Medicine makes people ill, mathematics make them sad and theology makes them sinful.

Medicine makes people ill, mathematics make them sad and theology makes them sinful.

[M]athematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.

In D. Burton,
Elementary Number
Theory, Boston:
Allyn and Bacon,
1980.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

In N. Rose,
Mathematical Maxims
and Minims, Raleigh
NC: Rome Press Inc.,
1988.

The theory of numbers is particularly liable to the accusation that some of its problems are the wrong sort of questions to ask. I do not myself think the danger is serious; either a reasonable amount of concentration leads to new ideas or methods of obvious interest, or else one just leaves the problem alone. "Perfect numbers" certainly never did any good, but then they never did any particular harm.

A Mathematician's
Miscellany, Methuen
Co. Ltd., 1953.

We come finally, however, to the relation of the ideal theory to real world, or "real" probability. If he is consistent a man of the mathematical school washes his hands of applications. To someone who wants them he would say that the ideal system runs parallel to the usual theory: "If this is what you want, try it: it is not my business to justify application of the system; that can only be done by philosophizing; I am a mathematician." In practice he is apt to say: "Try this; if it works that will justify it." But now he is not merely philosophizing; he is committing the characteristic fallacy. Inductive experience that the system works is not evidence.

I read in the proof sheets of Hardy on Ramanujan: "As someone said, each of the positive integers was one of his personal friends." My reaction was, "I wonder who said that; I wish I had." In the next proof sheets I read (what now stands), "It was Littlewood who said ..."

A Mathematician's
Miscellany, Methuen
Co. Ltd, 1953.

The surprising thing about this paper is that a man who could write it would.

A Mathematician's
Miscellany, Methuen
Co. Ltd., 1953.

A precisian professor had the habit of saying: "... quartic polynomial ax^4+bx^3+cx^2+dx+e, where e need not be the base of the natural logarithms."

A linguist would be shocked to learn that if a set is not closed this does not mean that it is open, or again that "E is dense in E" does not mean the same thing as "E is dense in itself."

In presenting a mathematical argument the great thing is to give the educated reader the chance to catch on at once to the momentary point and take details for granted: his successive mouthfuls should be such as can be swallowed at sight; in case of accidents, or in case he wishes for once to check in detail, he should have only a clearly circumscribed little problem to solve (e.g. to check an identity: two trivialities omitted can add up to an impasse). The unpractised writer, even after the dawn of a conscience, gives him no such chance; before he can spot the point he has to tease his way through a maze of symbols of which not the tiniest suffix can be skipped.

A Mathematician's Miscellany, Methuen Co. Ltd., 1953.