G.H. Hardy

1877–1947 · British mathematician

Topics: mathematics, creativity, learning

• [[Pure mathematics|[P]ure 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

• A man who could give a convincing account of mathematical reality would have solved very many of the most difficult problems of metaphysics. If he could include physical reality in his account, he would have solved them all.

  — G.H. Hardy

• The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

  — G.H. Hardy

• A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

  — G.H. Hardy

• Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

  — G.H. Hardy

• Chess problems are the hymn-tunes of mathematics.

  — G.H. Hardy

• [M]athematical reality lies outside us

  — 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

• It is... natural to suppose that there is a great difference in utility between 'pure' and 'applied' mathematics. This is a delusion...

  — G.H. Hardy

• I am interested in mathematics only as a creative art.

  — G.H. Hardy

• [T]here is no mathematician so pure that he feels no interest at all in the physical world; but, in so far as he succumbs to this temptation, he will be abandoning his purely mathematical position.

  — 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 so, because mathematical reality is built that way.

  — G.H. Hardy