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A man who has been shot at is a new realist, and what do you say to a realist when the war is a war of ideals?

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G. H. Hardy

If I could prove by logic that you would die in five minutes, I should be sorry you were going to die, but my sorrow would be very much mitigated by pleasure in the proof.

Logic, Minutes, Prove, Sorrow, Sorry, Would Be
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I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.

Believe, Describe, Discover, Lying, Mathematical, Science

All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.

Half, Hunting, Math, Spend, Use

I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways. "

Hoped, Lying, Numbers, Remember, Two, Unfavourable

It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.

Enough, Intelligent, Knowledge, Men, People, Worth

I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world. . . Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.

Creating, Differences, Escaping, Judged, Triviality
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