A Mathematician's Apology Quotes

“No one should ever be bored. One can be horrified, or disgusted, but one can't be bored.”
― G.H. Hardy, A Mathematician's Apology

“I am not suggesting that this is a defence which can be made by most people, since most people can do nothing at all well. But it is impregnable when it can be made without absurdity, as it can by a substantial minority: perhaps five or even ten percent of men can do something rather well. It is a tiny minority who can do something really well, and the number of men who can do two things well is negligible. If a man has any genuine talent he should be ready to make almost any sacrifice in order to cultivate it to the full.”
― G H Hardy, A Mathematician's Apology

“We have concluded that the trivial mathematics is, on the whole, useful, and that the real mathematics, on the whole, is not.”
― G.H. Hardy, A Mathematician's Apology

“It is the dull and elementary parts of applied mathematics, as it is the dull and elementary parts of pure mathematics, that work for good or ill. Time may change all this. No one foresaw the applications of matrices and groups and other purely mathematical theories to modern physics, and it may be that some of the 'highbrow' applied mathematics will become 'useful' in as unexpected a way; but the evidence so far points to the conclusion that, in one subject as in the other, it is what is commonplace and dull that counts for practical life.”
― G.H. Hardy, A Mathematician's Apology

“Judged by all practical standards, the value of my mathematical life is nil; and
outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of
complete triviality, that I may be judged to have created something worth creating. And
that I have created something is undeniable: the question is about its value.

The case for my life, then, or for that of any one else who has been a mathematician in the same sense in which I have been one, is this: that I have added something to knowledge, and helped others to add more; and that these somethings have a value which differs in degree only, and not in kind, from that of the creations of the great mathematicians, or of any of the other artists, great or small, who have left some kind of memorial behind them.”
― G.H. Hardy, A Mathematician's Apology

“I can remember Bertrand Russell telling me of a horrible dream. He was in the top floor of the University Library, about A.D. 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down books, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of Principia Mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated....”
― G.H. Hardy, A Mathematician's Apology

“If I had a statue on a column in London, would I prefer the columns to be so high that the statue was invisible, or low enough for the features to be recognizable? I would choose the first alternative, Dr Snow, presumably, the second.”
― G.H. Hardy, A Mathematician's Apology

“The play is independent of the pages on which it is printed, and ‘pure geometries’ are independent of lecture rooms, or of any other detail of the physical world.”
― G.H. Hardy, A Mathematician's Apology

“We must guard against a fallacy common among apologists of science, the fallacy of supposing that the men whose work most benefits humanity are thinking much of that while they do it, that physiologists, for example, have particularly noble souls.”
― G.H. Hardy, A Mathematician's Apology

“Αν η περιέργεια του πνεύματος, η επαγγελματική υπερηφάνεια και η φιλοδοξία είναι τα κύρια κίνητρα για την έρευνα, τότε σίγουρα κανείς δεν έχει πιο καλή ευκαιρία να τα ικανοποιήσει απ' ό,τι ένας μαθηματικός. Το αντικείμενό του είναι το πιο περίεργο απ' όλα - δεν υπάρχει κανένα άλλο στο οποίο η αλήθεια να παίζει τόσο παράξενα παιγνίδια. Το αντικείμενο αυτό έχει την πιο εκλεπτυσμένη και γοητευτική τεχνική, και δίνει ασυναγώνιστες ευκαιρίες για την επίδειξη μιας ανώτερης επαγγελματικής ικανότητας. Τελικά, όπως αποδεικνύει κατά πολλούς τρόπους η Ιστορία, τα μαθηματικά επιτεύγματα, ανεξάρτητα από την εγγενή τους αξία, αντέχουν στο χρόνο περισσότερο απ' όλα τα άλλα.
Μπορούμε να το δούμε αυτό, ακόμη και στους πρώιμους πολιτισμούς της Ιστορίας. Ο Βαβυλωνιακός και ο Ασσυριακός πολιτισμός έχουν χαθεί· ο Χαμουραμπί, ο Σαργκόν και ο Ναβουχοδονόσωρ είναι σκέτα ονόματα. Κι όμως, τα βαβυλωνιακά Μαθηματικά είναι ακόμη και σήμερα ενδιαφέροντα, και το βαβυλωνιακό σύστημα αρίθμησης με βάση το 60 χρησιμοποιείται ακόμη στην Αστρονομία. Αλλά φυσικά, η κρίσιμη περίπτωση είναι εκείνη των Ελλήνων.
Οι Έλληνες είναι οι πρώτοι μαθηματικοί που εξακολουθούν να είναι «πραγματικοί» και για μας σήμερα. Τα Μαθηματικά της Ανατολής μπορεί να προκαλούν το ενδιαφέρον, αλλά στα ελληνικά βρίσκεται η ουσία του πράγματος. Οι Έλληνες ήταν οι πρώτοι που μίλησαν με μια μαθηματική γλώσσα που μπορούν να την καταλάβουν οι σύγχρονοι μαθηματικοί. Όπως μου είπε κάποτε ο Littlewood, δεν πρόκειται για έξυπνους μαθητές σχολείου ούτε για «υποψήφιους υποτροφίας», αλλά για «Εταίρους από ένα άλλο πανεπιστήμιο». Έτσι, τα ελληνικά μαθηματικά είναι κάτι «μόνιμο», πιο μόνιμο και από την ελληνική Λογοτεχνία. Τον Αρχιμήδη θα τον θυμούνται ακόμη κι όταν ο Αισχύλος θά 'χει ξεχαστεί, επειδή οι γλώσσες πεθαίνουν ενώ οι μαθηματικές ιδέες όχι. Η «αθανασία» μπορεί να είναι μια ανόητη λέξη αλλά, κατά πάσα πιθανότητα, ένας μαθηματικός έχει περισσότερες ευκαιρίες για ό,τι μπορεί αυτή να σημαίνει.
Ο μαθηματικός δε χρειάζεται σοβαρά να φοβάται ότι το μέλλον θα τον αδικήσει. Η αθανασία είναι συχνά γελοία ή βάρβαρη: λίγοι από εμάς θα διάλεγαν να είναι ο Ωγ ή ο Ανανίας ή ο Γαλλίων. Ακόμη και στα Μαθηματικά, η ιστορία παίζει καμιά φορά περίεργες φάρσες. Ο Rolle ποζάρει στα βιβλία του Στοιχειώδους Λογισμού σαν να ήταν ένας μαθηματικός του διαμετρήματος του Νεύτωνα. Ο Farey είναι αθάνατος επειδή απέτυχε να κατανοήσει ένα θεώρημα που ο Haros είχε ήδη αποδείξει πριν από 14 χρόνια. Τα ονόματα πέντε άξιων Νορβηγών βρίσκονται ακόμη στον _Βίο_ του Abel, μόνο εξ αιτίας μιας ενέργειας ενσυνείδητης βλακείας που συνετελέσθη, από τυπολατρεία, εις βάρος του μεγαλύτερου άνδρα της χώρας τους. Αλλά, συνολικά, η ιστορία της επιστήμης είναι δίκαιη, και αυτό ισχύει ιδιαίτερα στα Μαθηματικά. Κανένα άλλο αντικείμενο μελέτης δεν έχει τόσο καθαρά οριοθετημένα ή ομόφωνα αποδεκτά υψηλά κριτήρι, και οι μαθηματικοί που θυμόμαστε είναι σχεδόν πάντα αυτοί που το αξίζουν. Η μαθηματική δόξα, αν μπορούσε να εξαγοραστεί, θα ήταν μια από τις πιο υγιείς και σταθερές επενδύσεις.”
― G.H. Hardy, A Mathematician's Apology

“Είναι μελαγχολική εμπειρία για έναν κατ' επάγγελμα μαθηματικό να βρεθεί στην θέση να γράφει για τα Μαθηματικά. Η λειτουργία ενός μαθηματικού είναι να δημιουργεί, να αποδεικνύει νέα θεωρήματα, να προσθέτει καινούργια πράγματα στα Μαθηματικά· και όχι να μιλά για τα επιτεύγματα του ίδιου ή άλλων μαθηματικών. Οι δημόσιοι άνδρες απεχθάνονται τους εκδότες, οι ζωγράφοι τους κριτικούς τέχνης, και οι γιατροί, οι φυσικοί, ή οι μαθηματικοί τρέφουν συνήθως για διάφορους παρόμοια συναισθήματα. Δεν υπάρχει πιο μεγάλος ψόγος, ή, εν γένει πιο δικαιολογημένος, από αυτόν που έχουν οι άνθρωποι που δημιουργούν για τους ανθρώπουν που αναλύουν. Η παρουσίαση, η κριτική, η εκτίμηση ενός πράγματος, θεωρείται έργο για μυαλά δευτέρας κατηγορίας.”
― G.H. Hardy, A Mathematician's Apology

“It is hardly possible to maintain seriously that the evil done by science is not altogether outweighed by the good. For example, if ten million lives were lost in every war, the net effect of science would still have been to increase the average length of life.”
― G.H. Hardy, A Mathematician's Apology

“3 A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it, whatever its value may be. The first question is often very difficult, and the answer very discouraging, but most people will find the second easy enough even then.”
― G.H. Hardy, A Mathematician’s Apology

“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.”
― G.H. Hardy, A Mathematician’s Apology

“A man who is always asking 'Is what I do worthwhile?' and 'Am I the right person to do it?' will always be ineffective himself and a discouragement to others.”
― G.H. Hardy, A Mathematician's Apology

“There is nothing that I can do particularly well. I do what I do because it came my way. I really never had a chance of doing anything else.’ And this apology too I accept as conclusive. It is quite true that most people can do nothing well. If so, it matters very little what career they choose, and there is really nothing more to say about it. It is a conclusive reply, but hardly one likely to be made by a man with any pride; and I may assume that none of us would be content with it.”
― G H Hardy, A Mathematician's Apology

“will end with a summary of my conclusions, but putting them in a more personal way. I said at the beginning that anyone who defends his subject will find that he is defending himself;”
― G.H. Hardy, A Mathematician’s Apology

“he had made such and such a move, then I had such and such a winning combination in mind.’ But the ‘great game’ of chess is primarily psychological, a conflict between one trained intelligence and another, and not a mere collection of small mathematical theorems.”
― G.H. Hardy, A Mathematician’s Apology

“We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases’, indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.”
― G.H. Hardy, A Mathematician’s Apology

“OLD BRANDY came to mean a taste that was eccentric, esoteric, but just within the bounds of reason.”
― G.H. Hardy, A Mathematician's Apology

“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...”
― G.H. Hardy, A Mathematician's Apology

“I spoke of the 'real' mathematics of Fermat and other great mathematicians, the mathematics which has permanent aesthetic value, as for example the best Greek mathematics has, the mathematics which is eternal because the best of it may, like the best literature, continue to cause intense emotional satisfaction to thousands of people after thousands of years. These men were all primarily pure mathematicians; but I was not thinking only of pure mathematics. I count Maxwell and Einstein, Eddington and Dirac, among 'real' mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are, at present at any rate, almost as 'useless' as the theory of numbers. It is the dull and elementary parts of applied mathematics, as it is the dull and elementary parts of pure mathematics, that work for good or ill.”
― G.H. Hardy, A Mathematician's Apology

“Even a pure mathematician may find his appreciation of this geometry [applied geometry] quickened, since there 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, A Mathematician's Apology

“If the theory of numbers could be employed for any practical and obviously honourable purpose, if it could be turned directly to the furtherance of human happiness or the relief of human suffering, as physiology and even chemistry can, then surely neither Gauss nor any other mathematician would have been so foolish as to decry or regret such applications. But science works for evil as well as for good; and both Gauss and lesser mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean.”
― G.H. Hardy, A Mathematician's Apology

“What the public wants is a little intellectual 'kick', and nothing else has quite the kick of mathematics.”
― G H Hardy, A Mathematician's Apology

“İnsanları araştırma yapmaya yönelten pek çok neden vardır; ancak bunlardan üçü diğerlerinden daha önemlidir. Birincisi (ki bu olmadan öbür nedenler işe yaramaz), entelektüel merak, gerçeği öğrenme arzusudur. İkincisi, profesyonel saygınlık, yaptıklarının kendini tatmin etmem endişesidir; ortaya koyduğu eser, yeteneği ile orantılı olmadığı zaman her onurlu zanaatçının duyduğu utanma hissidir. Sonuncusu da başarma hırsı, mevki ve üne kavuşma arzusu, hatta sağlanacak para ve onun getireceği güçtür.

A Mathematician's Apology”
― G.H. Hardy, A Mathematician's Apology

“Matematiksel sonuçlar, içerdikleri değerler ne olursa olsun, diğerlerinin içinde en kalıcı olanlardır.”
― G.H. Hardy, A Mathematician's Apology

“Matematiğin çok küçük bölümü pratik yarar sağlar; o küçük bölüm de oldukça sıkıcıdır.”
― G.H. Hardy, A Mathematician's Apology

“It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselves and with those above and below. The lower the stratum, the deeper (and in general more difficult) the idea. Thus the idea of an ‘irrational’ is deeper than that of an integer; and Pythagoras’s theorem is, for that reason, deeper than Euclid’s.”
― G.H. Hardy, A Mathematician's Apology

“In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest and the youngest of all.”
― G.H. Hardy, A Mathematician's Apology