Quotes & Sayings About Pure Mathematics

In mathematics I can report no deficiency, except it be that men do not sufficiently understand the excellent use of Pure Mathematics. — Francis Bacon

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry. — Albert Einstein

[Mathematics] is an independent world created out of pure intelligence. — William Wordsworth

And this is what I mainly learned up there, that the Parthenon was not a thing to study but to feel. It wasn't aloof, rational, timeless, pure. I couldn't locate the serenity of the place, the logic and steady sense. It wasn't a relic species of dead Greece but part of the living city below it. This was a surprise. I'd thought it was a separate thing, the sacred height, intact in its Doric order. I hadn't expected a human feeling to emerge from the stones but this is what I found, deeper than the art and mathematics embodied in the structure, the optical exactitudes. I found a cry for pity. — Don DeLillo

The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest lawsof atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. — Willard Van Orman Quine

Nature seems very conversant with the rules of pure mathematics, as our own mathematicians have formulated them in their studies, out of their own inner consciousness and without drawing to any appreciable extent on their experience of the outer world. — James Jeans

In general, it would be a peculiar type of 'justice' to declare a majority all the better and more just the more overwhelming it is, and to maintain abstractly that ninety-eight people abusing two persons is by far not so unjust as fifty-one people mistreating forty-nine. At this point, pure mathematics becomes simple inhumanity. — Carl Schmitt

Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be. — Charles Sanders Peirce

Schools were started to train human talents ...
The Guild ... emphasizes almost pure mathematics. Bene Gesserit performs ... politics. The original Bene Gesserit school was directed by those who saw the need of a thread of continuity in human affairs. They saw there count be no such continuity without separating human stock from animal stock - for breeding purposes. — Frank Herbert

The main application of Pure Mathematics is to make you happy. — Hendrik Lenstra

Hardly a pure science, history is closer to animal husbandry than it is to mathematics in that it involves selective breeding. The principal difference between the husbandryman and the historian is that the former breeds sheep or cows or such and the latter breeds (assumed) facts. The husbandryman uses his skills to enrich the future, the historian uses his to enrich the past. Both are usually up to their ankles in bullshit. — Tom Robbins

I am exclusively occupied with the problem of gravitation and hope with the help of a local mathematician friend [Marcel Grossman] to overcome all the difficulties. One thing is certain, however, that never in life have I been quite so tormented. A great respect for mathematics has been instilled within me, the subtler aspects of which, in my stupidity, I regarded until now as pure luxury. — Albert Einstein

In the pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist there when the last of their radiant host shall have fallen from heaven. — Edward Everett Hale

There are those who believe that mathematics can sustain itself and grow without any further contact with anything outside itself, and those who believe that nature is still and always will be one of the main (if not the main) sources of mathematical inspiration. The first group is identified as "pure mathematicians" (though "purist" would be more adequate) while the second is, with equal inadequacy, referred to as "applied". — Mark Kac

The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction ... Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about. — Alfred North Whitehead

Darwin's great gift to science was simplifying all life to pure mathematics: your one and only goal on earth is multiplication. Everything you do, every instinct you have, is an evolutionary urge to make babies and leave behind as many copies of yourself as possible. From that perspective, heroism makes no sense. Why risk the grave for someone else if there's no guarantee of a biological payoff? Dying for your own kids: smart. Dying for a rival's? Genetic suicide. — Christopher McDougall

You can see the meaning of the statement that "Literature is a living art" most easily and clearly, perhaps, by contrasting Science and Art at their two extremes - say Pure Mathematics and Acting. Science as a rule deals with things, Art with man's thought and emotion about things. — Arthur Quiller-Couch

Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. — Alfred Adler

What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant. — James Sanborn

Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal". — Bertrand Russell

Whether we like it or not, if we are to pursue a career in science, eventually we have to learn the "language of nature": mathematics. Without mathematics, we can only be passive observers to the dance of nature rather than active participants. As Einstein once said, "Pure mathematics is, in its way, the poetry of logical ideas." Let me offer an analogy. One may love French civilization and literature, but to truly understand the French mind, one must learn the French language and how to conjugate French verbs. The same is true of science and mathematics. Galileo once wrote, "[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles, and other geometrical figures, without which means it is humanly impossible to understand a single word. — Michio Kaku

That's how you write novels actually. You suddenly hit upon something and you realize this is the path you were meant to take. You'd be a fool if you didn't follow it. Perhaps it's like solving a difficult question in pure mathematics. There must be a moment when the solution is so simple and evident that you wonder why you hadn't come upon it before. When you do come upon it, you know it in the deepest part of your being. It carries its own logic. — Don DeLillo

I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics. — Benoit Mandelbrot

It might seem that the empirical philosopher is the slave of his material, but that the pure mathematician, like the musician, is a free creator of his world of ordered beauty. — Bertrand Russell

Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty. — Archimedes

While, on the one hand, the end of scientific investigation is the discovery of laws, on the other, science will have reached its highest goal when it shall have reduced ultimate laws to one or two, the necessity of which lies outside the sphere of our cognition. These ultimate laws-in the domain of physical science at least-will be the dynamical laws of the relations of matter to number, space, and time. The ultimate data will be number, matter, space, and time themselves. When these relations shall be known, all physical phenomena will be a branch of pure mathematics. — William Mitchinson Hicks

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [ ... ] Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate. — Bertrand Russell

Mathematics is one of the deepest and most powerful expressions of pure human reason, and, at the same time, the most fundamental resource for description and analysis of the experiential world. — Hyman Bass

This queer crotchet [of Hamilton's] that algebra is the science of pure time has attracted many philosophers, and quite recently it has been exhumed and solemnly dissected by owlish metaphysicians seeking the philosopher's stone in the gall bladder of mathematics. — Eric Temple Bell

The first successes were such that one might suppose all the difficulties of science overcome in advance, and believe that the mathematician, without being longer occupied in the elaboration of pure mathematics, could turn his thoughts exclusively to the study of natural laws. — Joseph Louis Francois Bertrand

Pure analysis puts at our disposal a multitude of procedures whose infallibility it guarantees; it opens to us a thousand different ways on which we can embark in all confidence; we are assured of meeting there no obstacles; but of all these ways, which will lead us most promptly to our goal? Who shall tell us which to choose? We need a faculty which makes us see the end from afar, and intuition is this faculty. It is necessary to the explorer for choosing his route; it is not less so to the one following his trail who wants to know why he chose it. — Henri Poincare

Pure concepts of the understanding. So the Humean problem is completely solved, though in a way that would have surprised its inventor. The solution secures an a priori origin for the pure concepts of the understanding, and for the universal laws of nature it secures a status as valid laws of the understanding; but it does this in such a way as to limit the use of these concepts to experience only, and it grounds them in a relation between the understanding and experience that is the complete reverse of anything that Hume envisaged - instead of the concepts being derived from experience, that experience is derived from them. My line of argument yields the following result: All synthetic a priori principles are simply principles of possible experience; they can never be applied to things in themselves, but only to appearances as objects of experience. Hence pure mathematics as well as pure natural science can never bear on anything except appearances — Anonymous

I have long admired Ron Whitehead. He is crazy as nine loons, and his poetry is a dazzling mix of folk wisdom and pure mathematics — Hunter S. Thompson

General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly generalized constructions of pure mathematics and the specific theories of the specialized disciplines. Mathematics attempts to organize highly general relationships into a coherent system, a system however which does not have any necessary connections with the "real" world around us. It studies all thinkable relationships abstracted from any concrete situation or body of empirical knowledge. — Kenneth E. Boulding

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience — Immanuel Kant

[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers, but things of thought to which there could correspond effective objects or relations, even though such a correspondence is not necessary. — Hermann Hankel

There is indeed a fundamental beauty in mathematical abstractions. They so attracted the Greek philosopher Plato that he declared that all those things that we can see and touch are, in fact, mere shadows of the true reality and that the real things of this universe can be found only through the use of pure reason. Plato's knowledge of mathematics was relatively naive, and many of the cherished purities of Greek mathematics have been shown to be flawed. — David Salsburg

Before creation, God did just pure mathematics. Then He thought it would be a pleasant change to do some applied. — John Edensor Littlewood

The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful. — Jules Henri Poincare

But the creative principle resides in mathematics. In a certain sense, therefore, I hold true that pure thought can grasp reality, as the ancients dreamed. — Albert Einstein

There is one thing only which a Muslim can profitably learn from the west, the exact sciences in their pure and applied form. Only natural sciences and mathematics should be taught in Muslim schools, while tuition of European philosophy, literature and history should lose the position of primacy which today it holds on the curriculum. — Muhammad Asad

As an exercise of the reasoning faculties, pure mathematics is an admirable exercise, because it consists of reasoning alone and does not encumber the student with any exercise of judgment. — Richard Whately

I didn't feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world. — Benoit Mandelbrot

Things were changing; I was changing. All swelling limbs and sweating brain, suddenly I had more body than I knew what to do with. Arms and legs became the prey of low desktops and narrow corridors, were ambushed by sharp corners. Mr Baxter ignored my plight. Bodies were inimical to mathematics, or so we were led to believe. Bad hair, acrid breath, lumpy skin, all vanished for an hour every Tuesday and Thursday. Young minds in the buff soared into the sphere of pure reason. Pages turned to parallelograms; cities, circumferences; recipes, ratios. Shorn of our bearings, we groped our way around in this rarefied air. — Daniel Tammet

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. — G.H. Hardy

In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. — Roger Bacon

There are fields of scientific work ... which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology ... in which every single notion receives a separate and different name from each group, and in which important work has been triplicated or quadruplicated, while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field. — Norbert Wiener

Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians. — Edsger Dijkstra

Pure 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. — G.H. Hardy

Is he not the celebrated author of The Dynamics of an Asteroid, a book which ascends to such rarefied heights of pure mathematics that it is said that there was no man in the scientific press capable of criticizing it? — Arthur Conan Doyle

The research reported on in our book "A=B", has moved a whole active field of mathematics from the province of human thought to the realm of computer-fodder. It is quite exciting to think about what other fields of pure mathematics, hitherto thought to be reserved to human intelligence, might be moved to that realm next. The goal is to put ourselves out of business completely, and the work is well underway. — Herbert Wilf

Pure mathematics is, in its way, the poetry of logical ideas. — Albert Einstein

I had changed from being a mathematician to a practicing scientist. I was increasingly embarassed that I could no longer follow some of the more modern branches of pure mathematics. — John Pople

It was as though applied mathematics was my spouse, and pure mathematics was my secret lover. — Edward Frenkel

In sum, the fruition of 50 years of research, and several hundred million dollars in government funds, has given us the following picture of sub-atomic matter. All matter consists of quarks and leptons, which interact by exchanging different types of quanta, described by the Maxwell and Yang-Mills fields. In one sentence, we have captured the essence of the past century of frustrating investigation into the subatomic realm, From this simple picture one can derive, from pure mathematics alone, all the myriad and baffling properties of matter. (Although it all seems so easy now, Nobel laureate Steven Weinberg, one of the creators of the Standard Model, once reflected on how tortuous the 50-year journey to discover the model had been. He wrote, "There's a long tradition of theoretical physics, which by no means affected everyone but certainly affected me, that said the strong interactions [were] too complicated for the human mind.") — Michio Kaku

In pure mathematics the mind deal only with its own creations and imaginations. The concepts of number and form have not been derived from any source other than the world of reality. The ten fingers on which men learned to count, that is, to carry out the first arithmetical operation, may be anything else, but they are certainly not only objects that can be counted, but also the ability to exclude all properties of the objects considered other than their number-and this ability is the product of a long historical evolution based on experience. Like the idea of number, so the idea of form is derived exclusively from the external world, and does not arise in the mind as a product of pure thought. — Friedrich Engels

Even in pure mathematics they can't remove all paradox, and the rest of us should also recognize we are going to have to endure a lot of paradox, like it or not. — Charlie Munger

Love was even more mathematical than poetry. It was the pure mathematics of the spirit. — Charles Williams

It is pure mythology that women cannot perform as well as men in science, engineering and mathematics. In my experience, the opposite is true: Women are often more adept and patient at untangling complex problems, multitasking, seeing the possibilities in new solutions and winning team support for collaborative action. — Weili Dai

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

The world is colors and motion, feelings and thoughts and what does math have to do with it? Not much, if 'math' means being bored in high school, but in truth mathematics is the one universal science. Mathematics is the study of pure pattern and everything in the cosmos is a kind of pattern. — Rudy Rucker

There is a close analogy between organic chemistry in its relation to biochemistry and pure mathematics in its relation to physics. — Robert Robinson

The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the laws of human intelligence. — James Joseph Sylvester

Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos [mathematics], where pure thought can dwell in its natural home ... — Bertrand Russell

The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit. — Alfred North Whitehead

You are following Jesus and shaping our world in the power of the Spirit. And when the final consummation comes, the work that you have done - whether in Bible study or biochemistry, whether in preaching or in pure mathematics, whether in digging ditches or in composing symphonies - will stand, will last.

The fact that we live between, so to speak, the beginning of the End and the end of the End, should enable us to come to terms with our vocation to be for the world that Jesus was for Israel, and in the power of the Spirit to forgive and retain sins. — N. T. Wright

This is not mathematics, it is theology.
(On being exposed to Hilbert's work in invariant theory.) — Paul Gordan

A chess problem is an exercise in pure mathematics. — G.H. Hardy

... That little narrative is an example of the mathematician's art: asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations. There is really nothing else quite like this realm of pure idea; it's fascinating, it's fun, and it's free! — Paul Lockhart

Mathematics is the bold luxury of pure reason, one of the few that remain today. — Robert Musil

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method-more daring than anything that the history of philosophy records-of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason. — Nicholas Murray Butler

The Night Dances A smile fell in the grass. Irretrievable! And how will your night dances Lose themselves. In mathematics? Such pure leaps and spirals - - Surely they travel The world forever, I shall not entirely Sit emptied of beauties, the gift Of your small breath, the drenched grass Smell of your sleeps, lilies, lilies. Their flesh bears no relation. Cold folds of ego, the calla, And the tiger, embellishing itself - - — Sylvia Plath

It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true. — Bertrand Russell

It has been a fortunate fact in the modern history of physical science that the scientist constructing a new theoretical system has nearly always found that the mathematics ... required ... had already been worked out by pure mathematicians for their own amusement ... The moral for statesmen would seem to be that, for proper scientific "planning", pure mathematics should be endowed fifty years ahead of scientists. — R. B. Braithwaite

The question as to which of these two theories applies to the actual world is, like all questions concerning the actual world, in itself irrelevant to pure mathematics.* But the argument against absolute position usually takes the form of maintaining that a space composed of points is logically inadmissible, and hence issues are raised which a philosophy of mathematics must discuss. In what follows, I am concerned only with the question: Is a space composed of points self-contradictory? It is true that, if this question be answered in the negative, the sole ground for denying that such a space exists in the actual world is removed; but this is a further point, which, being irrelevant to our subject, will be left entirely to the sagacity of the reader. — Bertrand Russell

There are worlds built on rainbows and worlds built on rain. There are worlds of pure mathematics, where every number chimes like crystal as it rolls into reality. There are worlds of light and worlds of darkness, worlds of rhyme and worlds of reason, and worlds where the only thing that matters is the goodness in a hero's heart. — Seanan McGuire

Mathematics, natural science, laws, arts, even morality, etc. do not completely fill the soul; there is always a space left over reserved for pure and speculative reason, the emptiness of which prompts us to seek in vagaries, buffooneries, and mysticism for what seems to be employment and entertainment, but what actually is mere pastime undertaken in order to deaden the troublesome voice of reason, which, in accordance with its nature, requires something that can satisfy it and does not merely subserve other ends or the interests of our inclinations. — Immanuel Kant

Except in pure mathematics, nothing is known for certain (although much is certainly false). — Carl Sagan

Pure mathematics, may it never be of any use to anyone. — Henry John Stephen Smith

Historical research of the truly scholastic kind is not connected with human beings at all. It is a pure study, like higher mathematics. — C.V. Wedgwood

The highest form of pure thought is in mathematics. — Plato

In the field of Egyptian mathematics Professor Karpinski of the University of Michigan has long insisted that surviving mathematical papyri clearly demonstrate the Egyptians' scientific interest in pure mathematics for its own sake. I have now no doubt that Professor Karpinski is right, for the evidence of interest in pure science, as such, is perfectly conclusive in the Edwin Smith Surgical Papyrus. — James Henry Breasted

Even in the realm of pure mathematics, the mathematician may use any set of symbols he desires within any given region of space-time; he may even go so far as to maintain that any one set of symbols fits the scheme as well as any other, but to erect this method into a philosophy and confuse independence of any one special meaning with independence of all meaning is unjustified and unwarranted. — Fulton J. Sheen

We have two chief survivors of those ancient schools: the Bene Gesserit and the Spacing Guild. The Guild, so we think, emphasizes almost pure mathematics. Bene Gesserit performs another function. — Frank Herbert

There are a multitude of allied branches of knowledge connected with mans condition; the relation of these to political economy is analogous to the connexion of mechanics, astronomy, optics, sound, heat, and every other branch more or less of physical science, with pure mathematics. — William Stanley Jevons

Applied mathematics will always need pure mathematics just as anteaters will always need ants. — Paul Halmos