Mathematics Quotes

For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated unto use with sufficient dexterity, without the aid and intervening of the mathematics, of which sort are perspective, music, astronomy, cosmography, architecture, engineery, and divers others. ~ Francis Bacon

Douady and Hubbard used a brilliant chain of new mathematics to prove that every floating molecule does indeed hang on a filigree that binds it to all the rest, a delicate web springing from tiny outcroppings on the main set, a "devil's polymer," in Mandelbrot's phrase. The mathematicians proved that any segment-no matter where, and no matter how small-would, when blown up by the computer microscope, reveal new molecules, each resembling the main set and yet not quite the same. Every new molecule would be surrounded by its own spirals and flame-like projections, and those, inevitably, would reveal molecules tinier still, always similar, never identical, fulfilling some mandate of infinite variety, a miracle of miniaturization in which every new detail was sure to be a universe of its own, diverse and entire. ~ James Gleick

Cardinal arithmetic will be quite important for us, so we spend some time on it. Since, however, it tends to be trivial, we shall not need to spend much of this time on proofs. ~ Keith Devlin

Mathematics catalogues everything that is not self-contradictory; within that vast inventory, physics is an island of structures rich enough to contain their own beholders. ~ Greg Egan

If it hadn't been for this chance hospital encounter, accidental in all senses, Victor might never have courted a girl. He already felt well on his way to middle age, and his social life was still limited to the chess club. Victor didn't really feel the need for another person in his life, in fact he found the concept of "sharing" a life bizarre. He had mathematics, which filled up his time almost completely, so he wasn't entirely sure what he wanted with a wife. Women seemed to him to be in possession of all kinds of undesirable properties, chiefly madness, but also a multiplicity of physical drawbacks - blood, sex, children - which were unsettling and other. ~ Kate Atkinson

It could be that the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof would not be invented for a hundred years. ~ Andrew Wiles

Most remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying 'No, that's wrong.' Rather, he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole of the art of teaching. ~ W.W. Sawyer

Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. ~ Nikola Tesla

One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics. ~ Henri Poincare

In 1908 Handy didn't know anything about the blues and he doesn't know anything about jazz and stomps to this day. I myself figured out the peculiar form of mathematics and harmonies that was strange to all the world but me. ~ Jelly Roll Morton

Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies. ~ Keith Devlin

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

All high mathematics serves to do is to beget higher mathematics. ~ Ashim Shanker

As a graduate student I studied mathematics fairly broadly, and I was fortunate enough, besides developing the idea which led to 'Non-Cooperative Games,' also to make a nice discovery relating to manifolds and real algebraic varieties. ~ John Forbes Nash, Jr.

That's the big difference between [the BookWorld] and [the RealWorld]," said Plum. "When things happen after a randomly pointless event, all that follows is simply unintended consequences, not a coherent narrative thrust that propels the story forward."
I rolled the idea of unintended consequences around in my head. "Nope, I said finally, "you've got me on that one."
"It confuses me, too," admitted Plum, "but that's the RealWorld for you. A brutal and beautiful place, run for the most part on passion, fads, incentives, and mathematics. A lot of mathematics. ~ Jasper Fforde

History, Geology, Psychology, Philosophy, Chemistry, Physics, Theology, Mathematics, Technology, Sociology, Biology, and the list goes on and on. If all this body of knowledge exist for human consumption, why would I specialize in only one field? ~ Allan Amanyire

You may not know this, but talking about mathematics eliminates any possibility of being kissed in the first place. ~ Lisa Kleypas

The oldest problem in economic education is how to exclude the incompetent. A certain glib mastery of verbiage-the ability to speak portentously and sententiously about the relation of money supply to the price level-is easy for the unlearned and may even be aided by a mildly enfeebled intellect. The requirement that there be ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device. ~ John Kenneth Galbraith

To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples ... ~ John B. Conway

Mathematicians deal with large numbers sometimes, but never in their income. ~ Isaac Asimov

I still don't like authority exercised without reason. But they laugh at you at Cambridge if you say that sort of thing. For them, the law is a system of rules not that different from mathematics. ~ John Lloyd

I was fortunate to grow up in a middle-class home with two hardworking parents who enjoyed both reading and mathematics. ~ Freeman A. Hrabowski III

Mathematicians tend to prefer a worst-case analysis, a kind of paranoia that is especially understandable if you live in Israel! ~ Noga Alon

I might not be all that good with mathematics in class; but go into my mind; and you will see that type of mathematic I put in; in my everyday life, and you can say that I am genius in a way in the terms of mentality; but retarded in class. ~ Temitope Owosela

There are some days where I feel like the sun, moon, and stars. And there are days like today when I feel like the 'e' in mathematics. ~ Thalia Skibo

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

Making mathematics accessible to the educated layman, while keeping high scientific standards, has always been considered a treacherous navigation between the Scylla of professional contempt and the Charybdis of public misunderstanding. ~ Gian-Carlo Rota

What would mathematics have amounted to without the imagination of its devotees-its giants and their followers? There never was a discovery made without the urge of imagination-of imagination which broke the roadway through the forest in order that cold logic might follow. ~ David Eugene Smith

The true man of science will know nature better by his finer organization; he will smell, taste, see, hear, feel, better than other men. His will be a deeper and finer experience. We do not learn by inference and deduction and the application of mathematics to philosophy, but by direct intercourse and sympathy. It is with science as with ethics,
we cannot know truth by contrivance and method; the Baconian is as false as any other, and with all the helps of machinery and the arts, the most scientific will still be the healthiest and friendliest man, and possess a more perfect Indian wisdom. ~ Henry David Thoreau

Good general theory does not search for the maximum generality, but for the right generality. ~ Saunders Mac Lane

{Before the time of Benjamin Peirce it never occurred to anyone that mathematical research} was one of the things for which a mathematical department existed. Today it is a commonplace in all the leading universities. Peirce stood alone - a mountain peak whose absolute height might be hard to measure, but which towered above all the surrounding country. ~ Julian Coolidge

What we mean when speaking of "myth" in general is story, the ability of story to explain ourselves to ourselves in ways that physics, philosophy, mathematics, chemistry - all very highly useful and informative in their own right - can't. ~ Thomas C. Foster

It seems to me there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally suprise me. I do not think of mathemaatics as invented but rather discovered. ~ George Andrews

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

I think there's something heavenly about numbers, anyway. ~ Agatha Christie

This is not mathematics; this is theology. ~ Paul Gordan

On the question of whether mathematics was discovered or invented, Pythagoras and the Pythagoreans had no doubt-mathematics was real, immutable, omnipresent, and more sublime than anything that could conceivably emerge from the feeble human mind. The Pythagoreans literally embedded the universe into mathematics. In fact, to the Pythagoreans, God was not a mathematician-mathematics was God!

The importance of the Pythagorean philosophy lies not only in its actual, intrinsic value. By setting the stage, and to some extent the agenda, for the next generation of philosophers-Plato in particular-the Pythagoreans established a commanding position in Western thought. ~ Mario Livio

Brain: an apparatus with which we think we think. ~ Ambrose Bierce

Pythagorean thought was dominated by mathematics, but it was also profoundly mystical. ~ Vanna Bonta

Mathematics takes us still further from what is human into the region of absolute necessity, to which not only the actual world, but ever possible world, must conform. ~ Bertrand Russell

Now I feel as if I should succeed in doing something in mathematics, although I cannot see why it is so very important ... The knowledge doesn't make life any sweeter or happier, does it? ~ Helen Keller

The geometer offers to the physicist a whole set of maps from which to choose. One map, perhaps, will fit the facts better than others, and then the geometry which provides that particular map will be the geometry most important for applied mathematics. ~ G.H. Hardy

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold. ~ Henri Poincare

As soon as a thought or word becomes a tool, one can dispense with actually 'thinking' it, that is, with going through the logical acts involved in verbal formulation of it. As has been pointed out, often and correctly, the advantage of mathematics the model of all neo-positivistic thinking lies in just this 'intellectual economy.' Complicated logical operations are carried out without actual performance of the intellectual acts upon which the mathematical and logical symbols are based ... Reason ... becomes a fetish, a magic entity that is accepted rather than intellectually experienced. ~ Max Horkheimer

I'm obviously attuned to pick up mathematics whenever I can see it. But in Mozart there is a lot of conscious use of mathematical symbolism and numbers in order to try and give messages. ~ Marcus Du Sautoy

I have a name for people who went to the extreme efficient market theory-which is "bonkers". It was an intellectually consistent theory that enabled them to do pretty mathematics. So I understand its seductiveness to people with large mathematical gifts. It just had a difficulty in that the fundamental assumption did not tie properly to reality. ~ Charlie Munger

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing-one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me. ~ Paul Halmos

The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules ... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms. ~ Kurt Godel

The best of ideas is hurt by uncritical acceptance and thrives on critical examination. ~ George Polya

Physics is to mathematics like sex is to masturbation. ~ Richard Feynman

This "Hawking temperature" of a black hole and its "Hawking radiation" (as they came to be called) were truly radical - perhaps the most radical theoretical physics discovery in the second half of the twentieth century. They opened our eyes to profound connections between general relativity (black holes), thermodynamics (the physics of heat) and quantum physics (the creation of particles where before there were none). For example, they led Stephen to prove that a black hole has entropy, which means that somewhere inside or around the black hole there is enormous randomness. He deduced that the amount of entropy (the logarithm of the hole's amount of randomness) is proportional to the hole's surface area. His formula for the entropy is engraved on Stephen's memorial stone at Gonville and Caius College in Cambridge, where he worked.
For the past forty-five years, Stephen and hundreds of other physicists have struggled to understand the precise nature of a black hole's randomness. It is a question that keeps on generating new insights about the marriage of quantum theory with general relativity - that is, about the ill-understood laws of quantum gravity. ~ Stephen Hawking

The afflicted are almost upon them. The air is a din of hypersonic bursts, snarls and empty shell casings. But still I hear him. As his people start to fall. As his pistol clicks empty. As he rises with only his knuckles left between him and the sheer brutality of mathematics. As the music swells above the carnage, still I hear him breathe the words. "Tell them I was thinking of them. At the end." They pile onto him. All snarls and teeth and fists. But as he falls, I am holding his hand. Easing him into his long good night. "I will tell them, David." The last words he will ever hear. 'I promise. ~ Amie Kaufman

Most expert, skilled behavior works this way, whether it is playing tennis or a musical instrument, or doing mathematics and science. Experts minimize the need for conscious reasoning. Philosopher ~ Donald A. Norman

What this committee needs, what this media center needs, is a good dose of Jeeves."
"I'm sorry," said Mr. Peabody, a mathematics lecturer who sat hunched at the far end of the table taking the minutes. "How do you spell that?"
"Is it possible," said Arthur, raising both his shoulders and his voice, "that we are working in a university where lecturers are not aware of the identity of one Reginald Jeeves, the gentleman's personal gentleman and the personal gentleman's gentleman? What has happened to cultural literacy, my fellow members of the Advisory Committee for the Media Center? This sort of ignorance is exactly what needs addressing. What I mean, Mr. Peabody, when I say that we need a dose of Jeeves, is that we need quiet and reasoned wisdom that leads to prompt and directed action. ~ Charlie Lovett

People who wish to analyze nature without using mathematics must settle for a reduced understanding. ~ Richard P. Feynman

It now becomes clear that consistency is not a property of a formal system per se, but depends on the interpretation which is proposed for it. By the same token, inconsistency is not an intrinsic property of any formal system. ~ Douglas R. Hofstadter

Einstein felt that he did not have great mathematical gifts and deliberately chose not to take courses and to continue in that area.

The fact that I neglected mathematics to a certain extent had its causes not merely in my stronger interest in science than in mathematics but also in the following strange experience....I saw that mathematics was split up into numerous specialties, each of which could easily absorb the short lifetime granted to us....In physics, however, I soon learned to scent out that which was able to lead to fundamentals and to turn aside from everything else, from the multitude of things that clutter up the mind and divert it from the essential.

This capacity to pick out important issues dovetailed with Einstein's search for the most general possible conception. "In a man of my type," he declared, "the turning point of the development lies in the fact that gradually the major interest disengages itself to a far reaching degree from the momentary and the merely personal and turns toward the striving for a mental grasp of things. ~ Howard Gardner

Not a lot of people know this, but I'm very good at mathematics. When I was an angry teenager, I used to sit in my room and do quadratic equations to calm myself down. ~ Samantha Bond

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics? ~ Richard Courant

If things are nice there is probably a good reason why they are nice: and if you do not know at least one reason for this good fortune, then you still have work to do. ~ Richard Askey

To solve math problems, you need to know the basic mathematics before you can start applying it. ~ Catherine Asaro

If equations are trains threading the landscape of numbers, then no train stops at pi. ~ Richard Preston

See appendix A for a proof that Winston Churchill was a carrot. ~ Charles Seife

I'm not really interested in religion or history or science or mathematics or psychology or politics or geography. I feel I am above them all, except geography. Geography is above me for now. ~ Bill Callahan

As John Adams famously wrote during the American Revolution, "I must study politics and war, that our sons may have liberty to study mathematics and philosophy. Our sons ought to study mathematics and philosophy, geography, natural history and naval architecture, navigation, commerce and agriculture in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry and porcelain." So maybe today they're writing apps rather than studying poetry, but that's an adjustment for the age. ~ Fareed Zakaria

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

The various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of how a self-aware substructure will perceive more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics! ~ Max Tegmark

Every formula which expresses a law of nature is a hymn of praise to God. ~ Maria Mitchell

A felicitous but unproved conjecture may be of much more consequence for mathematics than the proof of many a respectable theorem. ~ Atle Selberg

The greatest reward for a student is not a good grade. It is the willingness of his teacher to listen to him. ~ Nikolay Konstantinov

Petyr had been talking about mathematics again, boring everyone, when her mother looked up from her plate with a smile and announced that Julie had written a letter to say she'd quit the family. Clarissa's mouth had dropped open. It was like saying that the sun had decided to become a politician or that four had decided to be eight. It wasn't quite incomprehensible, but it lived on the edge. ~ James S.A. Corey

The Good Lord made all the integers; the rest is man's doing. ~ Leopold Kronecker

I am too good for philosophy and not good enough for physics. Mathematics is in between. ~ George Polya

Life is like mathematics,
with full of problems,
More you solve problems,
more you become expert,
Once you become expert,
you enjoy solving problems,
Once you enjoy solving problem,
you demand more problem of all type.
No matter wherever one goes,
there will be problems (opportunity)
One who loves to solve problems
is real mathematician. ~ V.B. Jadhav

Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility. ~ Charles Sanders Peirce

The works of Lavoisier and his associates operated upon many of us at that time like the Sun's rising after a night of moonshine: but Chemistry is now betrothed to the Mathematics, and is in consequence grown somewhat shy of her former admirers. ~ Johann Wolfgang Von Goethe

If you plug in a number and the math starts getting creepy (anything involving fractions or negative numbers is creepy) ... ~ Doug Pierce

We have such a great depth of human history in all of the arts, whether it's opera or mathematics or painting or classical music or jazz. There's so many things to study, new books to read, and certainly always ways to transform old ideas and to come up with new ones. ~ Patti Smith

I am not one of the "slower" talents, like Reason or Mathematics. I am Music. If I bless you singing, you can do so from your first attempt. ~ Mitch Albom

There are four great sciences, without which the other sciences cannot be known nor a knowledge of things secured ... Of these sciences the gate and key is mathematics ... He who is ignorant of this [mathematics] cannot know the other sciences nor the affairs of this world. ~ Roger Bacon

It would be nice if we could design a virtual reality in Hyperbolic Space, and meet each other there. ~ Donald Knuth

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds. ~ G.H. Hardy

I don't know whether guys are more promiscuous or just bigger liars. ~ Jennifer Tour Chayes

On the ostensible exactitude of certain branches of human knowledge, including mathematics. The exactness is a fake. ~ Alfred North Whitehead

Unless the chemist learns the language of mathematics, he will become a provincial and the higher branches of chemical work, that require reason as well as skill, will gradually pass out of his hands. ~ Alexander Crum Brown

There are two generic and invariable features that characterize utopias. One is the content: the authors of utopias paint what they consider to be ideal societies; translating this into the language of mathematics, we might say that utopias bear a + sign. The other feature, organically growing out of the content, is to be found in the form: a utopia is always static; it is always descriptive and has no, of almost no, plot dynamics. ~ Yevgeny Zamyatin

The word "art" means harmony for me. I never speak of mathematics and never bother with the Spirit. My only science is the choice of impressions that the light in the universe furnishes to my consciousness as an artisan which I try, by imposing an Order, and Art, an appropriate representative life, to organize ... ~ Robert Delaunay

It is not of the essence of mathematics to be conversant with the ideas of number and quantity. ~ George Boole

In music, musicians must be able to read musical notes and have developed the skill to follow the music from their studies. This skill allows them to read new musical notes and be capable of hearing most or all of the sounds (melodies, harmonies, etc.) in their head without having to play the music piece. By analogy, in Mathematics, we believe a scientist, engineer or mathematician must be able to read and understand mathematical codes (e.g., Maple, Mathematica) in their head without having to execute the problem. ~ Inna K. Shingareva

Mathematics directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars. ~ Edward Frenkel

Obscenity is a function of culture - a function in the mathematical sense, I mean, its value changing with that of the variables on which it depends. ~ A.P.

[The golden proportion] is a scale of proportions which makes the bad difficult [to produce] and the good easy. ~ Albert Einstein

Mathematics is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst. ~ Norbert Wiener

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense. ~ William Thomson, 1st Baron Kelvin

Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks ... Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can. ~ Silvanus P. Thompson

There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science. ~ Carl Friedrich Gauss

There are all sorts of things embodied in the LEGO brick - geometry and mathematics and truth and proportion and shape and colour ... It is a faintly spiritual activity that everybody connects with. ~ James May

Natural selection is a mechanism for generating an exceedingly high degree of improbability. ~ Ronald A. Fisher

The spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce and answer. ~ Paul R. Halmos

Mathematics is not merely an idle art form, it is an essential part of our society. ~ Richard Hamming