Mathematics What Makes Quotes & Sayings

I have tried, with little success, to get some of my friends to understand my amazement that the abstraction of integers for counting is both possible and useful. Is it not remarkable that 6 sheep plus 7 sheep makes 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, I find it both strange and unexplainable. — Richard Hamming

Infinite ambition and infinite loneliness, receiving neither help nor sympathy, I did it all for myself
navigation, mathematics, science, literature and what not. And history tells of opportunity that came to the slaves who rose to the purple. No man makes opportunity. All the great men ever did was to know it when it came to them. — Jack London

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. — Nenia Campbell

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

Reading music is something that's inherently hateful to me. It makes music like mathematics. — Robert Quine

Take this neat little equation here. It tells me all the ways an electron can make itself comfortable in or around an atom. That's the logic of it. The poetry of it is that the equation tells me how shiny gold is, how come rocks are hard, what makes grass green, and why you can't see the wind. And a million other things besides, about the way nature works. — Richard Feynman

Darwin's great gift to science was simplifying all life to pure mathematics: your one and only goal on earth is multiplication. Everything you do, every instinct you have, is an evolutionary urge to make babies and leave behind as many copies of yourself as possible. From that perspective, heroism makes no sense. Why risk the grave for someone else if there's no guarantee of a biological payoff? Dying for your own kids: smart. Dying for a rival's? Genetic suicide. — Christopher McDougall

As I considered the matter carefully it gradually came to light that all those matters only were referred to mathematics in which order and measurements are investigated, and that it makes no difference whether it be in numbers, figures, stars, sounds or any other object that the question of measurement arises. I saw consequently that there must be some general science to explain that element as a whole which gives rise to problems about order and measurement, restricted as these are to no special subject matter. This, I perceived was called 'universal mathematics'. — Rene Descartes

What makes this story so remarkable is that throughout my early childhood I had ongoing learning difficulties, particularly in mathematics. I struggled to learn the multiplication table, and no matter how hard I tried, I simply couldn't remember 6 times 7 or 7 times 8. — Andrew Lo

Every time you observe that more of a good thing is not always better; or you remember that improbable things happen a lot, given enough chances, and resist the lure of the Baltimore stockbroker; or you make a decision based not just on the most likely future, but on the cloud of all possible futures, with attention to which ones are likely and which ones are not; or you let go of the idea that the beliefs of groups should be subject to the same rules as beliefs of individuals; or, simply, you find that cognitive sweet spot where you can let your intuition run wild on the network of tracks formal reasoning makes for it; without writing down an equation or drawing a graph, you are doing mathematics, the extension of common sense by other means. When are you going to use it? You've been using mathematics since you were born and you'll probably never stop. Use it well. — Jordan Ellenberg

Mathematics is natural. Love is natural. It only makes sense that it's mathematically quantifiable. — Ally Blake

Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels. — Richard Askey

It is amusing to discover, in the twentieth century, that the quarrels between two lovers, two mathematicians, two nations, two economic systems, usually assumed insoluble in a finite period should exhibit one mechanism, the semantic mechanism of identification - the discovery of which makes universal agreement possible, in mathematics and in life. — Alfred Korzybski

Now we can see what makes mathematics unique. Only in mathematics is there no significant correction - only extension. Once the Greeks had developed the deductive method, they were correct in what they did, correct for all time. Euclid was incomplete and his work has been extended enormously, but it has not had to be corrected. His theorems are, every one of them, valid to this day. — Carl B. Boyer

But Mathematics are music,' Bach replied. And the reverse is also true. Whether you believe the word 'music' came from 'Musa,' the Muses, or from 'muta,'...it makes no difference. If you think 'mathematics' came from 'mathanein,' which is learning, or from 'Matrix," the womb or mother of all creation, it matters not... — Katherine Neville

If you're now noticing a certain family resemblance among this no-successive-instant problem, Zeno's Paradoxes, and some of the Real Line crunchers described in Paragraph 2c and -e, be advised that this is not a coincidence. They are all facets of the great continuity conundrum for mathematics, which is that (Infinity)-related entities can apparently be neither handled nor eliminated. Nowhere is this more evident than with 1/(Infinity)s. They're riddled with paradox and can't be defined, but if you banish them from math you end up having to posit an infinite density to any interval, in which the idea of succession makes no sense and no ordering of points in the interval can ever be complete, since between any two points there will be not just some other points but a whole infinity of them.
Overall point: However good calculus is at quantifying motion and change, it can do nothing to solve the real paradoxes of continuity. Not without a coherent theory of (Infinity), anyway. — David Foster Wallace

Pure analysis puts at our disposal a multitude of procedures whose infallibility it guarantees; it opens to us a thousand different ways on which we can embark in all confidence; we are assured of meeting there no obstacles; but of all these ways, which will lead us most promptly to our goal? Who shall tell us which to choose? We need a faculty which makes us see the end from afar, and intuition is this faculty. It is necessary to the explorer for choosing his route; it is not less so to the one following his trail who wants to know why he chose it. — Henri Poincare

To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer. — Ian Stewart

There is something in statistics that makes it very similar to astrology. — Gian-Carlo Rota

[The golden proportion] is a scale of proportions which makes the bad difficult [to produce] and the good easy. — Albert Einstein

Meteorology ... is quite as "scientific" as geology and far more so than archaeology - it actually makes more use of scientific instruments, computers, and higher mathematics ... Yet we laugh at the weatherman every other day; we are not overawed by his impressive paraphernalia, because we can check up on him any time we feel like it: he makes his learned pronouncements - and then it rains or it doesn't rain.
No scientific conclusion is to be trusted without testing - to the extent to which exact sciences are exact they are also experimental sciences; it is in the laboratory that the oracle must be consulted. But the archaeologist is denied access to the oracle. For him there is no neat and definitive demonstration; he is doomed to plod along, everlastingly protesting and fumbling through a laborious, often rancorous running debate that never ends. — Hugh Nibley

The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon ... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms. — Joseph Fourier

Mathematics is the source of a wicked intellect that, while making man the lord of the earth, also makes him the slave of the machine. — Robert Musil

Mathematics is so much easier than words mathematics makes things clear that words merely muddle and confuse and mess up. — John Maynard Smith

Everyone reads a different book. That's what's interesting. Everyone sees a different film, as well. We bring our past lives to whatever work of art we're experiencing at that moment, and that's what makes it interesting. It's not mathematics. There are different answers for different people. — Paul Auster

Each pleasure we feel is a pleasure less; each day a stroke on a calendar. What we will not accept is that the joy in the day and the passing of the day are inseparable. What makes our existence worthwhile is precisely that its worth and its while - its quality and duration - are as impossible to unravel as time and space in mathematics of relativity. — John Fowles

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

What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating. — Paul Dirac

MacPherson told me that my theorem can be viewed as blah blah blah Grothendieck blah blah blah, which makes it much more respectable. — Jim Propp

The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life. The world of existence is fleeting, vague, without sharp boundaries, without any clear plan or arrangement, but it contains all thoughts and feelings, all the data of sense, and all physical objects, everything that can do either good or harm, everything that makes any difference to the value of life and the world. According to our temperaments, we shall prefer the contemplation of the one or of the other. — Bertrand Russell

To give emphasis only to beauty makes me think of a mathematics that deals with positive numbers only. — Paul Klee

While physics and mathematics may tell us how the universe began, they are not much use in predicting human behavior because there are far too many equations to solve. I'm no better than anyone else at understanding what makes people tick, particularly women. — Stephen Hawking

Blindness to the aesthetic element in mathematics is widespread and can account for a feeling that mathematics is dry as dust, as exciting as a telephone book ... Contrariwise, appreciation of this element makes the subject live in a wonderful manner and burn as no other creation of the human mind seems to do. — Philip J. Davis

Mutuality is accomplished by two whole persons; and if each partner truly intends to be but the fraction of a relationship (thinking my whole makes up half of us) he or she will soon discover that these halves do not fit perfectly together. The mathematics can work only if each subtracts something of himself or herself, shears it off, and lays it aside forever. There will come, then, a moment of shock when one spouse realizes, 'you won't want the whole of me? Not the whole of me, but only a part of me, makes up the whole of us?" P 45 — Walter Wangerin Jr.

Because the observer's only freedom is the choice of which question to pose (Shall I look up at the sky?), it is here that the mind of the observer has a chance to affect the dynamics of the brain. An examination of the mathematics, Stapp argued, shows that "the conscious intentions of a human being [reflected in the choices he makes about what question to put to nature] can influence the activities of his brain....Each conscious event picks out from the multitude of...possibilities that comprise the quantum brain the subensemble that is compatible with the conscious experience." The physical event reduces the state of the brain to that branch of it that is compatible with the particular experience or observation. — Jeffrey M. Schwartz

One thing that definitely did calculate properly for me was the mathematics that makes sense every day, no matter how I look at it, I can't get around it. I try to get around it, I keep trying to find one plus one is not two, somehow. I can't. People can talk about string theory, parallel realities, different dimensions, it's still one plus one is two, baby. — RZA

Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this ... The imagination in a mathematician who creates makes no less difference than in a poet who invents ... Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer. — Jean Le Rond D'Alembert

Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion - not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to; to have a break-through idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it. — Paul Lockhart

Mathematics is very much like poetry ... what makes a good poem
a great poem
is that there is a large amount of thought expressed in very few words. In this sense formulas like
or are poems. — Lipman Bers

Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense. — Edward Kasner

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

Poetry and code - and mathematics - make us read differently from other forms of writing. Written poetry makes the silent reader read three kinds of pattern at once; code moves the reader from a static to an active, interactive and looped domain; while algebraic topology allows us to read qualitative forms and their transformations. — Stephanie Strickland

The first part, or the Aesthetics, which has nothing in common with art, disengages the a priori forms of sensible knowledge, namely, the forms of space and time, which furnish mathematics with their object. Aesthetics thus divorced mathematics from reality, for it makes the condition of mathematics not the real, but a mental form of space and time. — Fulton J. Sheen