"The function of a mathematician, then, is simply to observe the facts about his own intricate system of reality, that astonishingly beautiful complex of logical relations which forms the subject-matter of his science, as if he were an explorer looking at a distant range of mountains, and to record the results of his observations in a series of maps, each of which is a branch of pure mathematics. […] Among them there perhaps none quite so fascinating, with quite the astonishing contrasts of sharp outline and shade, as that which constitutes the theory of numbers." (Godfrey H. Hardy, "The Theory of Numbers", Nature 1922)
"I have myself always thought of a mathematician as in the first instance an observer, a man who gazes at a distant range of mountains and notes down his observations. His object is simply to distinguish clearly and notify to others as many different peaks as he can.” (Godfrey H Hardy, “Mathematical Proof”, Mind 38, 1929)
“[…] there is probably less difference between the positions of a mathematician and of a physicist than is generally supposed, [...] the mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as 'real', but [...] [a physicist] is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics.” (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
"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 as beautiful –‘important’ if you like, but the word is very ambiguous, and ‘serious’ expresses what I mean much better.” (Godfrey H Hardy, “A Mathematician's Apology”, 1940)
"A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.“ (Godfrey H Hardy, “A Mathematician’s Apology”, 1940)
"A mathematician, like a painter or a poet, is a maker of patterns. [...]. 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." (Godfrey H Hardy, “A Mathematician's Apology”, 1940)
"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 the notes of our observations." (Godfrey H Hardy, “A Mathematician's Apology”, 1940)
„In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.” (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
"It is a melancholic experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done [...] 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.“ (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
“Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon.” (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
“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.” (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
"The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done." (Godfrey H Hardy, “A Mathematician’s Apology”, 1940)
“When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge […]” (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
"[…] a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences." (Godfrey H Hardy)
"The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations.” (Godfrey H Hardy)
"I have myself always thought of a mathematician as in the first instance an observer, a man who gazes at a distant range of mountains and notes down his observations. His object is simply to distinguish clearly and notify to others as many different peaks as he can.” (Godfrey H Hardy, “Mathematical Proof”, Mind 38, 1929)
“[…] there is probably less difference between the positions of a mathematician and of a physicist than is generally supposed, [...] the mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as 'real', but [...] [a physicist] is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics.” (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
"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 as beautiful –‘important’ if you like, but the word is very ambiguous, and ‘serious’ expresses what I mean much better.” (Godfrey H Hardy, “A Mathematician's Apology”, 1940)
"A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.“ (Godfrey H Hardy, “A Mathematician’s Apology”, 1940)
"A mathematician, like a painter or a poet, is a maker of patterns. [...]. 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." (Godfrey H Hardy, “A Mathematician's Apology”, 1940)
"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 the notes of our observations." (Godfrey H Hardy, “A Mathematician's Apology”, 1940)
„In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.” (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
"It is a melancholic experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done [...] 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.“ (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
“Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon.” (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
“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.” (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
"The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done." (Godfrey H Hardy, “A Mathematician’s Apology”, 1940)
“When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge […]” (Godfrey H Hardy, "A Mathematician's Apology“, 1940)
"[…] a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences." (Godfrey H Hardy)
"The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations.” (Godfrey H Hardy)
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