G. H. Hardy - Mathematical Quotes

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Most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.

G. H. Hardy
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 our notes of our observations.

G. H. Hardy
317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is, because mathematical reality is built that way.

G. H. Hardy
Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

G. H. Hardy
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.

G. H. Hardy
Pure mathematics is on the whole distinctly more useful than applied. [...] For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

G. H. Hardy
I do not know an instance of a major mathematical advance initiated by a man past fifty

G. H. Hardy
As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

G. H. Hardy
There is, strictly, no such thing as mathematical proof; that we can::: do nothing but point; that proofs are what Littlewood and I call gas, rhetorical flourishes designed to affect psychology, pictures on the board in the lectures, devices to stimulate the imagination of pupils.

G. H. Hardy
The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.

G. H. Hardy
We may say, roughly, that a mathematical idea is "significant" if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas.

G. H. Hardy
Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.

G. H. Hardy
A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.

G. H. Hardy