Quotes & Sayings About Mathematical

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

There is a mathematical underpinning that you must first acquire, mastery of each mathematical subdiscipline leading you to the threshold of the next. In turn you must learn arithmetic, Euclidian geometry, high school algebra, differential and integral calculus, ordinary and partial differential equations, vector calculus, certain special functions of mathematical physics, matrix algebra, and group theory. For most physics students, this might occupy them from, say, third grade to early graduate school - roughly 15 years. Such a course of study does not actually involve learning any quantum mechanics, but merely establishing the mathematical framework required to approach it deeply. — Carl Sagan

I had made an empirical discovery and it carried all the weight of a mathematical proof. — Paul Auster

common sense observations of human behavior support a similar dissociation in reasoning abilities which cuts in both directions. We all know persons who are exceedingly clever in their social navigation, who have an unerring sense of how to seek advantage for themselves and for their group, but who can be remarkably inept when trusted with a nonpersonal, nonsocial problem. The reverse condition is just as dramatic: We all know creative scientists and artists whose social sense is a disgrace, and who regularly harm themselves and others with their behavior. The absent-minded professor is the benign variety of the latter type. At work, in these different personality styles, are the presence or absence of what Howard Gardner has called "social intelligence," or the presence or absence of one or the other of his multiple intelligences such as the "mathematical. — Antonio R. Damasio

no mathematical formula or econometric estimate can tell us exactly what tax rate ought to be applied to what level of income. Only collective deliberation and democratic experimentation can do that. — Thomas Piketty

There is no national science, just as there is no national multiplication table; what is national is no longer science. — Anton Chekhov

The circumstances of human society are too complicated to be submitted to the rigor of mathematical calculation. — Marquis De Custine

A free-enterprise economy depends only on markets, and according to the most advanced mathematical macroeconomic theory, markets depend only on moods: specifically, the mood of the men in the pinstripes, also known as the Boys on the Street. When the Boys are in a good mood, the market thrives; when they get scared or sullen, it is time for each one of us to look into the retail apple business. — Barbara Ehrenreich

The Quantified Self movement argues that the self is nothing but mathematical patterns. These patterns are so complex that the human mind has no chance of understanding them. So if you wish to obey the old adage and know thyself, you should not waste your time on philosophy, meditation or psychoanalysis, but rather you should systematically collect biometric data and allow algorithms to analyse them for you and tell you who your are and what you should do. — Yuval Noah Harari

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 word 'definition' has come to have a dangerously reassuring sound, owing no doubt to its frequent occurrence in logical and mathematical writings. — Willard Van Orman Quine

It seems to me there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally suprise me. I do not think of mathemaatics as invented but rather discovered. — George Andrews

It is more important to have beauty in one's equations than to have them fit experiment. — Paul Dirac

The fact that you are even here, alive, on this planet is a mathematical miracle, and you should not spend the time that you have being busy being miserable. — Philip DeFranco

It is from this absolute indifference and tranquillity of the mind, that mathematical speculations derive some of the most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiased to examine the point. All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater from lesser, from equality and inequality. — Edmund Burke

The practical man demands an appearance of reality at least. Always dealing in the concrete, he regards mathematical terms not as symbols or thought but as images of reality. A system acceptable to the mathematician because of its inner consistency may appear to the practical man to be full of contradictions because of the incomplete manner in which it represents reality. — Tobias Dantzig

I do not love to be printed on every occasion, much less to be dunned and teased by foreigners about mathematical things or to be thought by our own people to be trifling away my time about them when I should be about the king's business. — Isaac Newton

We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel. — David Hilbert

I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality. — Carl Friedrich Gauss

There are almost 200 currencies of the world, but there's only one international currency. There are almost 200 currencies controlled by central banks and governments, but there is only one mathematical currency today, and that is bitcoin. We are going to build more of them. Cryptographic currencies are going to be a mainstay of our financial future. They are going to be a part of the future of this planet because they have been invented. It's as simple as that. You cannot un-invent this technology. You cannot turn this omelette back into eggs. — Andreas M. Antonopoulos

The extraordinary fact is that the first idea I had which motivated me, that worked, is conjecture, a mathematical idea which may or may not be true. And that idea is still unproven. It is the foundation, what started me and what everybody failed to **** prove has so far defeated the greatest efforts by experts to be proven. — Benoit Mandelbrot

Many scientists (the most notable being Albert Einstein) think in visual, spatial, and physical images rather than in mathematical terms and words. (N.B.: That the theoretical physicist, Stephen Hawking, used an arboreal term to picture the cosmos [i.e., affirming that the universe "could have different branches,"] is a tribute to his [very visual] primate brain.) — David B. Givens

Then suddenly, he was struck by a powerful but simple little truth, and it was this: that English grammar is governed by rules that are almost mathematical in their strictness! — Roald Dahl

The attempt to apply rational arithmetic to a problem in geometry resulted in the first crisis in the history of mathematics. The two relatively simple problems
the determination of the diagonal of a square and that of the circumference of a circle
revealed the existence of new mathematical beings for which no place could be found within the rational domain. — David Van Dantzig

It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the names of thought. It only becomes possible at all after the mathematical notation has, as a result of genuine thought, been so developed that it does the thinking for us, so to speak. — Gottlob Frege

The control of large numbers is possible, and like unto that of small numbers, if we subdivide them. — Sun Tzu

I'm trying to justify it somehow, he thought, meaning it not in the moral sense but rather in the mathematical one. Buildings are built by observing certain natural laws; natural laws may be expressed by equations; equations must be justified. Where was the justification in what had happened less than half an hour ago? — Stephen King

The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new member of the solar system, and its exact location, were demonstrated with pencil and paper; there was left to observers only the routine task of pointing their telescopes at the spot the mathematicians had marked. — James R Newman

Neither agreeable nor disagreeable," I answered. "It just is."
Istigkeit - wasn't that the word Meister Eckhart liked to use? "Is-ness." The Being of Platonic philosophy - except that Plato seems to have made the enormous, the grotesque mistake of separating Being from becoming and identifying it with the mathematical abstraction of the Idea. He could never, poor fellow, have seen a bunch of flowers shining with their own inner light and all but quivering under the pressure of the significance with which they were charged; could never have perceived that what rose and iris and carnation so intensely signified was nothing more, and nothing less, than what they were - a transience that was yet eternal life, a perpetual perishing that was at the same time pure Being, a bundle of minute, unique particulars in which, by some unspeakable and yet self-evident paradox, was to be seen the divine source of all existence. — Aldous Huxley

Modern economics is a set of formal models and equations purporting to fully determine human behaviour, at least in the economic realm. And there is no way that uncertainty can be compressed into determinate mathematical models. — Murray Rothbard

Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity. — Mary Somerville

2. The news was prioritized in a way I could not understand. For instance, there was nothing on new mathematical observations or still-undiscovered polygons, but quite a bit about politics, which on this planet was essentially all about war and money. Indeed, war and money seemed to be so popular on the news, it should more accurately have been titled The War and Money Show. — Matt Haig

It took me 1057 pages to describe the hundreds of mathematical equations, algorithms and programming techniques that I invented and used. — Philip Emeagwali

But why has our physical world revealed such extreme mathematical regularity that astronomy superhero Galileo Galilei proclaimed nature to be "a book written in the language of mathematics," and Nobel Laureate Eugene Wigner stressed the "unreasonable effectiveness of mathematics in the physical sciences" as a mystery demanding an explanation? — Max Tegmark

The foundations of population genetics were laid chiefly by mathematical deduction from basic premises contained in the works of Mendel and Morgan and their followers. Haldane, Wright, and Fisher are the pioneers of population genetics whose main research equipment was paper and ink rather than microscopes, experimental fields, Drosophila bottles, or mouse cages. Theirs is theoretical biology at its best, and it has provided a guiding light for rigorous quantitative experimentation and observation. — Theodosius Dobzhansky

The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic. — Ronald Fisher

Another characteristic of mathematical thought is that it can have no success where it cannot generalize. — Charles Sanders Peirce

The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science. — David Hilbert

To tell the truth, in Pacific 231 I was on the trail of a very abstract and quite ideal concept, by giving the impression of a mathematical acceleration of rhythm, while the movement itself slowed . I first called this piece Mouvement symphonique. On reflection I found that a bit colorless. Suddenly, a rather romantic image crossed my mind, and when the work was finished, I wrote the title Pacific 231, which indicates a locomotive for heavy loads and high speeds (a type unfortunately disappeared, alas, and sacrificed to electric traction). — Arthur Honegger

. . .a scientific theory is just a mathematical model we make to describe our observations: it exists only in our minds. So it is meaningless to ask: which is real, "real" or "imaginary" time? It is simply a matter of which is the more useful description. — Stephen Hawking

It is by a mathematical point only that we are wise, as the sailor or fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course. — Henry David Thoreau

Simplify? Let me try. In school days, we are taught that if there are four animals in a room and you add two more, the total will be six. That is logic. But behind this logic, there are underlying assumptions. Now, if somebody tells you, there are four rats in the room and if you add two more cats in the room, how many animals in total exist in the room now? The answer will depend upon assumption. If you just use your mathematical brain, you will say six animals. If you use your human brain, you will say two animals. Why two animals? Because the two cats will eat the four rats in no time. — Ravindra Shukla

We often say that the earth is a sphere, but to be precise, the term sphere refers only to the surface. The correct mathematical term for the solid earth is a ball. — Leonard Susskind

I swam the race like I trained to swim it. It is not mathematical. I just let my body do it. It is a lot easier if you let your body do what it is trained for. — Ian Thorpe

In the beginning (if there was such a thing), God created Newton's laws of motion together with the necessary masses and forces. This is all; everything beyond this follows from the development of appropriate mathematical methods by means of deduction. — Albert Einstein

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong. — Hermann Weyl

More people have access to education today than ever before. But I cannot help but feel that the modern educational experience is not preparing us adequately to attend the rich banquet of life. Certainly the young people of today have mastered the use of technology and are capable of solving complex scientific and mathematical problems, but who and what do these serve if they cannot think for themselves? If they have no understanding of the meaning and purpose of their own lives? If they do not know who they are as individuals? — Matthew Kelly

The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics. — Edsger Dijkstra

In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language. — Georg C. Lichtenberg

By itself, the Holographic Principle was not enough to win the Black Hole War. It was too imprecise, and it lacked a firm mathematical foundation. The reaction to it was skepticism: The universe a hologram? Sounds like science fiction. The fictitious future physicist Steve passing to the "other side" while the emperor and the count watch him being immolated? Sounds like spiritualism. — Leonard Susskind

The universe can best be pictured as consisting of pure thought, the thought of what for want of a better word we must describe as a mathematical thinker. — James Jeans

College is the grinding machine of the Mathematical Establishment, a conveyor belt that takes individuals from one cookie cutter to another so that the product comes within tight control limits out of the assembly line. — Bill Gaede

Philosophical knowledge is knowledge which reason gains from concepts; mathematical knowledge is knowledge which reason gains from the construction of concepts. — Immanuel Kant

But he needed to be certain before committing to something so - the word, certain, arrested his thoughts. A person can't be absolutely certain about anything, not certainty in the sense of a mathematical proof. He wasn't certain about Kate. He saw her, observed her, wanted to be with her. Somehow, he just knew. For reasons already set in his heart, the way he was wired, Josh knew Kate was a person he wanted in his life. She was the proof. Would it be the same way with God? — H.L. Wegley

Our present work sets forth mathematical principles of philosophy. For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces. It is to these ends that the general propositions in books 1 and 2 are directed, while in book 3 our explanation of the system of the world illustrates these propositions. — Isaac Newton

We have never pushed it far enough to know, but we decided 47 percent was the right percentage. You can quote us on that. It's very mathematical. — Cinco Paul

The meaning of a logically consistent mathematical statement is not subject to interpretation. — Edward Frenkel

He had a particular facination with the I Ching, that art of tossing three coins three times and divining a pattern out of heads and tails. Pete would begin with questions:
What determined the pattern? Was it random? Was it a higher power? Was is mathematical? Wasn't poker based on mathematical probability and not just luck? Did that mean randomness was actually mathematical? And if the I Ching was governed by mathematics, hey, wouldn't that mean the I Ching was actually predictable, a prescribed answer? And if it was prescribed, did that mean that your life followed the I Ching, like some sort of equation? Or did the I Ching simply capture correctly what had already been determined as the next series of events in your life? — Amy Tan

Is that what happened to Mercier?" "No - not quite. In so far as I understood Sukhoi's work, it appeared that the zero-mass state would be very difficult to realise physically. As it neared the zero-mass state, the vacuum would be inclined to flip to the other side. Sukhoi called it a tunnelling phenomenon." Clavain raised an eyebrow. "The other side?" "The quantum-vacuum state in which matter has imaginary inertial mass. By imaginary I mean in the purely mathematical sense, in the sense that the square root of minus one is an imaginary number. Of course, you immediately see what that would imply." "You're talking about tachyonic matter," Clavain said. "Matter travelling faster than light. — Alastair Reynolds

Of course, the set of logically consistent mathematical structures is many times larger than the set of physical principles. Therefore, some mathematical structures, such as number theory (which some mathematicians claim to be the purest branch of mathematics), have never been incorporated into any physical theory. Some argue that this situation may always exist: Perhaps the human mind will always be able to conceive of logically consistent structures that cannot be expressed through any physical principle. However, there are indications that string theory may soon incorporate number theory into its structure as well. — Michio Kaku

Economists who speak the English tongue are strangely intimidated by mathematical symbols. — Al Nichol

The art of change-ringing is peculiar to the English, and, like most English peculiarities, unintelligible to the rest of the world. (The change-ringer's) passion - and it is a passion - finds its satisfaction in mathematical completeness and mechanical perfection, and as his bell weaves her way rhythmically up from lead to hinder place and down again, he is filled with the solemn intoxication that comes of intricate ritual faultlessly performed. — Dorothy L. Sayers

It is generally believed that our science is empirical and that we draw our concepts and our mathematical constructs from the empirical data. If this were the whole truth, we should, when entering into a new field, introduce only such quantities as can directly be observed, and formulate natural laws only by means of these quantities. — Werner Heisenberg

The 'seriousness' of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas. Thus a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences. — G.H. Hardy

Wisdom is not mathematical, nor astronomical, nor zoological; when it talks too much of any one thing it ceases to be itself. There are wise physicists, but wisdom is not physical; there are wise physicians, but wisdom is not medical. — George Sarton

When physicists create a mathematical model of a physical process, they rely on the mathematical framework that can represent that process as closely as possible. When Newton developed a model of forces and motion, the appropriate mathematical framework was calculus. When Einstein developed a model of wave-particle motion, he relied on the mathematics of wave equations and eigenvalues. For many models in scientific computation, the computational framework that best aligns with our need is object orientation. — Anthony Scopatz

Laplace would have found it child's-play to fix a ratio of progression in mathematical science between Descartes, Leibnitz, Newton and himself — Henry Adams

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

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

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

Has the mathematical abilities of a Clydesdale. — David Letterman

Scientific research is compounded of ... empirical procedures, general speculative ideas, and mathematical or abstract reasoning. — James Bryant Conant

A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales. — Benoit Mandelbrot

A mathematician says that an electromagnetic wave travels from Andromeda to your eye and that it also extends from Andromeda to your eye. — Bill Gaede

The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning, and when they cannot, it's a sign our Knowledge of them is very small and confus'd; and where a mathematical reasoning can be had, it's as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you. — John Arbuthnot

I soon found an opportunity to be introduced to a famous professor Johann Bernoulli ... True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand ... — Leonhard Euler

When I'm actually writing by hand, I get more of a sense of the rhythm of sentences, of syntax. The switch to the computer is when I actually start thinking about lines. That's the workhorse part. At that point, I'm being more mathematical about putting the poem on the page and less intuitive about the rhythm of the syntax. — Natasha Trethewey

I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common. — Isaac Newton

I am sorry for your disappointment,' he continued, glancing into her face. Their eyes having met, became, as it were, mutually locked together, and the single instant only which good breeding allows as the length of such a look, became trebled: a clear penetrating ray of intelligence had shot from each into each, giving birth to one of those unaccountable sensations which carry home to the heart before the hand has been touched or the merest compliment passed, by something stronger than mathematical proof, the conviction, 'A tie has begun to unite us.' Both faces also unconsciously stated that their owners had been much in each other's thoughts of late. Owen had talked to the young architect of his sister as freely as to Cytherea of the young architect. — Thomas Hardy

The calculative exactness of practical life which the money economy has brought about corresponds to the ideal of natural science: to transform the world by mathematical formulas. Only money economy has filled the days of so many people with weighing, calculating, with numerical determinations, with a reduction of qualitative values to quantitative ones. — Georg Simmel

It turned out keeping reality bound by mathematical laws was a useful hack preventing the Devil from existing. — Scott Alexander

her on the dorm board. We had only twenty girls in a batch of two hundred. Goodlooking ones were rare; girls don't get selected to IIM for their looks. They get in because they can solve mathematical problems faster than 99.99% of India's population and crack the CAT. Most IIM girls are above shallow things like makeup, fitting clothes, contact lenses, removal of facial hair, body odour and feminine charm. Girls like Ananya, if and when they arrive by freak chance, become instant pin-ups in out testosterone-charged, estrogen-starved campus. — Anonymous

Real life issues are not mathematical equations. We're not calculators crunching numbers. We're humans sorting through complex, multi-layered issues, and we're doing so while enduring the (sometimes profound) personal effects of our conclusions. While we want to be reasonable, we are inexorably pulled in the direction of our oldest mental habits and by our deepest life-impacting needs. We're repelled by those ideas which can jeopardize our comfort, safety, and happiness. We can try to be fair, but all the while we are fighting against our needs and fears. There are things we don't want to be true (or false). Our lives are built on certain beliefs which, if disproved, could wreck us. These are the truths that we 'can't handle'. — Daniel Ionson

Popularity is a mathematical formula based on desirability criteria. High schools are a classic anthropological case study, and getting people to respond in the way you want is psychology. All science. It's just not the type of science that you're used to. — Eileen Cook

If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming. — George Dantzig

I am not qualified to say whether or not God exists. I kind of doubt He does. Nevertheless I'm always saying that the SF( The SF is the supreme Fascist, the Number-One guy up there) has this transfinite book-transfinite being a concept in mathematics that is larger than infinite-that contains the best proofs of all mathematical theorems, proofs that are elegant and perfect. — Paul Erdos

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. — Mario Livio

Traditionally, scientists have treated the laws of physics as simply 'given,' elegant mathematical relationships that were somehow imprinted on the universe at its birth, and fixed thereafter. Inquiry into the origin and nature of the laws was not regarded as a proper part of science. — Paul Davies

The mathematical phenomenon always develops out of simple arithmetic, so useful in everyday life, out of numbers, those weapons of the gods: the gods are there, behind the wall, at play with numbers. — Le Corbusier

In modern times the belief that the ultimate explanation of all things was to be found in Newtonian mechanics was an adumbration of the truth that all science, as it grows towards perfection, becomes mathematical in its ideas. — Alfred North Whitehead

So mathematical truth prefers simple words since the language of truth is itself simple. — Tycho Brahe

The first man to understand the extraordinary magical power of applying mathematical calculation to things in nature was an Italian called Galileo Galilei. — E.H. Gombrich

So far has Western society departed from the ancient taboos against murder, theft, and rape that we are now faced with juvenile delinquents who have no inner check against wantonly assaulting other human beings at random 'for kicks' while we have adult delinquents capable of deliberately planning the extermination of tens of millions of human beings, in carrying out, also doubtless for kicks, a mathematical theory of games. Today our civilization is relapsing into a state far more primitive, far more irrational, than any taboo-ridden society now known-for lack of any effective taboos. If Western man could establish an inviolate taboo against random extermination, our society would enjoy a far more effective safeguard against both private violence and still impending collective nuclear horrors than the United Nations or the fallible mechanisms of Fail-Safe. — Lewis Mumford

It is in this mutual dependence of the functions and the aid which they reciprocally lend one another that are founded the laws which determine the relations of their organs and which possess a necessity equal to that of metaphysical or mathematical laws, since it is evident that the seemly harmony between organs which interact is a necessary condition of existence of the creature to which they belong and that if one of these functions were modified in a manner incompatible with the modifications of the others the creature could no longer continue to exist. — Georges Cuvier

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. — Alexander Grothendieck

Number, place, and combination ... the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred. — James Joseph Sylvester

The mathematical likelihood that God exists is astronomical. But the idea that our limited human mentality can understand the true nature of God borders on the ridiculous. For this reason the religionist and the ahteist are equally naive. — Keith David Henry

The mathematical difficulties of the theory of rotation arise chiefly from the want of geometrical illustrations and sensible images, by which we might fix the results of analysis in our minds. — James Clerk Maxwell

In fact a few simple mathematical calculations reveal that if reference librarians were paid at market rates for all the roles they play, they would have salaries well over $200,000. — Will Manley

Photography does not form a separate, barren field of art. It is only a means of execution, uniform, rapid and sure, which serves the artist by reproducing with mathematical precision the form and effect of objects and even that poetry which at once arises from any harmonious combination. — Charles Negre