Best 586 of Mathematics quotes - MyQuotes
G. Stanley Hall, a creature of his times, believed strongly that adolescence was determined – a fixed feature of human development that could be explained and accounted for in scientific fashion. To make his case, he relied on Haeckel's faulty recapitulation idea, Lombroso's faulty phrenology-inspired theories of crime, a plethora of anecdotes and one-sided interpretations of data. Given the issues, theories, standards and data-handling methods of his day, he did a superb job. But when you take away the shoddy theories, put the anecdotes in their place, and look for alternate explanations of the data, the bronze statue tumbles hard. I have no doubt that many of the street teens of Hall's time were suffering or insufferable, but it's a serious mistake to develop a timeless, universal theory of human nature around the peculiarities of the people of one's own time and place.
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.
A mathematician is an individual who constructs space with 0D particles and then places a bowling ball on this invisible canvas to explain how gravity works.
[Adams] supposed that, except musicians, everyone thought Beethoven a bore, as every one except mathematicians thought mathematics a bore.
Charles Sanders Peirce
... and it is probably that there is some secret here which remains to be discovered.
In my schooling through high school, I excelled mainly in chemistry, physics and mathematics.
Mathematics is a language
Existe una opinión generalizada según la cual la matemática es la ciencia más difícil cuando en realidad es la más simple de todas. La causa de esta paradoja reside en el hecho de que, precisamente por su simplicidad, los razonamientos matemáticos equivocados quedan a la vista. En una compleja cuestión de política o arte, hay tantos factores en juego y tantos desconocidos e inaparentes, que es muy difícil distinguir lo verdadero de lo falso. El resultado es que cualquier tonto se cree en condiciones de discutir sobre política y arte -y en verdad lo hace- mientras que mira la matemática desde una respetuosa distancia.
The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern.
Here, where we reach the sphere of mathematics, we are among processes which seem to some the most inhuman of all human activities and the most remote from poetry. Yet it is here that the artist has the fullest scope of his imagination.
For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.
Someone has said that all the great jugglers are dead.
Mathematics rightly viewed possesses not only truth but supreme beauty.
Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem.
I'd like to take some calculus, too. I have absolutely no ability in that direction and not much interest, either, but there's something going on in mathematics that I don't understand, and I'd like to find out what it is.
Mathematics is the gate and key to science.
John Edensor Littlewood
Mathematics is a dangerous profession; an appreciable proportion of us go mad.
Paul Tudor Jones
I believe that great success is possible in any field — from music to mathematics to macro trading.
So [in mathematics] we get to play and imagine whatever we want and make patterns and ask questions about them. But how do we answer these questions? It’s not at all like science. There’s no experiment I can do ... The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work.
Nicholas Murray Butler
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.
The language of mathematics, scientific observations, and our perceptivity together knit the window to reality.
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.
In Mathematics it is always best to cheat.
The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'.
All these people that I used to know, they're an illusion to me now. Some are mathematicians, some are carpenters' wives.
There is no national science, just as there is no national multiplication table; what is national is no longer science.
If it squirms, it's biology; if it stinks, it's chemistry; if it doesn't work, it's physics; and if you can't understand it, it's mathematics.
What Is Mathematics? This question, if asked in earnest, has no answer.
I knew my purpose well and clear: to show how Nature behaves without cluttering its beauty with abtruse mathematics.
You can only be twice someone’s age once.
The astonishing fact is that similar mathematics applies so well to planets and to clocks. It needn’t have been this way. We didn’t impose it on the Universe. That’s the way the Universe is. If this is reductionism, so be it.
I had made an empirical discovery and it carried all the weight of a mathematical proof.
Philosophy is written in this all-encompassing book that is constantly open to our eyes, that is the universe; but it cannot be understood unless one first learns to understand the language and knows the characters in which it is written. It is written in mathematical language, and its characters are triangles, circles, and other geometrical figures; without these it is humanly impossible to understand a word of it, and one wanders in a dark labyrinth.
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.
A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.
Teaching mathematics, like teaching any art, requires the ability to inspire the student. Inspiration requires marketing, and marketing requires stirring communication.
In mathematics we have long since drawn the rein, and given over a hopeless race.
My sub doesn't pay for me,” he says, pulling me to my feet. “That just doesn't happen.” “But we ordered so much,” I say helplessly. “It made you happy,” he says simply. “Now I get to play with you. And that makes me happy.” “I don't think it's that simple an equation.” “Maybe not,” he concedes. “But then, if if sex were the same thing as math, a lot more people would be lining up to take calculus.
I don't believe any scientific field to be superior to another.
We could, of course, use any notation we want; do not laugh at notations; invent them, they are powerful. In fact,mathematics is, to a large extent, invention of better notations.
God ever arithmetizes.
Thomas B. Macaulay
[I can] scarcely write upon mathematics or mathematicians. Oh for words to express my abomination of the science.
Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.
Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don't happen to have all the data. In mathematics we have all the data, brought together in the full light of demonstration, and yet we don't understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.
Mathematicians call it “the arithmetic of congruences.” You can think of it as clock arithmetic. Temporarily replace the 12 on a clock face with 0. The 12 hours of the clock now read 0, 1, 2, 3, … up to 11. If the time is eight o’clock, and you add 9 hours, what do you get? Well, you get five o’clock. So in this arithmetic, 8 + 9 = 5; or, as mathematicians say, 8 + 9 ≡ 5 (mod 12), pronounced “eight plus nine is congruent to five, modulo twelve.
We tend to teach mathematics as a long list of rules.You learn them in order and you have to obey them, because if you don't obey them you get a C-.This is not mathematics. Mathematics is the study if things that come out a certain way because there is no other way they could possibly be.
My theology, briefly, is that the universe was dictated but not signed.
Really, there was only one problem with Mr. Davis, as far as Gregory was concerned; He taught math.
If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither "number" nor "size", but always form. And among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other and continues to fascinate me, is the structure hidden in mathematical things.
Education makes your maths better, not necessarily your manners.