Joseph Louis Lagrange

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Joseph Louis Lagrange.

Joseph-Louis Lagrange, comte de l'Empire (January 25, 1736April 10, 1813) was an Italian-French mathematician and astronomer who made important contributions to all fields of analysis and number theory and to classical and celestial mechanics.


  • 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.
    • Lagrange, quoted by F. R. Moulton: Introduction to Astronomy (New York, 1906), p. 199.
  • 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.
  • 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.
    • Lagrange. Leçons Élémentaires sur les Mathematiques, Leçon cinquiéme. [McCormack]; Cited in: Moritz (1914, 261); Arithmetics
  • It took them only an instant to cut off that head, but France may not produce another like it in a century.
    • In: William Hughes (1997), Annual Editions: Western Civilization, p. 64 : About the beheading of his friend Antoine Lavoisier

Quotes about Lagrange[edit]

  • Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty [of the parallel axiom]. He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him which he had not observed : he muttered II faut que fy songe encore, and put the paper in his pocket.
    • Augustus De Morgan, Budget of Paradoxes, (London, 1872), p. 178; as cited in: Moritz (1914, 161); Persons and anecdotes
  • 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.
    • Johann Wolfgang von Goethe, Wilhelm Meister's Wanderjahre, Zweites Buck; Spriiche in Prosa; Natur, VI, 950; as cited in: Moritz (1914, 120); About the mathematician
  • The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.
    • W. W. Rouse Ball, History of Mathematics, (London, 1901), p. 463; as cited in: Moritz (1914, 160); Persons and anecdotes
  • Who has studied the works of such men as Euler, Lagrange, Cauchy, Riemann, Sophus Lie, and Weierstrass, can doubt that a great mathematician is a great artist? The faculties possessed by such men, varying greatly in kind and degree with the individual, are analogous with those requisite for constructive art. Not every mathematician possesses in a specially high degree that critical faculty which finds its employment in the perfection of form, hi conformity with the ideal of logical completeness; but every great mathematician possesses the rarer faculty of constructive imagination.
    • E. W. Hobson, "Presidential Address British Association for the Advancement of Science" (1910) in: Nature, Vol. 84, p. 290. Cited in: Moritz (1914, 182); Mathematics as a fine art

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