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.)
More Quotes from 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
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.
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
The infinitely competent can be uncreative.
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
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
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