What good your beautiful proof on the transcendence of Pi: Why investigate such problems, given that irrational numbers do not even exist?
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.
Die ganzen Zahlen hat der liebe Gatt gemacht, alles andere ist Menschenwerk.
The dear God has made the whole numbers, all the rest is man's work.
The Good Lord made all the integers; the rest is man's doing.
God made the natural numbers; all else is the work of man
Number theorists are like lotus-eaters -- having once tasted of this food they can never give it up.
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.
All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.
God made the integers, man made the rest.
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