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This is my endlessly recurrent temptation: to go down to that Sea, and there neither dive nor swim nor float, but only dabble and splash, careful not to get out of my depth and holding on to the lifeline which connects me with my things temporal.

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G. H. Hardy

Mathematics may, like poetry or music, "promote and sustain a lofty habit of mind. "

Habit, Like, Lofty, May, Mind, Science
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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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