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Leopold Kronecker
(7 Dec 1823 - 29 Dec 1891)
German mathematician.
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Science Quotes by Leopold Kronecker (4 quotes)
Almost everything, which the mathematics of our century has brought forth in the way of original scientific ideas, attaches to the name of Gauss.
— Leopold Kronecker
In Zahlentheorie, Teil 1 (1901), 43.
Number theorists are like lotus-eaters—having tasted this food they can never give it up.
— Leopold Kronecker
As quoted in Howard Eves, Mathematical Circles Squared (1972), 149. In Homer’s The Odyssey, lotus-eaters live in a state of dreamy forgetfulness and idleness from eating lotus fruit. Thus a lotus-eater pursues pleasure and luxury rather than dealing with practical concerns.
The whole numbers have been made by dear God, everything else is the work of man.
— Leopold Kronecker
Also often seen as “God made the integers, all else is the work of man.” From the original German, “Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk,” in Speech (1886) to the Berliner Naturforscher-Versammlung (Berlin Conference of Natural Scientists). As quoted by H. Weber, in obituary, 'Leopold Kronecker', Jahresbericht der Deutschen Mathematiker-Vereinigung (1893), 2, 19. (Yearbook of the German Mathematics Association.) In a message (26 May 1999) to the 'Historia Mathematica' mailing list, German mathematician Walter Felscher explained that “liebe Gott” (Dear God) is “a colloquial phrase usually used only when speaking to children.” When spoken to an adult audience, it signals that the statement is merely a witticism. Equally, it could have been expressed as “About the integers let us not ask, but all the rest came about by men.” Thus, the statement does not mean that Kronecker believed integers had a divine, pre-human origin. Therefore it should not be regarded as challenging “Dedekind’s viewpoint that also the integers are man-made (i.e. man-invented).”
What good your beautiful proof on [the transcendence of] π? Why investigate such problems, given that irrational numbers do not even exist?
— Leopold Kronecker
Quotes by others about Leopold Kronecker (2)
Our knowledge of the external world must always consist of numbers, and our picture of the universe—the synthesis of our knowledge—must necessarily be mathematical in form. All the concrete details of the picture, the apples, the pears and bananas, the ether and atoms and electrons, are mere clothing that we ourselves drape over our mathematical symbols— they do not belong to Nature, but to the parables by which we try to make Nature comprehensible. It was, I think, Kronecker who said that in arithmetic God made the integers and man made the rest; in the same spirit, we may add that in physics God made the mathematics and man made the rest.
From Address (1934) to the British Association for the Advancement of Science, Aberdeen, 'The New World—Picture of Modern Physics'. Printed in Nature (Sep 1934) 134, No. 3384, 356. As quoted and cited in Wilbur Marshall Urban, Language and Reality: The Philosophy of Language and the Principles of Symbolism (2004), Vol. 15, 542.
Objections … inspired Kronecker and others to attack Weierstrass’ “sequential” definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth—whatever that may be, if anything—precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals.
In Men of Mathematics (1937), 431-432.
See also:
- 7 Dec - short biography, births, deaths and events on date of Kronecker's birth.
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) -- 
