…the simplicity, the indispensableness of each word, each letter, each little dash, that among all artists raises the mathematician nearest to the World-creator; it establishes a sublimity which is equalled in no other art,—Something like it exists at most in symphonic music.

[An artist] will sooner and with more certainty, establish the character of skeletons, than the most learned anatomist, whose eye has not been accustomed to seize on every peculiarity.
Asserting his (incorrect) belief that the fossil teeth of the mastodon revealed it was a carnivorous animal.]

[First use of the term science fiction:] We hope it will not be long before we may have other works of Science-Fiction [like Richard Henry Horne's The Poor Artist], as we believe such books likely to fulfil a good purpose, and create an interest, where, unhappily, science alone might fail.
[Thomas] Campbell says, that “Fiction in Poetry is not the reverse of truth, but her soft and enchanting resemblance.” Now this applies especially to Science-Fiction, in which the revealed truths of Science may be given interwoven with a pleasing story which may itself be poetical and true—thus circulating a knowledge of Poetry of Science, clothed in a garb of the Poetry of life.

[Saint-Gaudens and Matthew Arnold] felt a railway train as power; yet they, and all other artists, constantly complained that the power embodied in a railway train could never be embodied in art. All the steam in the world could not, like the Virgin, build Chartres.

[Tom Bombadil is] an exemplar, a particular embodying of pure (real) natural science: the spirit that desires knowledge of other things, their history and nature, because they are ‘other’ and wholly independent of the enquiring mind, a spirit coeval with the rational mind, and entirely unconcerned with ‘doing’ anything with the knowledge: Zoology and Botany not Cattle-breeding or Agriculture. Even the Elves hardly show this: they are primarily artists.

Jobs: I look at myself as an artist if anything. Sort of a trapeze artist.
Levy: With or without a net?
Jobs: Without.

Neque enim ingenium sine disciplina aut disciplina sine ingenio perfectum artificem potest efficere
For neither talent without instruction nor instruction without talent can produce the perfect craftsman.

There is no such thing as a Scientific Mind. Scientists are people of very dissimilar temperaments doing different things in very different ways. Among scientists are collectors, classifiers, and compulsive tidiers-up; many are detectives by temperament and many are explorers; some are artists and others artisans. There are poet-scientists and philosopher-scientists and even a few mystics.

~~[Dubious]~~ A plagiarist steals from one person. A true artist steals from everybody.

A grove of giant redwoods or sequoias should be kept just as we keep a great or beautiful cathedral. The extermination of the passenger pigeon meant that mankind was just so much poorer; exactly as in the case of the destruction of the cathedral at Rheims. And to lose the chance to see frigate-birds soaring in circles above the storm, or a file of pelicans winging their way homeward across the crimson afterglow of the sunset, or a myriad terns flashing in the bright light of midday as they hover in a shifting maze above the beach—why, the loss is like the loss of a gallery of the masterpieces of the artists of old time.

A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same Nature.

A truly wise trapeze artist does not inspect his nails in mid jump.

After a certain high level of technical skill is achieved, science and art tend to coalesce in esthetics, plasticity, and form. The greatest scientists are always artists as well.

All great scientists have, in a certain sense, been great artists; the man with no imagination may collect facts, but he cannot make great discoveries.

Among all highly civilized peoples the golden age of art has always been closely coincident with the golden age of the pure sciences, particularly with mathematics, the most ancient among them.
This coincidence must not be looked upon as accidental, but as natural, due to an inner necessity. Just as art can thrive only when the artist, relieved of the anxieties of existence, can listen to the inspirations of his spirit and follow in their lead, so mathematics, the most ideal of the sciences, will yield its choicest blossoms only when life’s dismal phantom dissolves and fades away, when the striving after naked truth alone predominates, conditions which prevail only in nations while in the prime of their development.

Among the memoirs of Kirchhoff are some of uncommon beauty. … Can anything be beautiful, where the author has no time for the slightest external embellishment?—But—; it is this very simplicity, the indispensableness of each word, each letter, each little dash, that among all artists raises the mathematician nearest to the World-creator; it establishes a sublimity which is equalled in no other art, something like it exists at most in symphonic music. The Pythagoreans recognized already the similarity between the most subjective and the most objective of the arts.

Any artist or novelist would understand—some of us do not produce their best when directed. We expect the artist, the novelist and the composer to lead solitary lives, often working at home. While a few of these creative individuals exist in institutions or universities, the idea of a majority of established novelists or painters working at the “National Institute for Painting and Fine Art” or a university “Department of Creative Composition” seems mildly amusing. By contrast, alarm greets the idea of a creative scientist working at home. A lone scientist is as unusual as a solitary termite and regarded as irresponsible or worse.

Anyone who can leave the Yucatán with indifference has never been an artist and will never be a scholar.

Architecture is of all the arts the one nearest to a science, for every architectural design is at its inception dominated by scientific considerations. The inexorable laws of gravitation and of statics must be obeyed by even the most imaginative artist in building.

Art and religion are not professions: they are not occupations for which men can be paid. The artist and the saint do what they have to do, not to make a living, but in obedience to some mysterious necessity. They do not product to live - they live to produce.

Art and science work in quite different ways: agreed. But, bad as it may sound, I have to admit that I cannot get along as an artist without the use of one or two sciences. ... In my view, the great and complicated things that go on in the world cannot be adequately recognized by people who do not use every possible aid to understanding.

Artists are the antennae of the race.

As we cannot use physician for a cultivator of physics, I have called him a physicist. We need very much a name to describe a cultivator of science in general. I should incline to call him a Scientist. Thus we might say, that as an Artist is a Musician, Painter or Poet, a Scientist is a Mathematician, Physicist, or Naturalist.

But when great and ingenious artists behold their so inept performances, not undeservedly do they ridicule the blindness of such men; since sane judgment abhors nothing so much as a picture perpetrated with no technical knowledge, although with plenty of care and diligence. Now the sole reason why painters of this sort are not aware of their own error is that they have not learnt Geometry, without which no one can either be or become an absolute artist; but the blame for this should be laid upon their masters, who are themselves ignorant of this art.

Don't make me out to be an artist. I am an engineer. I am after the facts, only the facts.

Every man is ready to join in the approval or condemnation of a philosopher or a statesman, a poet or an orator, an artist or an architect. But who can judge of a mathematician? Who will write a review of Hamilton’s Quaternions, and show us wherein it is superior to Newton’s Fluxions?

For most scientists, I think the justification of their work is to be found in the pure joy of its creativeness; the spirit which moves them is closely akin to the imaginative vision which inspires an artist.

Gauss was not the son of a mathematician; Handel’s father was a surgeon, of whose musical powers nothing is known; Titian was the son and also the nephew of a lawyer, while he and his brother, Francesco Vecellio, were the first painters in a family which produced a succession of seven other artists with diminishing talents. These facts do not, however, prove that the condition of the nerve-tracts and centres of the brain, which determine the specific talent, appeared for the first time in these men: the appropriate condition surely existed previously in their parents, although it did not achieve expression. They prove, as it seems to me, that a high degree of endowment in a special direction, which we call talent, cannot have arisen from the experience of previous generations, that is, by the exercise of the brain in the same specific direction.

Give me a dozen healthy infants, well-formed, and my own specified world to bring them up in and I’ll guarantee to take any one at random and train him to become any type of specialist I might select—doctor, lawyer, artist, merchant-chief and, yes, even beggar-man and thief, regardless of his talents, penchants, tendencies, abilities, vocations, and race of his ancestors. (1930)

He scarce had ceased when the superior fiend
Was moving toward the shore; his ponderous shield
Ethereal temper, massy, large and round,
Behind him cast; the broad circumference
Hung on his shoulders like the moon, whose orb
Through optic glass the Tuscan artist views
At evening from the top of Fésolè,
Or in Valdarno, to descry new lands,
Rivers or mountains in her spotty globe.

He that knows the secrets of nature with Albertus Magnus, or the motions of the heavens with Galileo, or the cosmography of the moon with Hevelius, or the body of man with Galen, or the nature of diseases with Hippocrates, or the harmonies in melody with Orpheus, or of poesy with Homer, or of grammar with Lilly, or of whatever else with the greatest artist; he is nothing if he knows them merely for talk or idle speculation, or transient and external use. But he that knows them for value, and knows them his own, shall profit infinitely.

How often people speak of art and science as though they were two entirely different things, with no interconnection. An artist is emotional, they think, and uses only his intuition; he sees all at once and has no need of reason. A scientist is cold, they think, and uses only his reason; he argues carefully step by step, and needs no imagination. That is all wrong. The true artist is quite rational as well as imaginative and knows what he is doing; if he does not, his art suffers. The true scientist is quite imaginative as well as rational, and sometimes leaps to solutions where reason can follow only slowly; if he does not, his science suffers.

However far the calculating reason of the mathematician may seem separated from the bold flight of the artist’s phantasy, it must be remembered that these expressions are but momentary images snatched arbitrarily from among the activities of both. In the projection of new theories the mathematician needs as bold and creative a phantasy as the productive artist, and in the execution of the details of a composition the artist too must calculate dispassionately the means which are necessary for the successful consummation of the parts. Common to both is the creation, the generation, of forms out of mind.

However far the mathematician’s calculating senses seem to be separated from the audacious flight of the artist’s imagination, these manifestations refer to mere instantaneous images, which have been arbitrarily torn from the operation of both. In designing new theories, the mathematician needs an equally bold and inspired imagination as creative as the artist, and in carrying out the details of a work the artist must unemotionally reckon all the resources necessary for the success of the parts. Common to both is the fabrication, the creation of the structure from the intellect.

I have never done anything “useful.” No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world... 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 things I have added to knowledge do not differ from] the creations of the other artists, great or small, who have left some kind of memorial beind them.

I like to look at mathematics almost more as an art than as a science; for the activity of the mathematician, constantly creating as he is, guided though not controlled by the external world of the senses, bears a resemblance, not fanciful I believe but real, to the activity of an artist, of a painter let us say. Rigorous deductive reasoning on the part of the mathematician may be likened here to technical skill in drawing on the part of the painter. Just as no one can become a good painter without a certain amount of skill, so no one can become a mathematician without the power to reason accurately up to a certain point. Yet these qualities, fundamental though they are, do not make a painter or mathematician worthy of the name, nor indeed are they the most important factors in the case. Other qualities of a far more subtle sort, chief among which in both cases is imagination, go to the making of a good artist or good mathematician.

If you were an artist or novelist, or a poet or somebody like that, nobody would think it odd if you worked in your own home. In science there’s none of this at all. I’m almost the only independent scientist in Britain. Everybody else works in large institutions, universities, or industrial labs. Why should one expect scientists to work that way?

In assessing Audubon, whose firm grip on the popular imagination has scarcely lessened since 1826, we must as historians of science seriously ask who would remember him if he had not been an artist of great imagination and flair. ... The chances seem to be very poor that had he not been an artist, he would be an unlikely candidate for a dictionary of scientific biography, if remembered to science at all.

In one person he [Isaac Newton] combined the experimenter, the theorist, the mechanic and, not least, the artist in exposition.

Inspiration plays no less a role in science than it does in the realm of art. It is a childish notion to think that a mathematician attains any scientifically valuable results by sitting at his desk with a ruler, calculating machines or other mechanical means. The mathematical imagination of a Weierstrass is naturally quite differently oriented in meaning and result than is the imagination of an artist, and differs basically in quality. But the psychological processes do not differ. Both are frenzy (in the sense of Plato’s “mania”) and “inspiration.”

It is frequently the tragedy of the great artist, as it is of the great scientist, that he frightens the ordinary man.

It is here [in mathematics] that the artist has the fullest scope of his imagination.

It is only the unimaginative who ever invents. The true artist is known by the use he makes of what he annexes, and he annexes everything

It seems to be considered as a common right to all poets and artists, to live only in the world of their own thoughts, and to be quite unfitted for the world which other men inhabit.

Just now nuclear physicists are writing a great deal about hypothetical particles called neutrinos supposed to account for certain peculiar facts observed in β-ray disintegration. We can perhaps best describe the neutrinos as little bits of spin-energy that have got detached. I am not much impressed by the neutrino theory. In an ordinary way I might say that I do not believe in neutrinos… But I have to reflect that a physicist may be an artist, and you never know where you are with artists. My old-fashioned kind of disbelief in neutrinos is scarcely enough. Dare I say that experimental physicists will not have sufficient ingenuity to make neutrinos? Whatever I may think, I am not going to be lured into a wager against the skill of experimenters under the impression that it is a wager against the truth of a theory. If they succeed in making neutrinos, perhaps even in developing industrial applications of them, I suppose I shall have to believe—though I may feel that they have not been playing quite fair.

Lectures with demonstrations are certainly valuable—more valuable than the lectures with text-books alone. Yet analyzing the object itself is infinitely more valuable than to watch the results exposed by another. Wrestling with the part which is being studied, handling it and viewing it from all sides, and tabulating and classifying the parts worked out, give us the greatest reward. All this can be accomplished by practical laboratory work. If we can make the student work thoroughly and carefully, a great result is achieved. It makes of him an artist, an actor, an expert, not a dilettante. He is upon the stage, not in the audience.

Let poets dream, let artists dream, let philosophers dream: let all thinkers be dreamers.

Let the artist have just enough to eat, and the tools of this trade: ask nothing of him. Materially make the life of the artist sufficiently miserable to be unattractive, and no-one will take to art save those in whom the divine daemon is absolute.

Mathematicians go mad, and cashiers; but creative artists very seldom. I am not, as will be seen, in any sense attacking logic: I only say that the danger does lie in logic, not in imagination.

Mathematics and music, the most sharply contrasted fields of scientific activity which can be found, and yet related, supporting each other, as if to show forth the secret connection which ties together all the activities of our mind, and which leads us to surmise that the manifestations of the artist’s genius are but the unconscious expressions of a mysteriously acting rationality.

My price is five dollars for a miniature on ivory, and I have engaged three or four at that price. My price for profiles is one dollar, and everybody is willing to engage me at that price.
Explaining how as an artist he would create income to pay his debts while at college.

Nature! … She is the only artist; working-up the most uniform material into utter opposites; arriving, without a trace of effort, at perfection, at the most exact precision, though always veiled under a certain softness.

No history of civilization can be tolerably complete which does not give considerable space to the explanation of scientific progress. If we had any doubts about this, it would suffice to ask ourselves what constitutes the essential difference between our and earlier civilizations. Throughout the course of history, in every period, and in almost every country, we find a small number of saints, of great artists, of men of science. The saints of to-day are not necessarily more saintly than those of a thousand years ago; our artists are not necessarily greater than those of early Greece; they are more likely to be inferior; and of course, our men of science are not necessarily more intelligent than those of old; yet one thing is certain, their knowledge is at once more extensive and more accurate. The acquisition and systematization of positive knowledge is the only human activity which is truly cumulative and progressive. Our civilization is essentially different from earlier ones, because our knowledge of the world and of ourselves is deeper, more precise, and more certain, because we have gradually learned to disentangle the forces of nature, and because we have contrived, by strict obedience to their laws, to capture them and to divert them to the gratification of our own needs.

No nation can be really great unless it is great in peace, in industry, integrity, honesty. Skilled intelligence in civic affairs and industrial enterprises alike; the special ability of the artist, the man of letters, the man of science, and the man of business; the rigid determination to wrong no man, and to stand for righteousness—all these are necessary in a great nation.

Not since the Lord himself showed his stuff to Ezekiel in the valley of dry bones had anyone shown such grace and skill in the reconstruction of animals from disarticulated skeletons. Charles R. Knight, the most celebrated of artists in the reanimation of fossils, painted all the canonical figures of dinosaurs that fire our fear and imagination to this day.

Now and then, in the course of the century, a great man of science, like Darwin; a great poet, like Keats; a fine critical spirit, like M. Renan; a supreme artist, like Flaubert, has been able to isolate himself, to keep himself out of reach of the clamorous claims of others, to stand “under the shelter of the wall,” as Plato puts it, and so to realise the perfection of what was in him, to his own incomparable gain, and to the incomparable and lasting gain of the whole world.

On one occasion committee members were asked by the chairman, who was also in charge of the project, to agree that a certain machine be run at a power which was ten percent lower than the design value. [Franz Eugen] Simon objected, arguing that “design value” should mean what it said. Thereupon the chairman remarked, “Professor Simon, don’t you see that we are not talking about science, but about engineering, which is an art.” Simon was persistent: “What would happen if the machine were run at full power?” “It might get too hot.” “But, Mr. Chairman,” came Simon’s rejoinder, “Can’t artists use thermometers?”

Poets say science takes away from the beauty of the stars—mere globs of gas atoms. Nothing is “mere.” I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination—stuck on this carousel my little eye can catch one-million-year-old light. A vast pattern—of which I am a part. … What is the pattern, or the meaning, or the “why?” It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?

Science discovery is an irrational act. It’s an intuition which turns out to be reality at the end of it. I see no difference between a scientist developing a marvellous discovery and an artist making a painting

Science is a capital or fund perpetually reinvested; it accumulates, rolls up, is carried forward by every new man. Every man of science has all the science before him to go upon, to set himself up in business with. What an enormous sum Darwin availed himself of and reinvested! Not so in literature; to every poet, to every artist, it is still the first day of creation, so far as the essentials of his task are concerned. Literature is not so much a fund to be reinvested as it is a crop to be ever new-grown.

Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear. We are tending toward the condition of science and aspiring to do it. The artist works out his own formulas; the interest of science lies in the art of making science.

Scientists are people of very dissimilar temperaments doing different things in very different ways. Among scientists are collectors, classifiers and compulsive tidiers-up; many are detectives by temperament and many are explorers; some are artists and others artisans. There are poets–scientists and philosopher–scientists and even a few mystics. ... and most people who are in fact scientists could easily have been something else instead.

Scientists like myself merely use their gifts to show up that which already exists, and we look small compared to the artists who create works of beauty out of themselves. If a good fairy came and offered me back my youth, asking me which gifts I would rather have, those to make visible a thing which exists but which no man has ever seen before, or the genius needed to create, in a style of architecture never imagined before, the great Town Hall in which we are dining tonight, I might be tempted to choose the latter.

Society is becoming increasingly aware of the power of science to bring weal or woe to mankind. But now when it is seen that the same science that brings prosperity and comfort may lead to depression and discomfort, men are beginning to look with mixed feelings at this monster which society may exalt or persecute, but cannot view with indifference. Perhaps my topic today should have read “Ought Scientists to be Burnt at the Stake?” I shall not attempt to decide this question, but only to present in a cursory way some of the pros and cons … But if scientists are to be destroyed, let them not alone by the victims; every creative thought must be extirpated. A philosopher’s epigram may kindle a world war. So scientist, inventor, artist, poet and every sort of troublous enthusiast must together be brought before the bar of the new inquisition

Some paintings become famous because, being durable, they are viewed by successive generations, in each of which are likely to be found a few appreciative eyes. I know a painting so evanescent that it is seldom viewed at all, except by some wandering deer. It is a river who wields the brush, and it is the same river who, before I can bring my friends to view his work, erases it forever from human view. After that it exists only in my mind's eye. Like other artists, my river is temperamental; there is no predicting when the mood to paint will come upon him, or how long it will last. But in midsummer, when the great white fleets cruise the sky for day after flawless day, it is worth strolling down to the sandbars just to see whether he has been at work.

Surrealists … are not exactly artists and we are not exactly men of science; … we are carnivorous fish … swimming between two kinds of water, the cold water of art and the warm water of science.

The artist admires the work of his forerunners, but the scientist does more than admire, he makes actual use of it. The artist may find an inspiration in it, but the scientist tries to incorporate it entirely in his own work.

The artist and the scientist—and the physician, in a sense, is both—is a man who is presumed to be interested primarily in his work, not in its emoluments. He can do genuinely good work, indeed, only to the extent that he is so interested. The moment he begins habitually to engage in enterprises that offer him only profit he ceases to be either an artist or a scientist, and becomes a mere journeyman artisan.

The artist does not illustrate science; … [but] he frequently responds to the same interests that a scientist does, and expresses by a visual synthesis what the scientist converts into analytical formulae or experimental demonstrations.

The books of the great scientists are gathering dust on the shelves of learned libraries. ... While the artist's communication is linked forever with its original form, that of the scientist is modified, amplified, fused with the ideas and results of others and melts into the stream of knowledge and ideas which forms our culture. The scientist has in common with the artist only this: that he can find no better retreat from the world than his work and also no stronger link with the world than his work.

The discoveries of science, the works of art are explorations—more, are explosions, of a hidden likeness. The discoverer or artist presents in them two aspects of nature and fuses them into one. This is the act of creation, in which an original thought is born, and it is the same act in original science and original art.

The efforts of most human-beings are consumed in the struggle for their daily bread, but most of those who are, either through fortune or some special gift, relieved of this struggle are largely absorbed in further improving their worldly lot. Beneath the effort directed toward the accumulation of worldly goods lies all too frequently the illusion that this is the most substantial and desirable end to be achieved; but there is, fortunately, a minority composed of those who recognize early in their lives that the most beautiful and satisfying experiences open to humankind are not derived from the outside, but are bound up with the development of the individual's own feeling, thinking and acting. The genuine artists, investigators and thinkers have always been persons of this kind. However inconspicuously the life of these individuals runs its course, none the less the fruits of their endeavors are the most valuable contributions which one generation can make to its successors.

The experienced observer does more than merely report and recite. He guides the eager student to an understanding of the earth. He may chart the scientist’s steep, barren road of sober observation and strict deduction, or the artist’s gentle road of contemplation and empathy. And, finally, he may point out his own unique way, the path of the initiated, which leads him from the laboratories and libraries to the meadows and flower gardens of the living earth.

The great men of science are supreme artists.

The job of the artist is always to deepen the mystery

The lives of scientists, considered as Lives, almost always make dull reading. For one thing, the careers of the famous and the merely ordinary fall into much the same pattern, give or take an honorary degree or two, or (in European countries) an honorific order. It could be hardly otherwise. Academics can only seldom lead lives that are spacious or exciting in a worldly sense. They need laboratories or libraries and the company of other academics. Their work is in no way made deeper or more cogent by privation, distress or worldly buffetings. Their private lives may be unhappy, strangely mixed up or comic, but not in ways that tell us anything special about the nature or direction of their work. Academics lie outside the devastation area of the literary convention according to which the lives of artists and men of letters are intrinsically interesting, a source of cultural insight in themselves. If a scientist were to cut his ear off, no one would take it as evidence of a heightened sensibility; if a historian were to fail (as Ruskin did) to consummate his marriage, we should not suppose that our understanding of historical scholarship had somehow been enriched.

The new painters do not propose, any more than did their predecessors, to be geometers. But it may be said that geometry is to the plastic arts what grammar is to the art of the writer. Today, scholars no longer limit themselves to the three dimensions of Euclid. The painters have been lead quite naturally, one might say by intuition, to preoccupy themselves with the new possibilities of spatial measurement which, in the language of the modern studios, are designated by the term fourth dimension.

The sciences are monuments devoted to the public good; each citizen owes to them a tribute proportional to his talents. While the great men, carried to the summit of the edifice, draw and put up the higher floors, the ordinary artists scattered in the lower floors, or hidden in the obscurity of the foundations, must only seek to improve what cleverer hands have created.

The significance of a fact is relative to [the general body of scientific] knowledge. To say that a fact is significant in science, is to say that it helps to establish or refute some general law; for science, though it starts from observation of the particular, is not concerned essentially with the particular, but with the general. A fact, in science, is not a mere fact, but an instance. In this the scientist differs from the artist, who, if he deigns to notice facts at all, is likely to notice them in all their particularity.

The structural formula of the organic chemist is not the canvas on which the cubist artist should impose his drawings which he alone can interpret.

The study of economics does not seem to require any specialised gifts of an unusually high order. Is it not, intellectually regarded, a very easy subject compared with the higher branches of philosophy and pure science? Yet good, or even competent, economists are the rarest of birds. An easy subject, at which very few excel! The paradox finds its explanation, perhaps, in that the master-economist must possess a rare combination of gifts. He must reach a high standard in several different directions and must combine talents not often found together. He must be mathematician, historian, statesman, philosopher—in some degree. He must understand symbols and speak in words. He must contemplate the particular in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in the light of the past for the purposes of the future. No part of man's nature or his institutions must lie entirely outside his regard. He must be purposeful and disinterested in a simultaneous mood; as aloof and incorruptible as an artist, yet sometimes as near the earth as a politician.

The tendency of the sciences has long been an increasing proclivity of separation and dismemberment … The mathematician turns away from the chemist; the chemist from the naturalist; the mathematician, left to himself divides himself into a pure mathematician and a mixed mathematician, who soon part company … And thus science, even mere physical science, loses all traces of unity. A curious illustration of this result may be observed in the want of any name by which we can designate the students of the knowledge of the material world collectively. We are informed that this difficulty was felt very oppressively by the members of the British Association for the Advancement of Science, at their meetings at York, Oxford and Cambridge, in the last three summers. There was no general term by which these gentlemen could describe themselves with reference to their pursuits … some ingenious gentleman [William Whewell] proposed that, by analogy with artist, they might form Scientist, and added that there could be no scruple … when we have words such as sciolist, economist, and atheist—but this was not generally palatable.

The true mathematician is always a good deal of an artist, an architect, yes, of a poet. Beyond the real world, though perceptibly connected with it, mathematicians have intellectually created an ideal world, which they attempt to develop into the most perfect of all worlds, and which is being explored in every direction. None has the faintest conception of this world, except he who knows it.

The worst scientist is he who is not an artist; the worst artist is he who is no scientist.

There is a great deal of emotional satisfaction in the elegant demonstration, in the elegant ordering of facts into theories, and in the still more satisfactory, still more emotionally exciting discovery that the theory is not quite right and has to be worked over again, very much as any other work of art—a painting, a sculpture has to be worked over in the interests of aesthetic perfection. So there is no scientist who is not to some extent worthy of being described as artist or poet.

There is an influence which is getting strong and stronger day by day, which shows itself more and more in all departments of human activity, and influence most fruitful and beneficial—the influence of the artist. It was a happy day for the mass of humanity when the artist felt the desire of becoming a physician, an electrician, an engineer or mechanician or—whatnot—a mathematician or a financier; for it was he who wrought all these wonders and grandeur we are witnessing. It was he who abolished that small, pedantic, narrow-grooved school teaching which made of an aspiring student a galley-slave, and he who allowed freedom in the choice of subject of study according to one's pleasure and inclination, and so facilitated development.

Today the function of the artist is to bring imagination to science and science to imagination, where they meet, in the myth.

True artists are the antennae of nature.

Until its results have gone through the painful process of publication, preferably in a refereed journal of high standards, scientific research is just play. Publication is an indispensable part of science. “Publish or perish” is not an indictment of the system of academia; it is a partial prescription for creativity and innovation. Sustained and substantial publication favors creativity. Novelty of conception has a large component of unpredictability. ... One is often a poor judge of the relative value of his own creative efforts. An artist’s ranking of his own works is rarely the same as that of critics or of history. Most scientists have had similar experiences. One’s supply of reprints for a pot-boiler is rapidly exhausted, while a major monograph that is one’s pride and joy goes unnoticed. The strategy of choice is to increase the odds favoring creativity by being productive.

We are concerned to understand the motivation for the development of pure mathematics, and it will not do simply to point to aesthetic qualities in the subject and leave it at that. It must be remembered that there is far more excitement to be had from creating something than from appreciating it after it has been created. Let there be no mistake about it, the fact that the mathematician is bound down by the rules of logic can no more prevent him from being creative than the properties of paint can prevent the artist. … We must remember that the mathematician not only finds the solutions to his problems, he creates the problems themselves.

What I then got hold of, something frightful and dangerous, a problem with horns but not necessarily a bull, in any case a new problem—today I should say that it was the problem of science itself, science considered for the first time as problematic, as questionable. But the book in which my youthful courage and suspicion found an outlet—what an impossible book had to result from a task so uncongenial to youth! Constructed from a lot of immature, overgreen personal experiences, all of them close to the limits of communication, presented in the context of art—for the problem of science cannot be recognized in the context of science—a book perhaps for artists who also have an analytic and retrospective penchant (in other words, an exceptional type of artist for whom one might have to look far and wide and really would not care to look) …

What we do see depends mainly on what we look for. ... In the same field the farmer will notice the crop, the geologists the fossils, botanists the flowers, artists the colouring, sportmen the cover for the game. Though we may all look at the same things, it does not all follow that we should see them.

When students hear the story of Andrew J. Wiles’ proof of Fermat’s Last Theorem, it is not the result itself that stirs their emotions, but the revelation that a mathematician was driven by the same passion as any creative artist.

Where we reach the sphere of mathematics we are among processes which seem to some the most inhuman of all human activities and the most remote from poetry. Yet it is just here that the artist has the fullest scope for his imagination. … We are in the imaginative sphere of art, and the mathematician is engaged in a work of creation which resembles music in its orderliness, … It is not surprising that the greatest mathematicians have again and again appealed to the arts in order to find some analogy to their own work. They have indeed found it in the most varied arts, in poetry, in painting, and in sculpture, although it would certainly seem that it is in music, the most abstract of all the arts, the art of number and time, that we find the closest analogy.

While the artist’s communication is linked forever with its original form, that of the scientist is modified, amplified, fused with the ideas and results of others.

Who has studied the works of such men as Euler, Lagrange, Cauchy, Riemann, Sophus Lie, and Weierstrass, can doubt that a great mathematician is a great artist? The faculties possessed by such men, varying greatly in kind and degree with the individual, are analogous with those requisite for constructive art. Not every mathematician possesses in a specially high degree that critical faculty which finds its employment in the perfection of form, in conformity with the ideal of logical completeness; but every great mathematician possesses the rarer faculty of constructive imagination.

You may perceive something of the distinction which I think necessary to keep in view between art and science, between the artist and the man of knowledge, or the philosopher. The man of knowledge, the philosopher, is he who studies and acquires knowledge in order to improve his own mind; and with a desire of extending the department of knowledge to which he turns his attention, or to render it useful to the world, by discoveries, or by inventions, which may be the foundation of new arts, or of improvements in those already established. Excited by one or more of these motives, the philosopher employs himself in acquiring knowledge and in communicating it. The artist only executes and practises what the philosopher or man of invention has discovered or contrived, while the business of the trader is to retail the productions of the artist, exchange some of them for others, and transport them to distant places for that purpose.