J. E. Littlewood Quotes (14 Quotes)

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.

A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.

The infinitely competent can be uncreative.

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 precisian professor had the habit of saying '... quartic polynomial ax4bx3cx2dxe, where e need not be the base of the natural logarithms.'

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

I constantly meet people who are doubtful, generally without due reason, about their potential capacity as mathematicians. The first test is whether you got anything out of geometry. To have disliked or failed to get on with other mathematical subjects need mean nothing much drill and drudgery is unavoidable before they can get started, and bad teaching can make them unintelligible even to a born mathematician.

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.

I recall once saying that when I had given the same lecture several times I couldn't help feeling that they really ought to know it by now.

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.

It is true that I should have been surprised in the past to learn that Professor Hardy had joined the Oxford Group. But one could not say the adverse chance was 110. Mathematics is a dangerous profession an appreciable proportion of us go mad, and then this particular event would be quite likely.

It is possible for a mathematician to be 'too strong' for a given occasion. He forces through, where another might be driven to a different, and possible more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)

In passing, I firmly believe that research should be offset by a certain amount of teaching, if only as a change from the agony of research. The trouble, however, I freely admit, is that in practice you get either no teaching, or else far too much.

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'.