Best 579 quotes in «mathematics quotes» category

All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to vicissitudes. Mathematicians go backward and forward from one world to another. They’re adults in the crystalline world, infants in the real one.

All of these video games are rotting my brain. I'm gonna go watch T.V. instead

Although some of her passages seek to persuade the reader of the meaninglessness and marginalization of the mathematics, Hayles is content to use mathematics as a means for understanding Borges, perhaps in the same way a sponge riddled with holes is useful in sopping up fluid reality.

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.

A mathematician is an individual who proves his beliefs with equations.

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.

A mathematician tells you that the wall of warped space prevents the Moon from flying out of its orbit yet can't tell you why an astronaut can go back and forth across that same space.

An arguing couple spiraling into negativity and teetering on the brink of divorce is actually mathematically equivalent to the beginning of a nuclear war.

...and his analysis proved him to be the first of theoretical astronomers no less than the greatest of 'arithmeticians.

A remarkably consistent finding, starting with elementary school students, is that males are better at math than females. While the difference is minor when it comes to considering average scores, there is a huge difference when it comes to math stars at the upper extreme of the distribution. For example, in 1983, for every girl scoring in the highest percentile in the math SAT, there were 11 boys. Why the difference? There have always been suggestions that testosterone is central. During development, testosterone fuels the growth of a brain region involved in mathematical thinking and giving adults testosterone enhances their math skills. Oh, okay, it's biological. But consider a paper published in science in 2008. The authors examined the relationship between math scores and sexual equality in 40 countries based on economic, educational and political indices of gender equality. The worst was Turkey, United States was middling, and naturally, the Scandinavians were tops. Low and behold, the more gender equal the country, the less of a discrepancy in math scores. By the time you get to the Scandinavian countries it's statistically insignificant. And by the time you examine the most gender equal country on earth at the time, Iceland, girls are better at math than boys. Footnote, note that the other reliable sex difference in cognition, namely better reading performance by girls than by boys doesn't disappear in more gender equal societies. It gets bigger. In other words, culture matters. We carry it with us wherever we go.

As he learned more math, Brodt made the wonder-inspiring observation that mathematical laws seemed to be Someone's intention rather than just accidents in many concepts: infinity, unity being totality, irrational numbers in general and pi in particular as it illustrates such disparate occurrences as the relationship of height to base perimeter in the Great Pyramid of Giza and the course of any meandering river (over a surface smoothed for consistency). There was also the Fibonacci Sequence, that looping string of addends which, with their sums, describes the spirals on a nautilus shell, the distribution of leaves around a tree branch, and the genealogy of ants and bees. It all seemed too orderly, too regular and consistent to have occurred by chance. So many things in the world appeared as blotches, smears, or random spikes that these mathematically explained phenomena were extraordinary--he wanted to say mystical, but he wouldn't want to be caught using that word.

A Puritan twist in our nature makes us think that anything good for us must be twice as good if it's hard to swallow. Learning Greek and Latin used to play the role of character builder, since they were considered to be as exhausting and unrewarding as digging a trench in the morning and filling it up in the afternoon. It was what made a man, or a woman -- or more likely a robot -- of you. Now math serves that purpose in many schools: your task is to try to follow rules that make sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride. As you limp off with your aching mind and bruised soul, you know that nothing in later life will ever be as difficult. What a perverse fate for one of our kind's greatest triumphs! Think how absurd it would be were music treated this way (for math and music are both excursions into sensuous structure): suffer through playing your scales, and when you're an adult you'll never have to listen to music again. And this is mathematics we're talking about, the language in which, Galileo said, the Book of the World is written. This is mathematics, which reaches down into our deepest intuitions and outward toward the nature of the universe -- mathematics, which explains the atoms as well as the stars in their courses, and lets us see into the ways that rivers and arteries branch. For mathematics itself is the study of connections: how things ideally must and, in fact, do sort together -- beyond, around, and within us. It doesn't just help us to balance our checkbooks; it leads us to see the balances hidden in the tumble of events, and the shapes of those quiet symmetries behind the random clatter of things. At the same time, we come to savor it, like music, wholly for itself. Applied or pure, mathematics gives whoever enjoys it a matchless self-confidence, along with a sense of partaking in truths that follow neither from persuasion nor faith but stand foursquare on their own. This is why it appeals to what we will come back to again and again: our **architectural instinct** -- as deep in us as any of our urges.

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.

As the sensations of motion and discreteness led to the abstract notions of the calculus, so may sensory experience continue thus to suggest problem for the mathematician, and so may she in turn be free to reduce these to the basic formal logical relationships involved. Thus only may be fully appreciated the twofold aspect of mathematics: as the language of a descriptive interpretation of the relationships discovered in natural phenomena, and as a syllogistic elaboration of arbitrary premise.

As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer...

As long as I could connect every new thing I learned to this universe, I had an easy time with math. And I noticed that classmates who had problems with math weren’t struggling with math; they were struggling with connections. They were trying to memorize equations, but no one had successfully shown them how those equations connect with everything they had already learned. They were doomed

As the several items can be exchanged, they must be equal; but in what terms? Not in pounds, yards, or hours; they are equal in value. Then what is wanted is a unit of value to reckon by.

Berkeley was unable to appreciate that mathematics was not concerned with a world of "real" sense impressions. In much the same manner today some philosophers criticize the mathematical conceptions of infinity and continuum, failing to realize that since mathematics deals with relations rather than with physical existence, its criterion of truth is inner consistency rather than plausibility in the light of sense perception of intuition.

At his "World of Physics" Web site, Eric W. Weisstein notes that the fine structure constant continues to fascinate numerologists, who have claimed that connections exist between alpha, the Cheops pyramid, and Stonehenge!

[Benjamin Peirce's] lectures were not easy to follow. They were never carefully prepared. The work with which he rapidly covered the blackboard was very illegible, marred with frequent erasures, and not infrequent mistakes (he worked too fast for accuracy). He was always ready to digress from the straight path and explore some sidetrack that had suddenly attracted his attention, but which was likely to have led nowhere when the college bell announced the close of the hour and we filed out, leaving him abstractedly staring at his work, still with chalk and eraser in his hands, entirely oblivious of his departing class.

Before an experiment can be performed, it must be planned—the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted—nature's answer must be understood properly. These two tasks are those of the theorist, who finds himself always more and more dependent on the tools of abstract mathematics. Of course, this does not mean that the experimenter does not also engage in theoretical deliberations. The foremost classical example of a major achievement produced by such a division of labor is the creation of spectrum analysis by the joint efforts of Robert Bunsen, the experimenter, and Gustav Kirchhoff, the theorist. Since then, spectrum analysis has been continually developing and bearing ever richer fruit.

But physics is like carpentry: Using the right tool makes the job easier, not more difficult, and teaching quantum mechanics without the appropriate mathematical equipment is like asking the student to dig a foundation with a screwdriver. (On the other hand, it can be tedious and diverting if the instructor feels obliged to give elaborate lessons on the proper use of each tool. My own instinct is to hand the students shovels and tell them to start digging. They may develop blisters at first, but I still think this is the most efficient and exciting way to learn.)

But that can never be," said Milo, jumping to his feet. "Don't be too sure," said the child patiently, "for one of the nicest things about mathematics, or anything else you might care to learn, is that many of the things which can never be, often are. You see," he went on, "it's very much like your trying to reach Infinity. You know that it's there, but you just don't know where — but just because you can never reach it doesn't mean that it's not worth looking for.

Daniel Bernoulli: "Then this distinguished scholar informed me that the celebrated mathematician, Cramer, had developed a theory on the same subject several years before I produced my paper. Indeed I have found his theory so similar to mine that it seems miraculous that we independently reached sch close agreement on this sort of subject.

Dividing one number by another is mere computation ; knowing what to divide by what is mathematics.

Data Science takes the guesswork/emotions out of answering business questions by applying logic and mathematics to find better solutions.

Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner, published in the Annalen der Physik in 1905 five papers on entirely different subjects. Three of them were among the greatest in the history of physics. One, very simple, gave the quantum explanation of the photoelectric effect—it was this work for which, sixteen years later, he was awarded the Nobel prize. Another dealt with the phenomenon of Brownian motion, the apparently erratic movement of tiny particles suspended in a liquid: Einstein showed that these movements satisfied a clear statistical law. This was like a conjuring trick, easy when explained: before it, decent scientists could still doubt the concrete existence of atoms and molecules: this paper was as near to a direct proof of their concreteness as a theoretician could give. The third paper was the special theory of relativity, which quietly amalgamated space, time, and matter into one fundamental unity. This last paper contains no references and quotes to authority. All of them are written in a style unlike any other theoretical physicist's. They contain very little mathematics. There is a good deal of verbal commentary. The conclusions, the bizarre conclusions, emerge as though with the greatest of ease: the reasoning is unbreakable. It looks as though he had reached the conclusions by pure thought, unaided, without listening to the opinions of others. To a surprisingly large extent, that is precisely what he had done.

Do not try the parallels in that way: I know that way all along. I have measured that bottomless night, and all the light and all the joy of my life went out there. [Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.]

Education makes your maths better, not necessarily your manners.

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.

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.

Everything can be summed up into an equation.

E per tutto il giorno mi riempivano la testa di stronzate che volevano farmi tenere a mente, come ad esempio le equazioni per calcolare la distanza fra il posto dove ci trovavamo e quelle in cui volevano farci andare loro, e naturalmente quelle per tornare indietro; cazzate come le coordinate coassiali, il calcolo dei coseni, la trigonometria sferoide, l'algebra di Boolean, gli antilogaritmi, l'analisi di Fourier, quadrati e matrici. Mi dissero che io avrei dovuto fare da riserva al computer di riserva.

For the first time in his life, he decided to focus on his math homework.

For other great mathematicians or philosophers, he used the epithets magnus, or clarus, or clarissimus; for Newton alone he kept the prefix summus.

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.

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.

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.

God is a pure mathematician!' declared British astronomer Sir James Jeans. The physical Universe does seem to be organised around elegant mathematical relationships. And one number above all others has exercised an enduring fascination for physicists: 137.0359991.... It is known as the fine-structure constant and is denoted by the Greek letter alpha (α).

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.

God of Abraham, God of Isaac, God of Jacob, not of the philosophers and scholars...Joy, joy, joy, tears of joy...'This is life eternal that they might know you, the only true God, and Jesus Christ, whom you have sent.' Jesus Christ. Jesus Christ...May I not fall from him forever...I will not forget your word. Amen.

Golden Ratio is a powerful mathematical constant woven into the very fabric of biology. It is the unique visual tension between comforting symmetry and compelling asymmetry, and its thoughtful application can bring beauty and harmony and intrigue to all manner of designed things.

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.

He could not believe that any of them might actually hit somebody. If one did, what a nowhere way to go: killed by accident; slain not as an individual but by sheer statistical probability, by the calculated chance of searching fire, even as he himself might be at any moment. Mathematics! Mathematics! Algebra! Geometry! When 1st and 3d Squads came diving and tumbling back over the tiny crest, Bell was content to throw himself prone, press his cheek to the earth, shut his eyes, and lie there. God, oh, God! Why am I here? Why am I here? After a moment's thought, he decided he better change it to: why are we here. That way, no agency of retribution could exact payment from him for being selfish.

He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication were discovered. Algebra was invented and provided an interesting diversion for a minute or two. And then he felt the fog of numbers drift away, and looked up and saw the sparkling, distant mountains of calculus.

I always consider myself as being bad in equation, of being a failure at Math. But when I start to count down my Blessings I don't believe I'm bad at all!

Hippasus’ proof—or at least Nico’s retelling of it—was really so simple that when he finished sketching it out, I wasn’t even aware that we had actually proven anything. Nico paused for a few minutes to let us mull it over. It was Peter who broke the silence, “I’m not sure I understand what we have done.” Nico seemed to be expecting such a response. “Step back and examine the proof; in fact, you should try and do this with every proof you see or have to work out for yourself. ..." He again waited for his words to sink in, and it began to make sense for me. All my mathematics teachers (other than Bauji and Nico) always seemed to evade this part of their responsibility. They had been content to merely write out a proof on the blackboard and carry on, seemingly without concern for what the proof meant and what it told us. “But you should not stop here. Even when you have understood a proof, and I hope you have indeed understood this proof, ask yourself the next question, the obvious one, but as critical: So what? Or, why are we proving this? What is the point? What is the context? How does it relate to us? To answer these questions we have to step back a little. Let me show you—it’s really quite delightful.” Now there was excitement in Nico’s voice.

How do you quantify love? Can you weigh it, measure it, pin it down with equations? If the sum of all experiences is really just the interaction of a finite soup of chemicals copulating in nerve endings, how did this even dare articulate the infinite? Mathematicians will tell you there are different types of infinities. Some are countable, some are not. We can love someone more and more; we can stop loving. But we can never guess how much all this is. Love has no units.

I abandoned the assigned problems in standard calculus textbooks and followed my curiosity. Wherever I happened to be--a Vegas casino, Disneyland, surfing in Hawaii, or sweating on the elliptical in Boesel's Green Microgym--I asked myself, "Where is the calculus in this experience?

Humans are like Variables in mathematics, some Dependent, some Independent. Variables are in relationship but remain Variable. Of course, there are some Constants too both in mathematics and humans. Constants help define precisely the relationship between variables. Maybe, that is why humans keep adding (to problems), subtracting (from happiness), multiplying (what else, we are all over earth) and dividing (the earth among themselves).