Joseph Louis Lagrange: Geometry

Joseph Louis Lagrange was Italian mathematician and mathematical physicist. Explore interesting quotes on geometry.
Joseph Louis Lagrange: 12 quotes5 likes

“I cannot say whether I will still be doing geometry ten years from now. It also seems to me that the mine has maybe already become too deep and unless one finds new veins it might have to be abandoned. Physics and chemistry now offer a much more glowing richness and much easier exploitation. Also, the general taste has turned entirely in this direction, and it is not impossible that the place of Geometry in the Academies will someday become what the role of the Chairs of Arabic at the universities is now.”

Joseph Louis Lagrange

Letter to d'Alembert (1781) cited in R. Laubenbacher, D. Pengelly: Mathematical Expeditions: Chronicles by the Explorers (1999) Springer, pp. 233–234.

“An ancient writer said that arithmetic and geometry are the wings of mathematics; I believe one can say without speaking metaphorically that these two sciences are the foundation and essence of all the sciences which deal with quantity. Not only are they the foundation, they are also, as it were, the capstones; for, whenever a result has been arrived at, in order to use that result, it is necessary to translate it into numbers or into lines; to translate it into numbers requires the aid of arithmetic, to translate it into lines necessitates the use of geometry.”

Joseph Louis Lagrange

Dans Les Leçons Élémentaires sur les Mathématiques (1795) Leçon cinquiéme, Tr. McCormack, cited in Moritz, Memorabilia mathematica or, The philomath's quotation-book (1914) Ch. 15 Arithmetic, p. 261. https://archive.org/stream/memorabiliamathe00moriiala#page/260/mode/2up

“As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection.”

Joseph Louis Lagrange

Dans Les Leçons Élémentaires sur les Mathématiques (1795) Leçon cinquiéme,Tr. McCormack, cited in Robert Edouard Moritz, Memorabilia mathematica or, The philomath's quotation-book (1914) Ch. V The teaching of mathematics, p. 81. https://archive.org/stream/memorabiliamathe00moriiala#page/80/mode/2up