Fellows Of The Royal Society

"How gladly would I wander through some strange and savage land, The lasso at my saddle-bow, the rifle in my hand, A leash of gallant mastiffs bounding by my side, And, for a friend to love, the noble horse on which I ride! Alone, alone—yet not alone, for God is with me there, The tender hand of Providence shall guide me everywhere, While happy thoughts and holy hopes, as spirits calm and mild, Shall fan with their sweet wings the hermit-hunter of the wild!"

"Who shall guess what I may be? Who can tell my fortune to me? For, bravest and brightest that ever was sung May be — and shall be — the lot of the young!"

"For life, good youth, hath never an ill Which hope cannot scatter, and faith cannot kill; And stubborn realities never shall bind The free-spreading wings of a cheerful mind."

"Never give up! it is wiser and better Always to hope, than once to despair. Fling off the load of Doubt's cankering fetter, And break the dark spell of tyrannical care."

"Eye hath not seen, tongue hath not told, And ear hath not heard it sung, How buoyant and bold, though it seem to grow old, Is the heart, forever young; — Forever young, — though life's old age Hath every nerve unstrung: The heart, the heart, is a heritage That keeps the old man young!"

"I am not old, — I cannot be old, Though tottering, wrinkled, and gray ; Though my eyes are dim, and my marrow is cold, Call me not old to-day."

"I am not old, — I cannot be old, Though threescore years and ten Have wasted away, like a tale that is told, The lives of other men: I am not old ; though friends and foes Alike have gone to their graves, And left me alone to my joys or my woes, As a rock in the midst of the waves."

"His fashion is passion, sincere and intense, — His impulse is simple and true; Yet temper'd by judgment, and taught by good sense, And cordial with me and with you."

"Fearless in honesty, gentle yet just, He warmly can love, and can hate; Nor will he bow down, with his face in the dust, To Fashion's intolerant state;"

"Away with false fashion, so calm and so chill, Where pleasure itself cannot please; Away with cold breeding, that faithlessly still Affects to be quite at its ease; For the deepest in feeling is highest in rank, The freest is first of the band, Nature's own Nobleman, friendly and frank, Is a man with his heart in his hand!"

"O fair, false city, thou gay and gilded harlot! Wo for thy wanton heart, wo for thy wicked hardness! Wo unto thee, that the lightsomeness of life, beneath Italian suns, Should meet the solemnity of death, in a sepulchre so foul and fearful!"

"Naples sitteth by the sea, keystone of an arch of azure, Crowned by consenting nations peerless queen of gayety: She laugheth at the wrath of Ocean, she mocketh the fury of Vesuvius, She spurneth disease, and misery, and famine, that crowd her sunny streets."

"Who can wrestle against Sleep? — Yet is that giant very gentleness."

"Clamorous pauperism feasteth While honest Labor, pining, hideth his sharp ribs."

"Wait, thou child of hope, for Time shall teach thee all things."

"If the mind is wearied by study, or the body worn with sickness, It is well to lie fallow for a while, in the vacancy of sheer amusement ; But when thou prosprest in health, and thine intellect can soar untired, To seek uninstructive pleasure is to slumber on the couch of indolence."

"Tell me, ye that strive in vain to cramp and dwarf the soul, Wherefore should it cease to be, and when shall essence die?"

"God, from a beautiful necessity, is Love in all he doeth, Love, a brilliant fire, to gladden or consume: The wicked work their woe by looking upon love, and hating it: The righteous find their joys in yearning on its loveliness for ever."

"A babe in the house is a well-spring of pleasure, a messenger of peace and love, a resting place for innocence on earth, a link between angels and men."

"A good book is the best of friends, the same today and forever."

"Well-timed silence hath more eloquence than speech."

"There is a limit to enjoyment, though the sources of wealth be boundless And the choicest pleasures of life lie within the ring of moderation."

"Error is a hardy plant; it flourisheth in every soil; In the heart of the wise and good, alike with the wicked and foolish; For there is no error so crooked, but it hath in it some lines of truth; Nor is any poison so deadly, that it serveth not some wholesome use."

"The Greeks first spoke a language which modern mathematicians can understand; as Littlewood said to me once, they are not clever schoolboys or "scholarship candidates", but "Fellows of another college"."

"In 1908 Herman quoted to my father an extract from the main report on my first Fellowship thesis. 'He is to be a great mathematician, and his work is singularly mature.' (Herman, on the evidence of my Minor Scholarship and perhaps a first term's work, broke it to my father that he couldn't expect much of me. I'm not sure when this was reversed, and my father knew the ropes enough not to build too much on a Senior Wranglership. I remember, to my surprise, as being a prodigy of 14 in South Africa, his implying that I might expect at Cambridge to be nearly as good as himself, or possibly a shade better. The Fellowship report was something of a surprise; he said 'I feel like a hen that has hatched an eagle.')"

"To illustrate to what extent Hardy and Littlewood in the course of the years came to be considered as the leaders of recent English mathematical research, I may report what an excellent colleague once jokingly said: 'Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy-Littlewood.'"

"There is much to be said for being a mathematician. To begin with, he has to be completely honest in his work, not from any superior morality, but because he simply cannot get away with a fake. ... A mathematician's normal day contains hours of close concentration, and leaves him jaded in the evening. ... This is why we tend to relax either on mild nonfiction like biographies, or - to be crude, and to the derision of arts people - on trash. There is, of course, good trash and bad trash. ... Minor depressions will occur, and most of a mathematician's life is spent in frustration, punctuated with rare inspirations. A beginner can't expect quick results; if they are quick they are pretty sure to be poor. ... When one has finished a substantial paper there is commonly a mood in which it seems that there is really nothing in it. Do not worry, later on you will be thinking 'At least I could do something good then.' At the end of a particularly long and exacting work there can be a strange melancholy. This, however, is romantic, and mildly pleasant, like some other melancholies."

"I had been struggling for two months to prove a result I was pretty sure was true. When I was walking up a Swiss mountain, fully occupied by the effort, a very odd device emerged - so odd that, though it worked, I could not grasp the resulting proof as a whole. But not only so; I had a sense that my subconscious was saying, 'Are you never going to do it, confound you; try this.'"

"'Always verify references.' This is so absurd in mathematics that I used to say provocatively: 'never...' When I began writing I innocently adopted the French habit of M. (Monsieur) in front of any surname. I thus created a ghost mathematician M. Landau (to whom some 'non-verified' references were made)."

"It was Mr. Littlewood (I believe) who remarked that "every positive integer was one of his personal friends.""

"G. H. Hardy said he thought on paper ('with my pen'). He wrote everything out (in his invariably admirable handwriting), scrapping and copying whenever a page got into a mess. When I am thinking about a difficult problem everything goes onto a single page - all over the place with odd equations, diagrams, rings. However appalling the mess, I feel that to scrap this page would somehow break threads in the unconscious."

"[For an unproved Lemma] I had what looked like a promising idea for this, but it was fallacious. In the middle of a three week holiday - mathematics completely below the horizon - the idea came again out of the blue when I was in bed. I forgot it had been rejected as fallacious, and this forgetting did the trick; because this time I noticed that it did prove something, and, by what was nearly, or quite, automatic writing, a proof got written down which deduced the Lemma from the something. ... I did experience automatic writing again. ... my pencil wrote down the formula [omitted] for no reason at all, and almost unattended by consciousness. On the face of it the formula has no apparent connexion with the problem, but it turns out to be an essential key to the proof. ... as if my subconsciousness knew the thing all the time, and finally got impatient."

"It is possible for a mathematician to be 'too strong' for a given occasion. He forces through, where another might be driven to a different, and possibly more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)"

"The Astronomer's fallacy. It is very hard to make a random selection of stars. If, for example, you see a star (with the naked eye) it is probably bright (as stars go). A lecturer was once making the point that middle class families were smaller than lower class ones. As a test he asked everyone to write down the number of children in his family. The average was larger than the lower class average. The obvious point he overlooked were that zero families were unrepresented in the audience. But further, families of n have a probability of being represented proportional to n; with all this, the result is to be expected."

"Besicovitch and Harry Williams asked me what God was doing before the Creation. I said: 'Millions of words must have been written on this; but he was doing Pure Mathematics and thought it would be a pleasant change to do some Applied.'"

"Improbabilities are apt to be overestimated. It is true that I should have been surprised in the past to learn that Professor Hardy had joined the Oxford Group. But one could not say the adverse chance was 10⁶ : 1. Mathematics is a dangerous profession; an appreciable proportion of us go mad, and then this particular event would be quite likely. ... There must exist a collection of well-authenticated coincidences, and I regret that I am not better acquainted with them. ... I sometimes ask the question: what is the most remarkable coincidence you have experienced, and is it, for the most remarkable one, remarkable? (With a lifetime to choose from, 10⁶ : 1 is a mere trifle.) ... Eddington once told me that information about a new (newly visible, not necessarily unknown) comet was received by an Observatory in misprinted form; they looked at the place indicated (no doubt sweeping a square degree or so), and saw a new comet. ..."

"The derivates theorem enables one to reject certain parts of the thing one wants to tend to zero. One day I was playing round with this, and a ghost of an idea entered my mind of making r, the number of differentiations, large. At that moment the spring cleaning that was in progress reached the room I was working in, and there was nothing for it but to go walking for 2 hours, in pouring rain. The problem seethed violently in my mind: the material was disordered and cluttered up with irrelevant complications cleared away in the final version, and the 'idea' was vague and elusive. Finally I stopped, in the rain, gazing blankly for minutes on end over a little bridge into a stream (near Kenwith wood), and presently a flooding certainty came into my mind that the thing was done. The 40 minutes before I got back and could verify were none the less tense."

"My research began, naturally, in the Long Vacation of my 3rd year, 1906. My director of studies (and tutor) E. W. Barnes suggested the subject of integral functions of order 0... [After success,] Barnes was now encouraged to suggest a new problem: 'Prove the Riemann Hypothesis'."

"The difference when you do know (when, for example, we are looking for a new proof) is enormous. Like a Bridge problem 'if the thing is possible it must be necessary to lead the Ace and trump with the Ace in Dummy.'"

"I began on a question on elementary theory of numbers, in which I felt safe in my school days. It did not come out, nor did it on a later attack. I had occasion to fetch more paper; when passing a desk my eye lit on a heavy mark against the question. The candidate was not one of the leading people, and I half unconsciously inferred that I was making unnecessarily heavy weather; the question then came out fairly easily. The perfectly high-minded man would no doubt have abstained from further attack; I wish I had done so, but the offence does not lie very heavily on my conscience."

"If he is consistent a man of the mathematical school washes his hands of applications. To someone who wants them he would say that the ideal system runs parallel to the usual theory: 'If this is what you want, try it: it is not my business to justify application of the system; that can only be done by philosophizing; I am a mathematician'. In practice he is apt to say: 'try this; if it works that will justify it'. But now he is not merely philosophizing; he is committing the characteristic fallacy. Inductive experience that the system works is not evidence."

"I recall once saying that when I had given the same lecture several times I couldn't help feeling that they really ought to know it by now."

"I read in the proof-sheets of Hardy on Ramanujan: 'As someone said, each of the positive integers was one of his personal friends.' My reaction was, 'I wonder who said that; I wish I had.' In the next proof-sheets I read (what now stands): 'It was Littlewood who said...' (What had happened was that Hardy had received the remark in silence and with a poker face, and I wrote it off as a dud....)"

"Landau kept a printed form for dealing with proofs of Fermat's last theorem. 'On page blank, lines blank to blank, you will find there is a mistake.'"

"'The surprising thing about this paper is that a man who could write it--would.'"

"(A. S. Besicovitch) A mathematician's reputation rests on the number of bad proofs he has given. (Pioneer work is clumsy.)"

"A good mathematical joke is better, and better mathematics, than a dozen mediocre papers."

"[About Fortran] On October 11, 1963, my suggestion was to pass on a request of our customers to relax the ALGOL 60 rule of compulsory declaration of variable names and adopt some reasonable default convention such as that of FORTRAN. […] The story of the Mariner space rocket to Venus, lost because of the lack of compulsory declarations in FORTRAN, was not to be published until later."

"Premature optimization is the root of all evil."

"One fine morning, when the emperor felt hot and bored, he extricated himself carefully from under the mountain of clothes and is now living happily as a swineherd in another story. The tailor is canonized as the patron saint of all consultants, because in spite of the enormous fees he extracted, he was never able to convince his clients of his dawning realization that their clothes have no Emperor."