Math Mathematics Quotes & Sayings

The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede. — Edward Gibbon

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them. — George Polya

The appearance of Professor Benjamin Peirce, whose long gray hair, straggling grizzled beard and unusually bright eyes sparkling under a soft felt hat, as he walked briskly but rather ungracefully across the college yard, fitted very well with the opinion current among us that we were looking upon a real live genius, who had a touch of the prophet in his make-up. — William Elwood Byerly

Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world. — Keith Devlin

No old Men (excepting Dr. Wallis) love Mathematicks. — Isaac Newton

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean. — G.H. Hardy

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. — John Von Neumann

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

They shouldn't be allowed to teach math so early in the morning. — Kendare Blake

We humans have a wide range of abilities that help us perceive and analyze mathematical content. We perceive abstract notions not just through seeing but also by hearing, by feeling, by our sense of body motion and position. Our geometric and spatial skills are highly trainable, just as in other high-performance activities. In mathematics we can use the modules of our minds in flexible ways - even metaphorically. A whole-mind approach to mathematical thinking is vastly more effective than the common approach that manipulates only symbols. — William Thurston

The Planeswalker know
YOu take the card from the library
And bury it when you're done.
On the path, you face history.
Walk the path, do the math:

Start with the prime numbers under 100
Whose digits give you 10.
Choose the happy median.
Add it to: The square root of
The cube of five divided by
The sum of 3 and 2. — Megan Frazer Blakemore

Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense - or deciding whether the method is the right one to use in the first place - requires a guiding human hand. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel. — Jordan Ellenberg

From the age of 13, I was attracted to physics and mathematics. My interest in these subjects derived mostly from popular science books that I read avidly. Early on I was fascinated by theoretical physics and determined to become a theoretical physicist. I had no real idea what that meant, but it seemed incredibly exciting to spend one's life attempting to find the secrets of the universe by using one's mind. — David Gross

A typical mathematician does not actively try to be useful. Individual mathematicians are motivated primarily by a subtle mixture of ambition and intellectual curiosity, and not by a wish to benefit society, nevertheless, mathematics as a whole does benefit society. — Timothy Gowers

Tengo's lectures took on uncommon warmth, and the students found themselves swept up in his eloquence. He taught them how to practically and effectively solve mathematical problems while simultaneously presenting a spectacular display of the romance concealed in the questions it posed. Tengo saw admiration in the eyes of several of his female students, and he realized that he was seducing these seventeen- or eighteen-year-olds through mathematics. His eloquence was a kind of intellectual foreplay. Mathematical functions stroked their backs; theorems sent warm breath into their ears. — Haruki Murakami

Le Verrier - without leaving his study, without even looking at the sky - had found the unknown planet [Neptune] solely by mathematical calculation, and, as it were, touched it with the tip of his pen! — Camille Flammarion

God made the integers; all the rest is the work of Man. — Leopold Kronecker

There have been many authorities who have asserted that the basis of science lies in counting or measuring, i.e. in the use of mathematics. Neither counting nor measuring can however be the most fundamental processes in our study of the material universe - before you can do either to any purpose you must first select what you propose to count or measure, which presupposes a classification. — Roy A. Crowson

If men had known how to permeate the soul with mathematics in the right way in the arithmetic lessons during these past years, we should not now have Bolshevism in Eastern Europe. — Rudolf Steiner

Whereas Nature does not admit of more than three dimensions ... it may justly seem very improper to talk of a solid ... drawn into a fourth, fifth, sixth, or further dimension. — John Wallis

I was always told that I was good in mathematics, and I guess my grades and standardized test scores supported that. My worst subjects were those that generally involved a lot of reading - English and history. So, having good test scores in math and mediocre ones in reading, I was naturally advised to major in engineering in college. — Henry Petroski

We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years. — Mark Twain

There was a footpath leading across fields to New Southgate, and I used to go there alone to watch the sunset and contemplate suicide. I did not, however, commit suicide, because I wished to know more of mathematics. — Bertrand Russell

Abel has left mathematicians enough to keep them busy for five hundred years. — Charles Hermite

Mathematics is the queen of science, and arithmetic the queen of mathematics. — Carl Friedrich Gauss

And they're also very good at math, these super boogers, and so they teach Billy the ways of mathematics. — William Joyce

My main concern with the condition of mathematics in high school is that there's a lot of fear involved! Math is not, generally speaking, presented in a fun way. The concepts, as I see them, are fun, and that's the way I'd like to convey them myself. — Danica McKellar

As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D'Alembert's principle for dynamics, the latter is again reduced to statics. Although it is is very much in order that in gradual training of science and in the instruction of the individual the easier precedes the more difficult, the simple precedes the more complicated, the special precedes the general, yet the min, once it has arrived at the higher standpoint, demands the reverse process whereby all statics appears only as a very special case of mechanics. — Carl Friedrich Gauss

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers. — Hans Reichenbach

From now on whenever I read a math book, I'm going to try to figure out by myself how everything was done, before looking at the solution. Even if I don't figure it out, I think I'll be able to see the beauty of a proof then. — Donald E. Knuth

Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems - general and specific statements - can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences. — Christopher Zeeman

The whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning. — Alfred North Whitehead

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

The only thing I am interested in using mathematics for is to have a good time and to help others do the same. — Paul Lockhart

You're probably better at math than I am, because pretty much everyone's better at math than I am, but it's okay, I'm fine with it. See, I excel at other, more important things - guitar, sex, and consistently disappointing my dad, to name a few. — Jennifer Niven

No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence
a duty and a duty alone
and no hint of magic or beauty of the subject might be allowed to come through. — Roger Penrose

The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing.
[Statement of the second law of thermodynamics, 1862] — Rudolf Clausius

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

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

It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts. — Paul Halmos

Perhaps the greatest paradox of all is that there are paradoxes in mathematics. — Edward Kasner

We often hear that mathematics consists mainly of 'proving theorems.' Is a writer's job mainly that of 'writing sentences? — Gian-Carlo Rota

With my full philosophical rucksack I can only climb slowly up the mountain of mathematics. — Ludwig Wittgenstein

All mathematicians share ... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics. — Martin Gardner

Desar's chosen field in mathematics was so esoteric that nobody in the Institute or the Math Federation could really check on his progress. That was precisely why he had chosen it. — Ursula K. Le Guin

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

There was, I think, a feeling that the best science was that done in the simplest way. In experimental work, as in mathematics, there was 'style' and a result obtained with simple equipment was more elegant than one obtained with complicated apparatus, just as a mathematical proof derived neatly was better than one involving laborious calculations. Rutherford's first disintegration experiment, and Chadwick's discovery of the neutron had a 'style' that is different from that of experiments made with giant accelerators. — John Ashworth Ratcliffe

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

Mathematics, in the common lay view, is a static discipline based on formulas ... But outside the public view, mathematics continues to grow at a rapid rate ... the guid to this growth is not calculation and formulas, but an open ended search for pattern. — Lynn Steen

I will never listen to ocean waves or view a beautiful sunset in quite the same way again. That is perhaps the greatest gift one can gain by delving into calculus: It is a whole new way of looking at the world, accessible only through the realm of mathematics. — Jennifer Ouellette

The only way to learn mathematics is to do mathematics. — Paul Halmos

I will also talk about my experience of growing up in the former Soviet Union, where mathematics became an outpost of freedom in the face of an oppressive regime. I was denied entrance to Moscow State University because of the discriminatory policies of the Soviet Union. The doors were slammed shut in front of me. I was an outcast. But I didn't give up. I would sneak into the University to attend lectures and seminars. I would read math books on my own, sometimes late at night. And in the end, I was able to hack the system. They didn't let me in through the front door; I flew in through a window. When you are in love, who can stop you? — Edward Frenkel

Mathematics is the gate and key to science. — Roger Bacon

Mathematics may be compared to a mill of exquisite workmanship, which grinds your stuff to any degree of fineness. — Thomas Huxley

But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting. — Julian Coolidge

Mathematics is about making up rules and seeing what happens. — Vi Hart

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

I had an excellent math and physics teacher in high school named T.C. Patel, and in the university, I had truly dedicated professors in both physics and mathematics who gave me a sound foundation with which to pursue graduate studies. — Venkatraman Ramakrishnan

It is the story that matters not just the ending. — Paul Lockhart

The book of nature is written in the language of mathematics. — Galileo Galilei

This concept is central to understanding what distinguishes the Arrowsmith approach: cognitive exercises do not teach content or skill in, say, mathematics; the aim is to forge new neural pathways in the brain so that later, when math is taught, number concepts actually make sense. — Barbara Arrowsmith-Young

I recognize that I have a unique position to be a role model to young girls because I am doing something that they consider glamorous, which is acting, and yet I took a time to really get my education and study mathematics, and I think math is the cat's meow. — Danica McKellar

It will be another million years, at least, before we understand the primes. — Paul Erdos

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

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

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

Mathematics is one of the surest ways for a man to feel the power of thought and the magic of the spirit. Mathematics is one of the eternal truths and, as such, raises the spirit to the same level on which we feel the presence of God. — Julio Cesar De Mello E Souza

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

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

In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide
a relief from daily life, an anodyne to the practical workaday world. — Paul Lockhart

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

Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency. — Rene Descartes

As a teacher, Tengo pounded into his students' heads how voraciously mathematics demanded logic. Here things that could not be proven had no meaning, but once you had succeeded in proving something, the world's riddles settled into the palm of your hand like a tender oyster. — Haruki Murakami

If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics ... — Roger Bacon

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

[In high school] my interests outside my academic work were debating, tennis, and to a lesser extent, acting. I became intensely interested in astronomy and devoured the popular works of astronomers such as Sir Arthur Eddington and Sir James Jeans, from which I learnt that a knowledge of mathematics and physics was essential to the pursuit of astronomy. This increased my fondness for those subjects. — Allan McLeod Cormack

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

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

Mathematics is for lazy people. — Peter Hilton

As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from other contexts, so as to develop a sense of the structure, not just familiarity with a particular tour through the structure. — William Thurston

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

The mathematical giant [Gauss], who from his lofty heights embraces in one view the stars and the abysses ... — Farkas Bolyai

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

Circles, homework coupons, what foolishness would she next hear? And so she began to teach him mathematics - she called it "maths" and he called it "math — Chimamanda Ngozi Adichie

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds. — Paul Cohen

We come astonishingly close to the mystical beliefs of Pythagoras and his followers who attempted to submit all of life to the sovereignty of numbers. Many of our psychologists, sociologists, economists and other latter-day cabalists will have numbers to tell them the truth or they will have nothing ... We must remember that Galileo merely said that the language of nature is written in mathematics. He did not say that everything is. And even the truth about nature need not be expressed in mathematics. For most of human history, the language of nature has been the language of myth and ritual. These forms, one might add, had the virtues of leaving nature unthreatened and of encouraging the belief that human beings are part of it. It hardly befits a people who stand ready to blow up the planet to praise themselves too vigorously for having found the true way to talk about nature. — Neil Postman

Some of the greatest advances in mathematics have been due to the invention of symbols, which it afterwards became necessary to explain; from the minus sign proceeded the whole theory of negative quantities. — Aldous Huxley

My first feeling was that there was no way to continue. Writing isn't like math;in math, two plus two always equals four no matter what your mood is like. With writing, the way you feel changes everything. — Stephenie Meyer

Mathematics is a body of knowledge, but it contains no truths. — Morris Kline

No one shall expel us from the paradise which Cantor has created for us.

{Expressing the importance of Georg Cantor's set theory in the development of mathematics.} — David Hilbert

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

Mathematics is the Life of the Gods. — Novalis

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

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

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. — Nikolai Lobachevsky

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game. — G.H. Hardy

Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them. — Joseph Fourier

I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go. — Winston S. Churchill