Quotes & Sayings About Mathematics

One cannot understand ... the universality of laws of nature, the relationship of things, without an understanding of mathematics. There is no other way to do it. — Richard P. Feynman

In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture. — Brian Greene

By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists. — M.C. Escher

I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind.
(Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.) — Andrew John Wiles

In adolescence, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics. — Bertrand Russell

I mean that they (students) should not play life, or study it merely, while the community supports them at this expensive game, but earnestly live it from beginning to end. How could youths better learn to live than by at once trying the experiment of living? Methinks this would exercise their minds as much as mathematics. — Henry David Thoreau

Luck is the grand equalizer. — Nassim Nicholas Taleb

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

What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else. — Stanislaw Ulam

I write rhymes with addition and algebra, mental geometry. — Ice-T

Music at times is more like perfume than mathematics. — Gabriel Marcel

The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation. — G.H. Hardy

I tell them that if they will occupy themselves with the study of mathematics they will find in it the best remedy against the lusts of the flesh. — Thomas Mann

It is insufficient to protect ourselves with laws; we need to protect ourselves with mathematics. — Bruce Schneier

If a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that it would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields. Such a sacrifice could be justified only by economic necessity of age. — G.H. Hardy

The study of mathematics is apt to commence in disappointment ... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it. — Alfred North Whitehead

At 20, I realized that I could not possibly adjust to a feminine role as conceived by my father and asked him permission to engage in a professional career. In eight months I filled my gaps in Latin, Greek and mathematics, graduated from high school, and entered medical school in Turin. — Rita Levi-Montalcini

I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it. — Malcolm X

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

I doubt not, but from self-evident Propositions, by necessary Consequences, as incontestable as those in Mathematics, the measures of right and wrong might be made out. — John Locke

I am not qualified to say whether or not God exists. I kind of doubt He does. Nevertheless I'm always saying that the SF( The SF is the supreme Fascist, the Number-One guy up there) has this transfinite book-transfinite being a concept in mathematics that is larger than infinite-that contains the best proofs of all mathematical theorems, proofs that are elegant and perfect. — Paul Erdos

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. — Mario Livio

Courses in prosody, rhetoric and comparative philology would be required of all students, and every student would have to select three courses out of courses in mathematics, natural history, geology, meteorology, archaeology, mythology, liturgics, cooking. — W. H. Auden

the theorem of incompleteness . . . [shows] there is nothing on this level of existence that can fully explain this level of existence. — Pat Cadigan

Even farts made no impression on it. I can't help it, gas escapes from my fundament on the least pretext, it's hard not to mention it now and then, however great my distaste. One day I counted them. Three hundred and fifteen farts in nineteen hours, or an average of over sixteen farts an hour. After all it's not excessive. Four farts every fifteen minutes. It's nothing. Not even one fart every four minutes. It's unbelievable. Damn it, I hardly fart at all, I should never have mentioned it. Extraordinary how mathematics help you to know yourself. — Samuel Beckett

... 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

I appreciate and enjoy mathematics and science and all that side of things. I definitely have that side of me even though I'm not by any means an expert, but I love reading about physics and math and that kind of stuff. I wish I knew more than I did. I mean, I read books written for laymen, not textbooks or anything. — Chris Parnell

Like musicians who can read and write complicated scores in a world without sounds, for us mathematics is a source of delight, excitement, and even controversy which are hard to share with non mathematicians. In our small micro-cosmos we should ever seek the right balance between competition and solidarity, criticism and empathy, exclusion and inclusion. — Gil Kalai

It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true. — George Bernard Shaw

Economics is haunted by more fallacies than any other study known to man. This is no accident. The inherent difficulties of the subject would be great enough in any case, but they are multiplied a thousandfold by a factor that is insignificant in, say, physics, mathematics or medicine - the special pleading of selfish interests. — Henry Hazlitt

Mathematics is universal. It's discovered by human beings, but the rules of mathematics are the same throughout the universe and the laws of the universe. — Paul Davies

If I had inherited a fortune I should probably not have cast my lot with mathematics. — Joseph-Louis Lagrange

Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation. — Hermann Weyl

There are few humanities that could surpass in discipline, in beauty, in emotional and aesthetic satisfaction, those humanities which are called mathematics, and the natural sciences. — Robert Watson-Watt

David Henderson's 1970 poem "Keep on Pushing," also analyzed the geographies of urban warfare in the Summer of 1964's Harlem Riots. Henderson warned of the crude mathematics of wide avenues that can swallow protest pickets, easily dismantle popular barricades, and muster five hundred cops in fifteen minutes, but he also suggests how, "For Harlem/ reinforcements come from the Bronx / just over the three-borough Bridge. / a shot a cry a rumor / can muster five hundred Negroes / from idle and strategic street corners / bars stoops hallways windows. — Anonymous

The effort of the economist is to "see," to picture the interplay of economic elements. The more clearly cut these elements appear in his vision, the better; the more elements he can grasp and hold in his mind at once, the better. The economic world is a misty region. The first explorers used unaided vision. Mathematics is the lantern by which what before was dimly visible now looms up in firm, bold outlines. The old phantasmagoria disappear. We see better. We also see further. — Irving Fisher

Much of what we know about mathematics and trade comes from the Arabs. Then came stagnation, and now they're the West's whipping boy. This is a problem that cannot be solved overnight, and certainly not militarily. — Brent Scowcroft

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

One of the strangest features of string theory is that it requires more than the three spatial dimensions that we see directly in the world around us. That sounds like science fiction, but it is an indisputable outcome of the mathematics of string theory. — Brian Greene

Most people would have probably lost count around seven. This was, Harry knew
from his extensive reading on logic and arithmetic, the largest number that most people
could visually appreciate. Put seven dots on a page, and most people can take a quick
glance and declare, "Seven." Switch to eight, and the majority of humanity was lost. — Julia Quinn

For centuries, everything was taught through music. History was taught through music; language and mathematics were taught through music. — T Bone Burnett

Einstein and the Quantum is delightful to read, with numerous historical details that were new to me and cham1ing vignettes of Einstein and his colleagues. By avoiding mathematics, Stone makes his book accessible to general readers, but even physicists who are well versed in Einstein and his physics are likely to find new insights into the most remarkable mind of the modern era. — Daniel Kleppner

There are no creeds in mathematics. — Peter Drucker

Whoever despises the high wisdom of mathematics nourishes himself on delusion and will never still the sophistic sciences whose only product is an eternal uproar. — Leonardo Da Vinci

I descended to the ocean floor and encountered bloated, symmetrical creatures with pumping white hearts and translucent skin. Collapsed blue civilizations lived down there, fissured and antiseptic, craggy with barnacles and blistering rust. I reached into the heart of the earth, the sky, the moon. I colonized language, mathematics, schemes of chemical order and atomic weight. I studied the manufacture of automobiles, microcircuitry, Kleenex and planets. I memorized the gross national products of nations and hemispheres, the populations of cities and states and principalities, the achievements of presidents, tyrants and kings. I was trying to learn what I suspect Mom had learned already: that there were journeys we all make alone that take us far away from one another. — Scott Bradfield

Increasingly, the mathematics will demand the courage to face its implications. — Michael Crichton

Getting even was the basis of many primate semantic confusions, such as"expropriating the expropriators," "an absolute crime demands an absolute penalty," "they did it to me so I can do it to them," and, in general, the emotional mathematics of "one plus one equals zero" (1 + 1 = 0).

The primates were so dumb they didn't realize that one plus one equals two (1 + 1 = 2) and one murder plus one murder equals two murders, one crime plus one crime equals two crimes, etc. — Robert Anton Wilson

The mathematics is not there till we put it there. — Arthur Eddington

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

A report released by the Partnership for a New American Economy and the Partnership for New York City predicts that by 2018, there will be 800,000 science, technology, engineering, and mathematics (STEM) jobs in the United States that require a master's degree or higher - and only around 550,000 American-graduates with this training. — Marvin Ammori

When the twins asked what cuff-links were for - "To link cuffs together," Ammu told them - they were thrilled by this morsel of logic in what had so far seemed an illogical language. Cuff+link = cuff-link. This, to them, rivaled the precision of logic and mathematics. Cuff-links gave them an inordinate (if exaggerated) satisfaction, and a real affection for the English language. — Arundhati Roy

The latest authors, like the most ancient, strove to subordinate the phenomena of nature to the laws of mathematics. — Isaac Newton

Actually, most mathematics courses do not teach reasoning of any kind. Students are so baffled by the material that they are obliged to memorize in order to pass examinations. — Morris Kline

Sex is mathematics. Individuality no longer an issue. What does intelligence signify? Define reason. Desire - meaningless. Intellect is not a cure. Justice is dead. — Bret Easton Ellis

Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. — Yuri Manin

I'd like to be able to design as easily as if I was using Photoshop. I'd like to be able to create a multicolumn layout and control source order without having to do advanced mathematics or hire Eric Meyer or Dan Cederholm to figure out the CSS, because I can't. — Jeffrey Zeldman

Shut up about Leibniz for a moment, Rudy, because look here: You - Rudy - and I are on a train, as it were, sitting in the dining car, having a nice conversation, and that train is being pulled along at a terrific clip by certain locomotives named The Bertrand Russell and Riemann and Euler and others. And our friend Lawrence is running alongside the train, trying to keep up with us - it's not that we're smarter than he is, necessarily, but that he's a farmer who didn't get a ticket. And I, Rudy, am simply reaching out through the open window here, trying to pull him onto the fucking train with us so that the three of us can have a nice little chat about mathematics without having to listen to him panting and gasping for breath the whole way. — Neal Stephenson

When physicists create a mathematical model of a physical process, they rely on the mathematical framework that can represent that process as closely as possible. When Newton developed a model of forces and motion, the appropriate mathematical framework was calculus. When Einstein developed a model of wave-particle motion, he relied on the mathematics of wave equations and eigenvalues. For many models in scientific computation, the computational framework that best aligns with our need is object orientation. — Anthony Scopatz

For most people, the major hurdle in grasping modern insights into the nature of the universe is that these developments are usually phrased using mathematics. — Brian Greene

Mathematics is the Life of the Gods. — Novalis

Emotion is not a defect in an otherwise perfect reasoning machine. Reason, unfettered from human feeling, has led to as many horrors as any crusader's zeal. What use is pity in a world devoted to maximizing efficiency and productivity? Scientific husbandry tells us to weed out the sick, the infirm, the weak. The ruthless efficiency of euthanasia initiatives and ethnic cleansing are but the programmatic application of Nietzsche's point: from any quantifiable cost-benefit analysis, the principles of animal husbandry should apply to the human race. Charles Darwin himself acknowledged that strict obedience to "hard reason" rather than sympathy for fellow humans would represent a sacrifice of "the noblest part of our nature."6 It is the human heart resonating with empathy, not the logical brain attuned to the mathematics of efficiency, that revolts at cruelty and inhumanity. In — Terryl L. Givens

More often than not, at the end of the day (or a month, or a year), you realize that your initial idea was wrong, and you have to try something else. These are the moments of frustration and despair. You feel that you have wasted an enormous amount of time, with nothing to show for it. This is hard to stomach. But you can never give up. You go back to the drawing board, you analyze more data, you learn from your previous mistakes, you try to come up with a better idea. And every once in a while, suddenly, your idea starts to work. It's as if you had spent a fruitless day surfing, when you finally catch a wave: you try to hold on to it and ride it for as long as possible. At moments like this, you have to free your imagination and let the wave take you as far as it can. Even if the idea sounds totally crazy at first. — Edward Frenkel

Medicine makes people ill, mathematics make them sad and theology makes them sinful. — Martin Luther

The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking. — John Von Neumann

Always preoccupied with his profound researches, the great Newton showed in the ordinary-affairs of life an absence of mind which has become proverbial. It is related that one day, wishing to find the number of seconds necessary for the boiling of an egg, he perceived, after waiting a minute, that he held the egg in his hand, and had placed his seconds watch (an instrument of great value on account of its mathematical precision) to boil!
This absence of mind reminds one of the mathematician Ampere, who one day, as he was going to his course of lectures, noticed a little pebble on the road; he picked it up, and examined with admiration the mottled veins. All at once the lecture which he ought to be attending to returned to his mind; he drew out his watch; perceiving that the hour approached, he hastily doubled his pace, carefully placed the pebble in his pocket, and threw his watch over the parapet of the Pont des Arts. — Camille Flammarion

After years of finding mathematics easy, I finally reached integral calculus and came up against a barrier. I realized that this was as far as I could go, and to this day I have never successfully gone beyond it in any but the most superficial way. — Isaac Asimov

Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions. — Georg Cantor

A mathematician says that an electromagnetic wave travels from Andromeda to your eye and that it also extends from Andromeda to your eye. — Bill Gaede

There is no great religion without a great schism. All of them have it. And that's because you're dealing with something called faith. And faith is not something you can prove; faith is personal opinion. Uh, when you're dealing with something with certainty, like, y'know, science or logic, you don't have the
there's no wiggle room; that's why history is not filled with warring math cults, y'know, because you can settle the issue; you can prove something to be right or wrong, and that's the end of the argument: next case. Whereas, when you're dealing with faith, you can forever argue your point, or another point, because you're dealing with intangibles. Personally, I think, faith is what you ask of somebody when you don't have the goods to prove your point. — Tom Quinn

But I quite like the way you can talk about science without necessarily using mathematics, but using metaphors instead. — Scarlett Thomas

Mathematics speaks to the transcendental, as does this extraordinary friendship. A beautiful book! — James Tanton

We have not begun to understand the relationship between combinatorics and conceptual mathematics. — Jean Dieudonne

[The error in the teaching of mathematics is that] mathematics is expected either to be immediately attractive to students on its own merits or to be accepted by students solely on the basis of the teacher's assurance that it will be helpful in later life. [And yet,] mathematlcs is the key to understanding and mastering our physical, social and biological worlds. — Morris Kline

NAEP data show beyond question that test scores in reading and math have improved for almost every group of students over the past two decades; slowly and steadily in the case of reading, dramatically in the case of mathematics. Students know more and can do more in these two basic skills subjects now than they could twenty or forty years ago... So the next time you hear someone say that the system is "broken," that American students aren't as well educated as they used to be, that our schools are failing, tell that person the facts. — Diane Ravitch

In his ... 'Geometrical peculiarities of the Pyramids', Ballard shows the relationship between the equal area theory and the golden number. After checking Herodotus' statement via dimensions Ballard concludes: 'I have therefore the authority of Herodotus to support the theory which I shall subsequently set forth, that this pyramid was the exponent of lines divided in mean and extreme ratio. — Roger Herz-Fischler

The art of the colorist has in some ways elements of mathematics and music. — Paul Signac

At the risk of being forgotten completely by the media, I went to college and pursued a passion that had nothing to do with acting: mathematics. — Danica McKellar

Let me also remind you that zero, like all of mathematics, is fictional and an idealization. It is impossible to reach absolute zero temperature or to get perfect vacuum. Luckily, mathematics is a fairyland where ideal and fictional objects are possible. — Doron Zeilberger

One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories. — Philip J. Davis

In the past, there was active discrimination against women in science. That has now gone, and although there are residual effects, these are not enough to account for the small numbers of women, particularly in mathematics and physics. — Stephen Hawking

Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use. — Giuseppe Peano

The creative person wants to be a know-it-all. He wants to know about all kinds of things-ancient history, nineteenth century mathematics, current manufacturing techniques, hog futures. Because he never knows when these ideas might come together to form a new idea. It may happen six minutes later, or six months, or six years. But he has faith that it will happen. — Carl Ally

Look, this island is an attempt to re-create a natural environment from the past. To make an isolated world where extinct creatures roam freely. Correct?" "Yes." "But from my point of view, such an undertaking is impossible. The mathematics are so self-evident that they don't need to be calculated. It's rather like my asking you whether, on a billion dollars in income, you had to pay tax. You wouldn't need to pull out your calculator to check. You'd know tax was owed. And, similarly, I know overwhelmingly that one cannot successfully duplicate nature in this way, or hope to isolate it. — Michael Crichton

Mathematics began to seem too much like puzzle solving. Physics is puzzle solving, too, but of puzzles created by nature, not by the mind of man. — Maria Goeppert-Mayer

All creative people hate mathematics. It's the most uncreative subject you can study. — Alec Guinness

Indeed art is fundamental : to science, mathematics and to language. Unfortunately theorists, educators, parents and administrators have not fully understood its importance, relegating it to a secondary role, or that of an add on. — John A. Hiigli

Further, the same Arguments which explode the Notion of Luck, may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design to be, as it were, in Competition with each other, for the production of some sorts of Events, and many calculate what Probability there is, that those Events should be rather be owing to the one than to the other. — Abraham De Moivre

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this. — Andrew John Wiles

Companies want to innovate. Companies that don't innovate wither on the vine. The connection between STEM fields (science, technology, engineering, and mathematics) and the financial stability of a nation is what needs to established. — Neil DeGrasse Tyson

When we talk about the impact inside mathematics, and applications in the sciences, [Mandelbrot] is one of the most important figures of the last 50 years. — Heinz-Otto Peitgen

The 'Muse' is not an artistic mystery, but a mathematical equation. The gift are those ideas you think of as you drift to sleep. The giver is that one you think of when you first awake. — Roman Payne

But Miss Ferguson preferred science over penmanship. Philosophy over etiquette. And, dear heavens preserve them all, mathematics over everything. Not simply numbering that could see a wife through her household accounts. Algebra. Geometry. Indecipherable equations made up of unrecognizable symbols that meant nothing to anyone but the chit herself. It was enough to give Miss Chase hives.

The girl wasn't even saved by having any proper feminine skills. She could not tat or sing or draw. Her needlework was execrable, and her Italian worse. In fact, her only skills were completely unacceptable, as no one wanted a wife who could speak German, discuss physics, or bring down more pheasant than her husband. — Eileen Dreyer

He had a particular facination with the I Ching, that art of tossing three coins three times and divining a pattern out of heads and tails. Pete would begin with questions:
What determined the pattern? Was it random? Was it a higher power? Was is mathematical? Wasn't poker based on mathematical probability and not just luck? Did that mean randomness was actually mathematical? And if the I Ching was governed by mathematics, hey, wouldn't that mean the I Ching was actually predictable, a prescribed answer? And if it was prescribed, did that mean that your life followed the I Ching, like some sort of equation? Or did the I Ching simply capture correctly what had already been determined as the next series of events in your life? — Amy Tan

Of course, the set of logically consistent mathematical structures is many times larger than the set of physical principles. Therefore, some mathematical structures, such as number theory (which some mathematicians claim to be the purest branch of mathematics), have never been incorporated into any physical theory. Some argue that this situation may always exist: Perhaps the human mind will always be able to conceive of logically consistent structures that cannot be expressed through any physical principle. However, there are indications that string theory may soon incorporate number theory into its structure as well. — Michio Kaku

I had done quite a bit of research about math education when I spoke before Congress in 2000 about the importance of women in mathematics. The session of Congress was all about raising more scholarships for girls in college. I told them I felt that it's too late by college. — Danica McKellar

Steele found, for example, that if he could convince women who took difficult mathematics examinations that everyone connected with the test assumed they would perform as well as men, that they did. — Ken Bain

You will perceive that economy, scientifically speaking, is a very contracted science; it is in fact a sort of vague mathematics which calculates the causes and effects of man's industry, and shows how it may be best applied. — William Stanley Jevons

Everyone knows that physicists are concerned with the laws of the universe and have the audacity sometimes to think they have discovered the choices God made when He created the universe in thus and such a pattern. Mathematicians are even more audacious. What they feel they discover are the laws that God Himself could not avoid having to follow. — David Mumford

The 'seriousness' of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas. Thus a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences. — G.H. Hardy

The word "Verse" is used here as the term most convenient for expressing, and without pedantry, all that is involved in the consideration of rhythm, rhyme, meter, and versification ... the subject is exceedingly simple; one tenth of it, possibly may be called ethical; nine tenths, however, appertains to the mathematics. — Edgar Allan Poe