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Home > Dictionary of Science Quotations > Scientist Names Index J > Karl Jacobi Quotes

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Karl Jacobi
(10 Dec 1804 - 18 Feb 1851)

German mathematician.


Science Quotes by Karl Jacobi (7 quotes)

Man muss immer generalisieren
One must always generalize.
— Karl Jacobi
Quoted, without citation, in Arnold Dresden, An Invitation to Mathematics (1936), 231. Dresden states this is a “principle usually attributed to Jacobi”.
Science quotes on:  |  Generalize (15)

God ever arithmetizes.
— Karl Jacobi
As quoted, without citation, in Eric Temple Bell, Men of Mathematics (1937), Vol. 2, 21, and in Joseph Jastrow, The Story of Human Error (1936), 163. Both authors also compare the quote to Plato, “God ever geometrizes”.
Science quotes on:  |  God (535)

It is often more convenient to possess the ashes of great men than to possess the men themselves during their lifetime.
— Karl Jacobi
Commenting on the return of Descartes’ remains to France. Quoted, without citation, in Eric Temple Bell Men of Mathematics (1937), 52.
Science quotes on:  |  Ash (19)  |  Convenience (34)  |  Great (534)  |  Lifetime (28)  |  Man (373)  |  Often (106)  |  Possess (56)

It is true that Fourier had the opinion that the principal end of mathematics was public utility and the explanation of natural phenomena; but a philosopher as he is should have known that the unique end of science is the honor of the human mind and that from this point of view a question of [the theory of] number is as important as a question of the system of the world.
— Karl Jacobi
From letter to Legendre, translation as given in F.R. Moulton, 'The Influence of Astronomy on Mathematics', Science (10 Mar 1911), N.S. Vol. 33, No. 845, 359. A different translation begins, “It is true that M. Fourier believed…” on the Karl Jacobi Quotes web page on this site.
Science quotes on:  |  End (195)  |  Explanation (177)  |  Baron Jean-Baptiste-Joseph Fourier (17)  |  Honor (31)  |  Human (550)  |  Important (205)  |  Mathematics (1205)  |  Mind (760)  |  Natural (173)  |  Opinion (176)  |  Phenomenon (278)  |  Philosopher (166)  |  Point Of View (41)  |  Principal (28)  |  Public (94)  |  Question (404)  |  Science (2067)  |  System (191)  |  Theory Of Numbers (5)  |  Unique (41)  |  Utility (33)  |  World (898)

It is true that M. Fourier believed that the main aim of mathematics was public utility and the explanation of natural phenomena; but a philosopher of his ability ought to have known that the sole aim of science is the honour of the human intellect, and that on this ground a problem in numbers is as important as a problem on the system of the world.
— Karl Jacobi
In Letter to Legendre, as quoted in an Address by Emile Picard to the Congress of Science and Art, St. Louis (22 Sep 1904), translated in 'Development of Mathematical Analysis', The Mathematical Gazette (Jul 1905), 3, No. 52, 200. A different translation begins, “It is true that Fourier had the opinion…” on the Karl Jacobi Quotes web page on this site.
Science quotes on:  |  Aim (89)  |  End (195)  |  Explanation (177)  |  Fourier (5)  |  Honor (31)  |  Human Mind (82)  |  Know (556)  |  Mathematics (1205)  |  Natural (173)  |  Number (282)  |  Opinion (176)  |  Phenomenon (278)  |  Philosopher (166)  |  Principal (28)  |  Public (94)  |  Question (404)  |  Science (2067)  |  Sole (21)  |  System (191)  |  Title (18)  |  True (208)  |  Utility (33)  |  World (898)  |  Worth (99)

Mathematics is the science of what is clear by itself.
— Karl Jacobi
As quoted in James R. Newman (ed.) The World of Mathematics (1956), 1747. From by the original German, “Die Math, als Wissenschaft von dem, was sich von selbst versteht”, in Maximilian Simon, Didaktik und Methodik des Rechnens und der Mathematik (1908), 37, which cites Jacobi, Inaugural Speech, Königsberg (7 Jul 1832).
Science quotes on:  |  Clear (98)  |  Doctrine (75)  |  Mathematics (1205)  |  Science (2067)

The sole end of science is the honor of the human mind.
— Karl Jacobi
From Letter to Legendre, as quoted in an Address by Emile Picard to the Congress of Science and Art, St. Louis (22 Sep 1904), translated in 'Development of Mathematical Analysis', The Mathematical Gazette (Jul 1905), 3, No. 52, 200. The word “sole” is also seen translated as “unique” or “real”. This is part of a longer quote which begins, “It is true that M. Fourier believed that…” on the Karl Jacobi Quotes web page on this site.
Science quotes on:  |  End (195)  |  Honor (31)  |  Human Mind (82)  |  Real (149)  |  Science (2067)  |  Sole (21)  |  Unique (41)



Quotes by others about Karl Jacobi (3)

Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence”.
In 'A Plea for the Mathematician', Nature, 1, 238 in Collected Mathematical Papers, Vol. 2, 655-56.
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It is said of Jacobi, that he attracted the particular attention and friendship of Böckh, the director of the philological seminary at Berlin, by the great talent he displayed for philology, and only at the end of two years’ study at the University, and after a severe mental struggle, was able to make his final choice in favor of mathematics.
In Collected Mathematical Papers, Vol. 2 (1908), 661.
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Ultima se tangunt. How expressive, how nicely characterizing withal is mathematics! As the musician recognizes Mozart, Beethoven, Schubert in the first chords, so the mathematician would distinguish his Cauchy, Gauss, Jacobi, Helmholtz in a few pages.
In Ceremonial Speech (15 Nov 1887) celebrating the 301st anniversary of the Karl-Franzens-University Graz. Published as Gustav Robert Kirchhoff: Festrede zur Feier des 301. Gründungstages der Karl-Franzens-Universität zu Graz (1888), 29, as translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 186-187. From the original German, “Ultima se tangunt. Und wie ausdrucksfähig, wie fein charakterisirend ist dabei die Mathematik. Wie der Musiker bei den ersten Tacten Mozart, Beethoven, Schubert erkennt, so würde der Mathematiker nach wenig Seiten, seinen Cauchy, Gauss, Jacobi, Helmholtz unterscheiden.” [The Latin words translate as “the final touch”. —Webmaster]
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See also:
  • 10 Dec - short biography, births, deaths and events on date of Jacobi's birth.

Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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