibility theorems.[8]
^Wantzel, L. (1837), "Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas" [Investigations into means of knowing if a problem of geometry can be solved with a straightedge and compass], Journal de Mathématiques Pures et Appliquées (in French), 2: 366–372
^Echegaray, José (1887), "Metodo de Wantzel para conocer si un problema puede resolverse con la recta y el circulo", Revista de los Progresos de las Ciencias Exactas, Físicas y Naturales (in Spanish), 22: 1–47
^Echegaray, José (1887), (PDF) (in Spanish), Imprenta de la Viuda é Hijo de D. E. Aguado, archived from the original (PDF) on 4 June 2016, retrieved 15 May 2016
^Lützen, Jesper (2009), "Why was Wantzel overlooked for a century? The changing importance of an impossibility result", Historia Mathematica, 36 (4): 374–394, doi:10.1016/j.hm.2009.03.001
^Wantzel, M. L. (1843), "Classification des nombres incommensurables d'origine algébrique" (PDF), Nouvelles Annales de Mathématiques (in French), 2: 117–127
^"ScienceDirect.com | Science, health and medical journals, full text articles and books". www.sciencedirect.com. Retrieved 2023-09-10.
^"TANGENT:", Tales of Impossibility, Princeton University Press, pp. 34–37, 2019-10-08, retrieved 2023-09-10
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French Wikisource has original text related to this article:
Pierre-Laurent Wantzel
Profile from School of Mathematics and Statistics; University of St Andrews, Scotland
January 01, 1970
pierre, wantzel, pierre, laurent, wantzel, june, 1814, paris, 1848, paris, french, mathematician, proved, that, several, ancient, geometric, problems, were, impossible, solve, using, only, compass, straightedge, pierre, laurent, wantzelborn, 1814, june, 1814pa. Pierre Laurent Wantzel 5 June 1814 in Paris 21 May 1848 in Paris was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge 1 Pierre Laurent WantzelBorn 1814 06 05 5 June 1814Paris FranceDied21 May 1848 1848 05 21 aged 33 Paris FranceNationalityFrenchKnown forSolving several ancient Greek geometry problemsScientific careerFieldsMathematics Geometry In a paper from 1837 2 Wantzel proved that the problems of doubling the cube and trisecting the angle are impossible to solve if one uses only compass and straightedge In the same paper he also solved the problem of determining which regular polygons are constructible a regular polygon is constructible if and only if the number of its sides is the product of a power of two and any number of distinct Fermat primes i e that the sufficient conditions given by Carl Friedrich Gauss are also necessary The solution to these problems had been sought for thousands of years particularly by the ancient Greeks However Wantzel s work was neglected by his contemporaries and essentially forgotten Indeed it was only 50 years after its publication that Wantzel s article was mentioned either in a journal article 3 or in a textbook 4 Before that it seems to have been mentioned only once by Julius Petersen in his doctoral thesis of 1871 It was probably due to an article published about Wantzel by Florian Cajori more than 80 years after the publication of Wantzel s article 1 that his name started to be well known among mathematicians 5 Wantzel was also the first person to prove in 1843 6 that if a cubic polynomial with rational coefficients has three real roots but is irreducible in Q x the so called casus irreducibilis then the roots cannot be expressed from the coefficients using real radicals alone that is complex non real numbers must be involved if one expresses the roots from the coefficients using radicals This theorem would be rediscovered decades later by and sometimes attributed to Vincenzo Mollame and Otto Holder Ordinarily he worked evenings not lying down until late then he read and took only a few hours of troubled sleep making alternately wrong use of coffee and opium and taking his meals at irregular hours until he was married He put unlimited trust in his constitution very strong by nature which he taunted at pleasure by all sorts of abuse He brought sadness to those who mourn his premature death Adhemar Jean Claude Barre de Saint Venant on the occasion of Wantzel s death 1 Wantzel is often overlooked for his contributions to mathematics 7 In fact for over a century there was great confusion as to who proved the impossibility theorems 8 References edit a b c Cajori Florian 1918 Pierre Laurent Wantzel Bull Amer Math Soc 24 7 339 347 doi 10 1090 s0002 9904 1918 03088 7 MR 1560082 Wantzel L 1837 Recherches sur les moyens de reconnaitre si un Probleme de Geometrie peut se resoudre avec la regle et le compas Investigations into means of knowing if a problem of geometry can be solved with a straightedge and compass Journal de Mathematiques Pures et Appliquees in French 2 366 372 Echegaray Jose 1887 Metodo de Wantzel para conocer si un problema puede resolverse con la recta y el circulo Revista de los Progresos de las Ciencias Exactas Fisicas y Naturales in Spanish 22 1 47 Echegaray Jose 1887 Disertaciones matematicas sobre la cuadratura del circulo El metodo de Wantzel y la division de la circunferencia en partes iguales PDF in Spanish Imprenta de la Viuda e Hijo de D E Aguado archived from the original PDF on 4 June 2016 retrieved 15 May 2016 Lutzen Jesper 2009 Why was Wantzel overlooked for a century The changing importance of an impossibility result Historia Mathematica 36 4 374 394 doi 10 1016 j hm 2009 03 001 Wantzel M L 1843 Classification des nombres incommensurables d origine algebrique PDF Nouvelles Annales de Mathematiques in French 2 117 127 ScienceDirect com Science health and medical journals full text articles and books www sciencedirect com Retrieved 2023 09 10 TANGENT Tales of Impossibility Princeton University Press pp 34 37 2019 10 08 retrieved 2023 09 10External links edit nbsp French Wikisource has original text related to this article Pierre Laurent Wantzel Profile from School of Mathematics and Statistics University of St Andrews Scotland Retrieved from https en wikipedia org w index php title Pierre Wantzel amp oldid 1222449733, wikipedia, wiki, book, books, library,
