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All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.
Leopold Kronecker -
What good your beautiful proof on the transcendence of Pi: Why investigate such problems, given that irrational numbers do not even exist?
Leopold Kronecker
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Analysis does not owe its really significant successes of the last century to any mysterious use of sqrt(-1), but to the quite natural circumstances that one has infinitely more freedom of mathematical movement if he lets quantities vary in a plane instead of only on a line.
Leopold Kronecker -
Number theorists are like lotus-eaters -- having once tasted of this food they can never give it up.
Leopold Kronecker -
Definitions must contain the means of reaching a decision in a finite number off steps, and existence proofs must be conducted so that the quantity in question can be calculated with any degree of accuracy.
Leopold Kronecker -
God made the integers, man made the rest.
Leopold Kronecker -
God made the natural numbers; all else is the work of man.
Leopold Kronecker -
Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.
Leopold Kronecker