# G. H. Hardy quotes

Young Men should prove theorems, old men should write books.
In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy.
It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.
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.
A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.
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 play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
Real mathematics must be justified as art if it can be justified at all.
I am interested in mathematics only as a creative art.

### G. H. Hardy about Importance, Writing, Beauty

##### Also about

Mathematics, Music, Science, Glory, Ideas
I wrote a great deal... but very little of any importance; there are not more than four of five papers which I can still remember with some satisfaction.
Beauty is the first test: there is no permanent place in the world for ugly mathematics.
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.
The fact is that there are few more "popular" subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances may suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.
Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.

### G. H. Hardy about Criticism, Inspiration, Achievements

There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.
A person's first duty, a young person's at any rate, is to be ambitious, and the noblest ambition is that of leaving behind something of permanent value.