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Saturday, October 13, 2018

Joseph-Louis Lagrange and arithmetic


Photo source: Wikimedia Commons


Joseph-Louis Lagrange (1736-1813) was an Italian mathematician best known for his contributions to analysis, number theory and classical mechanics. Writer Johann Wolfgang von Goethe said,


"The mathematician is perfect only in so far as he is a perfect being, in so far as he perceives the beauty of truth; only then will his work be thorough, transparent, comprehensive, pure, clear, attractive and even elegant. All this is necessary to resemble Lagrange." (Wilhelm Meister's Wanderjahre, Zqeites Buck)


Mathematician Dirk Jan Struik said,


"Full use of Lagrange's own calculus of variations made the unification of the varied principles of statistics and dynamics possible - in statistics by the use for the principle of virtual velocities, in dynamics by the use of D'Alembert's principle." (A Concise History of Mathematics, 1948)


The rest of this post is some quotes from Lagrange.


Arithmetic and geometry


"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." (Dans Les Lecons Elementaires sur les Mathematiques, 1795)


"As long as algebra and geometry proceed 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." (Dans Les Lecons Elementaires sur les Mathematiques, 1795)


"We have already various treatises on Mechanics, but the plan of this one is entirely new... The methods that I explain require neither geometrical, nor mechanical, constructions or reasoning, but only algebraical operations in accordance with regular and uniform procedure." (Quoted in Mathematics, from the points of view of the Mathematician and of the Physicist, 1912)


Applied knowledge


"I regarded as quite useless the reading of large treatises of pure analysis: too large a number of methods pass at once before the eyes. It is in the works of application that one must study them; one judges their utility there and appraises the manner of making use of them." (Quoted in Moniteur Universel by J. F. Maurice)


History of science


"Newton was the greatest genius that ever existed, and the most fortunate, for we cannot find more than once a system of the world to establish." (Introduction to Astronomy by F. R. Moulton)


"It took them only an instant to cut off that head, but France may not produce another like it in a century." (Quoted in Annual Editions: Western Civilization by William Hughes regarding the beheading of Antoine Lavoisier)