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.
More Quotes from J. E. Littlewood:
A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.J. E. Littlewood
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.)
J. E. Littlewood
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'.
J. E. Littlewood
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.
J. E. Littlewood
A precisian professor had the habit of saying '... quartic polynomial ax4bx3cx2dxe, where e need not be the base of the natural logarithms.'
J. E. Littlewood
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.
J. E. Littlewood
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