I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that… — G. H. Hardy Copy Share Image
A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well… — G. H. Hardy Copy Share Image
Cricket is the only game where you are playing against eleven of the other side and ten of your own. — G. H. Hardy Copy Share Image
The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas… — G. H. Hardy Copy Share Image
No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity… — G. H. Hardy Copy Share Image
It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something,… — G. H. Hardy Copy Share Image
Beauty is the first test: there is no permanent place in the world for ugly mathematics. — G. H. Hardy Copy Share Image
They [formulae 1.10 - 1.12 of Ramanujan] must be true because, if they were not true, no one would have had the imagination to invent them. — G. H. Hardy Copy Share Image
When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the… — G. H. Hardy Copy Share Image
Asked if he believes in one G-d, a mathematician answered: "Yes, up to isomorphism". — G. H. Hardy Copy Share Image
No one should ever be bored. … One can be horrified, or disgusted, but one can’t be bored. — G. H. Hardy Copy Share Image
I propose to put forward an apology for mathematics; and I may be told that it needs none, since there are now few studies… — G. H. Hardy Copy Share Image
For my part, it is difficult for me to say what I owe to Ramanujan - his originality has been a constant source of… — G. H. Hardy Copy Share Image
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they… — G. H. Hardy Copy Share Image
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