Joseph-Louis Lagrange was an Italian-born mathematician, later naturalized French, who made significant contributions to analysis, number theory, and both classical and celestial mechanics, developing Lagrangian mechanics and the calculus of variations. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
BirthplaceTurin, Kingdom of Sardinia 1 Death PlaceParis, First French Empire 1 Nationality / CultureItalian, later naturalized French 1 Notable WorkTransformed Newtonian mechanics into analytical (Lagrangian) mechanics and proved Lagrange's theorem in group theory. 1 AwardGrand Officer of the Legion of Honour and Count of the Empire (1808); Grand Croix of the Ordre Imperial de la Reunion (1813); buried in the Pantheon; name on the Eiffel Tower. 1 Disputed
Defining ContributionLagrange stated, for permutations of polynomial variables, that the number of distinct polynomials obtained is always a factor of n!, the special case later generalized into the theorem bearing his name. 2 Lagrange's name is attached to the theorem that a finite group's subgroup order divides the group's order, but he stated only a special case about permutations of polynomial variables; the general statement for all groups was proved later, by Camille Jordan in 1861. Connections
Namesake Of
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Proofs Credited
Why this is disputed. Lagrange stated only the special case for permutations of polynomial variables; he did not prove the general theorem that bears his name.
Source Lagrange's Theorem, Group Theory (Wikipedia)
Sources
1. Joseph-Louis Lagrange (Wikipedia)
Wikimedia Foundationlead paragraph
He made significant contributions to the fields of analysis, number theory, and both classical and celestial mechanics.
infobox
Italian and naturalized French
infobox/opening paragraph
Joseph-Louis Lagrange ... was an Italian and naturalized French mathematician, physicist and astronomer.
Scientific Contribution section
Lagrange is best known for transforming Newtonian mechanics into a branch of analysis, Lagrangian mechanics.
infobox IPA
UK: /læˈɡrɒ̃ʒ/, US: /ləˈɡreɪndʒ, ləˈɡrɑːndʒ, ləˈɡrɒ̃ʒ/; French: [ʒozɛf lwi laɡʁɑ̃ʒ]
Prizes and Distinctions section
He was awarded the Grand Croix of the Ordre Imperial de la Reunion in 1813, a week before his death in Paris, and was buried in the Pantheon, a mausoleum dedicated to the most honoured French people.
Lead section, gender reference
He made significant contributions to the fields of analysis, number theory, and both classical and celestial mechanics.
View the Source 2. Lagrange's Theorem, Group Theory (Wikipedia)
Wikimedia FoundationHistory sectionQuote, History section
Lagrange himself did not prove the theorem in its general form
Dissenting Readings (1 dissenting reading)
Proofs Credited: Lagrange's Theorem (Group Theory)
Lagrange's own 1771 paper (Reflexions sur la resolution algebrique des equations) proves only a special case, about the number of distinct polynomials produced by permuting the variables of a polynomial in n variables, always a factor of n!. The general theorem, that the order of any subgroup of a finite group divides the order of the group, was not established by Lagrange himself. It was proved for all permutation groups only in 1861, by Camille Jordan, after partial extensions by Gauss in 1801 and Cauchy in 1844. Attributing the general theorem to Lagrange by eponym overstates what Lagrange actually proved.
A dissenting reading, from a reviewerLagrange's Theorem, Group Theory (Wikipedia), Wikimedia Foundation
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