The infinitely competent can be uncreative.
More Quotes from 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
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.
J. E. Littlewood
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.
J. E. Littlewood
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.
J. E. Littlewood
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...'
J. E. Littlewood
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