Best 579 quotes in «mathematics quotes» category

When a branch of mathematics ceases to interest any but the specialists, it is very near its death, or at any rate dangerously close to a paralysis, from which it can be rescued only by being plunged back into the vivifying source of the science.

When I give this talk to a physics audience, I remove the quotes from my 'Theorem'.

Wherefore in all great works are Clerks so much desired? Wherefore are Auditors so well-fed? What causeth Geometricians so highly to be enhaunsed? Why are Astronomers so greatly advanced? Because that by number such things they find, which else would farre excell mans minde.

Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional propositions a priori, and it will be your task to find out the false deduction in each case.

Why do children dread mathematics? Because of the wrong approach. Because it is looked at as a subject.

With randomness it is very unlikely to be embarrassed, but even if you get embarrassed, you can't replicate it.

Without computers we will be stuck only proving theorems that have short proofs.

You know, I'm not terribly fast at my times tables, because that's not what I think mathematics is about.

You can not apply mathematics as long as words still becloud reality.

You are the mountain and the valley.

4.19. Dedekind's approach is a singular combination of Descartes' Cogito and the idea of the idea in Spinoza. The starting point is the very space of the Cogito, as 'closed' configuration of all possible thoughts, existential point of pure thought. It is claimed (but only the Cogito assures us of this) that something like the set of all my possible thoughts exists. From Spinoza's causal 'serialism' (regardless of whether or not he figured in Dedekind's historical sources) are taken both the existence of a parallelism' which allows us to identify simple ideas by way of their object (Spinoza says: through the body of which the idea is an idea), and the existence of a reflexive redoubling, which secures the existence of 'complex' ideas, whose object is no longer a body, but another idea. For Spinoza, as for Dedekind, this process of reflexive redoubling must go to infinity. An idea of an idea (or the thought of a thought of an object) is an idea. So there exists an idea of the idea of a body, and so on.

4.23..If 'thought' means: instance of the subject in a truth-procedure, then there is no thought of this thought, because it contains no knowledge.

You want to know how to rhyme, then learn how to add. It's mathematics.

99 percent of all statistics only tell 49 percent of the story.

… Fourier's great mathematical poem ... {Referring to Joseph Fourier's mathematical theory of the conduction of heat, one of the precursors to thermodynamics.}

A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science: 'The probability of an event is the reason we have to believe that it has taken place, or that it will take place.' 'The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible' (equally like to happen). From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33... Working in total isolation from the main currents of his field, he was able to rederive 100 years’ worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics.

Kepler’s discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler—such penetrating minds as Descartes and Pascal—were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.

He is like the fox, who effaces his tracks in the sand with his tail. {Describing the writing style of famous mathematician Carl Friedrich Gauss}

A key ingredient in appreciating what mathematics is about is to realize that it is concerned with ideas, understanding, and communication more than it is with any specific brand of symbols....It is almost as if ideas set in mathematical form melt and become liquid and just as rivers can, from the most humble beginnings, flow for thousands of miles, through the most varied topography bringing nourishment and life with them wherever they go, so too can ideas cast in mathematical form flow far from their original sources, along well-defined paths, electrifying and dramatically affecting much of what they touch. pp. xii - xiii.

A brick can be used to represent the zero probability of this book being any good.

Add Snow White and her seven dwarfs, 2 droids for Luke Skywalker, of course. 1 true ring to rule them all. A decimal is a place to stall. Snow White's gone, the dwarfs alone. This system your next clue has shown. Now you might ask, this little key, Just what does it mean for me? Hold on tight and you will see, Someday it will set clues free.

Euclid's Elements has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her.

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

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

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.

Ohm found that the results could be summed up in such a simple law that he who runs may read it, and a schoolboy now can predict what a Faraday then could only guess at roughly. By Ohm's discovery a large part of the domain of electricity became annexed by Coulomb's discovery of the law of inverse squares, and completely annexed by Green's investigations. Poisson attacked the difficult problem of induced magnetisation, and his results, though differently expressed, are still the theory, as a most important first approximation. Ampere brought a multitude of phenomena into theory by his investigations of the mechanical forces between conductors supporting currents and magnets. Then there were the remarkable researches of Faraday, the prince of experimentalists, on electrostatics and electrodynamics and the induction of currents. These were rather long in being brought from the crude experimental state to a compact system, expressing the real essence. Unfortunately, in my opinion, Faraday was not a mathematician. It can scarcely be doubted that had he been one, he would have anticipated much later work. He would, for instance, knowing Ampere's theory, by his own results have readily been led to Neumann's theory, and the connected work of Helmholtz and Thomson. But it is perhaps too much to expect a man to be both the prince of experimentalists and a competent mathematician.

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.

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 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.

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.

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

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.

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 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 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.

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 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 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.

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.

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!

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.

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.

[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.

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.

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

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.