G. H. Hardy
G. H. Hardy
Godfrey Harold "G. H." Hardy FRS was an English mathematician, known for his achievements in number theory and mathematical analysis...
NationalityBritish
ProfessionMathematician
Date of Birth7 February 1877
real silly exercise
If a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that it would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields. Such a sacrifice could be justified only by economic necessity of age.
taught technique 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.
science reality common-sense
The mathematician is in much more direct contact with reality. ... [Whereas] the physicist's reality, whatever it may be, has few or none of the attributes which common sense ascribes instinctively to reality. A chair may be a collection of whirling electrons.
believe mathematician ifs
Asked if he believes in one G-d, a mathematician answered: "Yes, up to isomorphism".
good-man example waste
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 proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.
beauty math apology
Beauty is the first test: there is no permanent place in the world for ugly mathematics.
beautiful math patterns
The mathematician's patterns, like the painter's or the poet's, must be beautiful.
art real justified
Real mathematics must be justified as art if it can be justified at all.
humble eye hard-work
Good work is no done by "humble" men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking "Is what I do worth while?" and "Am I the right person to do it?" will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly.
art past men
No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. ... Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; ... [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. ... A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.
blow ramanujan suggestions
For my part, it is difficult for me to say what I owe to Ramanujan - his originality has been a constant source of suggestion to me ever since I knew him, and his death is one of the worst blows I have ever had.
math original-ideas patterns
A mathematician, like a painter or a poet, is a maker of patterns.
knowledge science simplicity
Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.
passion science boys
I do not remember having felt, as a boy, any passion for mathematics, and such notions as I may have had of the career of a mathematician were far from noble. I thought of mathematics in terms of examinations and scholarships: I wanted to beat other boys, and this seemed to be the way in which I could do so most decisively.