Mathematicians Quotes

Another factor: Christianity offered opportunities for advancement in the church to intelligent young men, some of whom might otherwise have become mathematicians or scientists. Bishops and presbyters were generally exempt from the jurisdiction of the ordinary civil courts, and from taxation. A bishop such as Cyril of Alexandria or Ambrose of Milan could exercise considerable political power, much more than a scholar at the Museum in Alexandria or the Academy in Athens. This was something new. Under paganism religious offices had gone to men of wealth or political power, rather than wealth and power going to men of religion. For instance, Julius Caesar and his successors won the office of supreme pontiff, not as a recognition of piety or learning, but as a consequence of their political power. ~ Steven Weinberg

And while the black women are the most hidden of the mathematicians who worked at the NACA, the National Advisory Committee for Aeronautics, and later at NASA, they were not sitting alone in the shadows: the white women who made up the majority of Langley's computing workforce over the years have hardly been recognized for their contributions to the agency's long-term success. Virginia Biggins worked the Langley beat for the Daily Press newspaper, covering the space program starting in 1958. "Everyone said, 'This is a scientist, this is an engineer,' and it was always a man," she said in a 1990 panel on Langley's human computers. She never got to meet any of the women. "I just assumed they were all secretaries," she said. Five ~ Margot Lee Shetterly

Douady and Hubbard used a brilliant chain of new mathematics to prove that every floating molecule does indeed hang on a filigree that binds it to all the rest, a delicate web springing from tiny outcroppings on the main set, a "devil's polymer," in Mandelbrot's phrase. The mathematicians proved that any segment-no matter where, and no matter how small-would, when blown up by the computer microscope, reveal new molecules, each resembling the main set and yet not quite the same. Every new molecule would be surrounded by its own spirals and flame-like projections, and those, inevitably, would reveal molecules tinier still, always similar, never identical, fulfilling some mandate of infinite variety, a miracle of miniaturization in which every new detail was sure to be a universe of its own, diverse and entire. ~ James Gleick

Many errors, of a truth, consist merely in the application of the wrong names of things. For if a man says that the lines which are drawn from the centre of the circle to the circumference are not equal, he understands by the circle, at all events for the time, something else than mathematicians understand by it. ~ Baruch Spinoza

Most geometricians, chemists, mathematicians, and great scientists submit religion to reason only to discover a problem as unsolvable as that of squaring a circle. ~ Honore De Balzac

Good mathematicians see analogies. Great mathematicians see analogies between analogies. ~ Stefan Banach

Mathematicians do not study objects, but relations between objects. ~ Henri Poincare

Mathematicians deal with large numbers sometimes, but never in their income. ~ Isaac Asimov

Mathematicians tend to prefer a worst-case analysis, a kind of paranoia that is especially understandable if you live in Israel! ~ Noga Alon

They ask how the universe is arranged, philosophers, mathematicians, and they draw pretty pictures, impossibilities on the page. They save phenomena by telling one ugly lie after another, epicycles upon epicycles, and the fools care not. It is not enough, I tell you, to ask how the cosmos is designed. We must ask why. ~ Robin Wasserman

Truth isn't pretty, I thought, and the pursuit of it doesn't make pretty people. Truth isn't elegant; that's just mathematicians' sentimentality. Truth is squalid and full of blots, and you can only find it in the accumulation of dusty and broken facts, in the cellars and sewers of the human mind ~ Hilary Mantel

Answer my question: Why do smart people tend to be stupid?" "Because we think we know better. We think that our intellect affords us special privileges and lets us beat the odds. That's why talented mathematicians try to defraud casinos and young brilliant mages make bargains with forces beyond their control. ~ Jeaniene Frost

I am a Christian which means that I believe in the deity of Christ, like Tycho de Brahe, Copernicus, Descartes, Newton, Leibnitz, Pascal ... like all great astronomers mathematicians of the past. ~ Augustin-Louis Cauchy

I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won't get there unless we dump the stereotype that math is only worthwhile for kid geniuses. ~ Jordan Ellenberg

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold. ~ Henri Poincare

The reason that I have concentrated on non-computability, in my arguments, rather than on complexity, is simply that it is only with the former that I have been able to see how to make the necessary strong statements. It may well be that in the working lives of most mathematicians, non-computability issues play, if anything, only a very small part. But that is not the point at issue. I am trying to show that (mathematical) understanding is something that lies beyond computation, and the Godel (-Turing) argument is one of the few handles that we have on that issue. It is quite probable that our mathematical insights and understandings are often used to achieve things that could in principle also be achieved computationally-but where blind computation without much insight may turn out to be so inefficient that it is unworkable (cf. 3.26). However, these matters are much more difficult to address than the non-computability issue. ~ Roger Penrose

If things are nice there is probably a good reason why they are nice: and if you do not know at least one reason for this good fortune, then you still have work to do. ~ Richard Askey

Mathematicians - for what they do - are really poorly rewarded. And it's a very competitive field, almost as bad as being a concert pianist. ~ Gian-Carlo Rota

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds. ~ G.H. Hardy

I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts ... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'. ~ Roger Penrose

Therefore Godel's theorem had an electrifying effect upon logicians, mathematicians, and philosophers interested in the foundations of mathematics, for it showed that no fixed system, no matter how complicated could represent the complexity of the whole numbers: 0,1,2,3,..... ~ Douglas R. Hofstadter

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper. ~ George Polya

What is a look of absolute fear? Popescu asked. The doctor belched a few times, shifted in his chair, and answered that it was a kind of look of mercy, but empty, as if all that were left of mercy, after a mysterious voyage, was the skin, as if mercy were a skin of water, say, in the hands of a Tatar horseman who gallops away over the steppe and dwindles untile he vanishes, and then the horseman returns, or the ghost of the horseman returns, or his shadow, or the idea of him, and he has the skin, empty of water now, because he drank it all during his trip, or he and his horse drank it, and the skin is empty now, it's a normal skin, an empty skin, because after all the abnormal thing is a skin swollen with water, but this skin swollen with water, this hideous skin swollen with water doesn't arouse fear, doesn't awaken it, much less isolate it, but the empty skin does, and that was what he saw in the mathematician's face, absolute fear. ~ Roberto Bolano

Silicon Valley, "the largest legal creation of wealth in history," was built largely by unprofessional amateurs using math, sand, and the institutions of freedom. The Soviet Union had the greatest mathematicians on earth, and plenty of sand, but without the institutions of freedom their brilliant mathematicians were not empowered to create those devices that are changing the world. ~ Michael Strong

Read an article about a group of mathematicians who developed a financial model to accurately compare apples and oranges. I was stunned. Never thought I'd see the day. Preliminary indications are that the model allows any two kinds of fruit to be compared, although guava still causes minor rounding errors. Further testing is ongoing.
Gomez Porter, blogspace entry ~ Graham Parke

A result once generally accepted by mathematicians is seldom retracted, and then only with great pangs.
The Nature of Mathematics ~ Max Black

The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events. ~ Gian-Carlo Rota

Like musicians who can read and write complicated scores in a world without sounds, for us mathematics is a source of delight, excitement, and even controversy which are hard to share with non mathematicians. In our small micro-cosmos we should ever seek the right balance between competition and solidarity, criticism and empathy, exclusion and inclusion. ~ Gil Kalai

It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it. ~ Bernhard Riemann

The good Christian should beware of mathematicians. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell. ~ Augustine Of Hippo

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design. ~ Freeman Dyson

Some time after, asking a friend at court how they came to fix on that determinate number, he told me that his majesty's mathematicians, having taken the height of my body by the help of a quadrant, and finding it to exceed theirs in the proportion of twelve to one, they concluded from the similarity of their bodies, that mine must contain at least 1724 of theirs, and consequently would require as much food as was necessary to support that number of Lilliputians. By ~ Jonathan Swift

In various ways, methods of approaching the mathematician's ideal were sought, and the resulting suggestions were the source of much that was mistaken in metaphysics and theory of knowledge. ~ Bertrand Russell

It's specifically this Z = 2^(Aleph0) that he couldn't prove. Ever. Despite years of unimaginable doodling. Whether it's what unhinged him or not is an unanswerable question, but it is true that his inability to prove the C.H. caused Cantor pain for the rest of his life; he considered it his great failure. This too, in hindsight, is sad, because professional mathematicians now know exactly why G. Cantor could neither prove nor disprove the C.H. The reasons are deep and important and go corrosively to the root of axiomatic set theory's formal Consistency, in rather the same way that K. Godel's Incompleteness proofs deracinate all math as a formal system. Once again, the issues here can be only sketched or synopsized (although this time Godel is directly involved, so the whole thing is probably fleshed out in the Great Discoveries Series' Godel booklet). ~ David Foster Wallace

It's not like that, as we've seen. Mathematicians aren't crazy, and we aren't aliens, and we aren't mystics.

What's true is that the sensation of mathematical understanding-of suddenly knowing what's going on, with total certainty, all the way to the bottom-is a special thing, attainable in few if any other places in life. You feel you've reached into the universe's guts and put your hand on the wire. It's hard to describe to people who haven't experienced it. ~ Jordan Ellenberg

All mathematicians share ... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics. ~ Martin Gardner

And in that same way, law school breaks a mind down. Novelists, poets, and artists don't often do well in law school, but neither, necessarily, do mathematicians, logicians and scientists. The first group fails because their logic is their own; the second fails because logic is all they own. ~ Hanya Yanagihara

Where there is matter, there is geometry. ~ Johannes Kepler

These estimates may well be enhanced by one from F. Klein (1849-1925), the leading German mathematician of the last quarter of the nineteenth century. 'Mathematics in general is fundamentally the science of self-evident things.' ... If mathematics is indeed the science of self-evident things, mathematicians are a phenomenally stupid lot to waste the tons of good paper they do in proving the fact. Mathematics is abstract and it is hard, and any assertion that it is simple is true only in a severely technical sense - that of the modern postulational method which, as a matter of fact, was exploited by Euclid. The assumptions from which mathematics starts are simple; the rest is not. ~ Eric Temple Bell

In his wretched life of less than twenty-seven years Abel accomplished so much of the highest order that one of the leading mathematicians of the Nineteenth Century (Hermite, 1822-1901) could say without exaggeration, 'Abel has left mathematicians enough to keep them busy for five hundred years.' Asked how he had done all this in the six or seven years of his working life, Abel replied, 'By studying the masters, not the pupils. ~ Eric Temple Bell

[John Wheeler] rejuvenated general relativity; he made it an experimental subject and took it away from the mathematicians ~ Freeman Dyson

It was love, she thought, love that never clutch its object; but, like the love which mathematicians bear their symbols, or poets their phrases, was meant to be spread over the world and become part of human gain. The world by all means should have shared it, could Mr Bankes have said why that woman pleased him so; why the sight of her reading a fairy tale to her boy had upon him precisely the same effect as the solution of a scientific problem. ~ Virginia Woolf

The only way to comprehend what mathematicians mean by Infinity is to contemplate the extent of human stupidity. ~ Voltaire

Whenever I want to represent or depict the official version, I will refer to them as 'mathematicians' or 'mathematical physicists' or idiots or something like that. There are no physicists in mainstream 'Physics.' From Newton to Einstein to Hawking, they are all just mathematicians as far as Science and Physics are concerned. ~ Bill Gaede

Lecter sits in his armchair with a big pad of butcher paper doing calculations. The pages are filled with the symbols both of astrophysics and particle physics. There are repeated efforts with the symbols of string theory. The few mathematicians who could follow him might say his equations begin brilliantly and then decline, doomed by wishful thinking. Dr. Lecter wants time to reverse - no longer should increasing entropy mark the direction of time. He wants increasing order to point the way. ~ Thomas Harris

As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable. ~ Abraham Robinson

Geniuses of certain kinds - mathematicians, chess players, computer programmers - seem, if not mad, at least lacking in the social skills most easily identified with sanity. ~ James Gleick

Mathematicians grow very old; it is a healthy profession. The reason you live long is that you have pleasant thoughts. Math and physics are very pleasant things to do. ~ Dirk Jan Struik

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

Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate. ~ Leonhard Euler

Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them. ~ Joseph Fourier

We must establish all over the country schools of our own to train our own children to become scientists, to become mathematicians. We must realize the need for adult education and for job retraining programs that will emphasize a changing society in which automation plays the key role. We intend to use the tools of education to help raise our people to an unprecedented level of excellence and self respect through their own efforts. ~ Malcolm X

Instruction tables will have to be made up by mathematicians with computing experience and perhaps a certain puzzle-solving ability. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself. ~ Alan Turing

It would be better for the true physics if there were no mathematicians on earth. ~ Daniel Bernoulli

In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, "this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere." He immediately protested: "No, no. These concepts were not dreamed up. They were natural and real." ~ Chen-Ning Yang

Most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, but largely went their own way. ~ Benoit Mandelbrot

I have also known some of the world's finest brains and some of these, though passionately fond of chess, have been pretty poor players. I used to know one of the world's leading mathematicians and whenever we played chess I had to give him the odds of a Queen to make matters more equal, and even then I always won. ~ Harry Golombek

Did you know that in mathematics they determined what was real by what was not imaginary?" Finn's voice was just a soft rumble beneath my fingertips that had found his lips
"What?"
"When mathematicians came up with imaginary numbers, accepted them, defined them, they had to come up with a name for everything that wasn't imaginary. Everything that wasn't an imaginary number from that point on became a 'real' number."
What's an imaginary number?"
"The square root of negative one is an imaginary number."
"Is that all?"
"Any number that was once the square root of a negative number becomes an imaginary number. Square root of -4 becomes 2i, square root of -100 becomes 10i."
"Is infinity an imaginary number?"
"No."
"Is it a real number?"
"No. It isn't a number at all. It's a concept of endlessness, unreachableness.
"I knew it. See? You are just a figment of my imagination. ~ Amy Harmon

Because of the overwhelmingly white public face of the space program, the black engineers, scientists, and mathematicians who were deeply involved with the space race nevertheless lived in its shadows, even within the black community. Katherine ~ Margot Lee Shetterly

It was love, she thought, pretending to move her canvas, distilled and filtered; love that never attempted to clutch its object; but, like the love which mathematicians bear their symbols, or poets their phrases, was meant to be spread over the world and become part of the human gain. ~ Virginia Woolf

Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us. ~ Freeman Dyson

I count Maxwell and Einstein, Eddington and Dirac, among "real" mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as "useless" as the theory of numbers. ~ G.H. Hardy

The world ain't ready for true black genius. In every nigger is a cup of African blood from kings and queens of divine nature, mathematicians, craftsmen, men and women of the land. I have known some sisters and brothers would scare Einstein back into East European caves with the magnificence of their minds. We are a people with a practical nature and great vision. We have built nations, discovered treasures for everyday use. Our people are a great race of people, and though the Europeans raped and plundered, we have kept inner riches. You got a cup of African blood and that mean something, means you got a responsibility to be proud of it and use your talents or suffer self-destruction. ~ Shay Youngblood

Then there's the silliest of all cliches, 'on a pace for' 'Pace' is a figment of the mathematician's imagination. ~ Leonard Koppett

Elegance? It may seem odd to non-scientists, but there is an aesthetic in software as there is in every other area of intellectual endeavour. Truly great programmers are like great poets or great mathematicians - they can achieve in a few lines what lesser mortals can only approach in three volumes ~ John Naughton

Mathematicians need to understand a problem only for themselves; math teachers need both to know the math and to know how 30 different minds might understand (or misunderstand) it. Then they need to take each mind from not getting it to mastery. And they need to do this in 45 minutes or less. ~ Elizabeth Green

Female physicists, astronomers and mathematicians are up against more than 2,000 years of convention that has long portrayed these fields as inherently male. ~ Margaret Wertheim

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

It is obvious that mathematics needs both sorts of mathematicians, theory-builders and problem-solvers. ~ Timothy Gowers

The final story of randomness - utter chaos - has not yet been told to us by the mathematicians. It seems remarkable that something so fundamental for probability theory has not been defined and even more remarkable that we can go so far in mathematics lacking a definition. By simply assuming randomness exists, mathematicians assign elementary probabilities to events, and that is their starting point. But they have not captured chaos and looked it in the eye. ~ Heinz R. Pagels

Intuition is a combination of insight and imagination that was once attributed to spiritual communication. Mathematicians call it 'fuzzy logic,' drawing conclusions from vague or subjective input. The mind becomes aware without the direct intervention of reasoning. Once you can imagine something you can begin the process of creating it. Executives use intuition to make many product, investment, and hiring decisions, even if they deny it. Success in business may depend on an accurate gut. ~ Jennifer James

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. ~ Sean J Halford

I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain ... But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further - then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty. ~ Hermann Von Helmholtz

Q7. The total output of all the mathematicians who have ever lived, together with the output of all the human mathematicians of the next (say) thousand years is finite and could be contained in the memory banks of an appropriate computer. Surely this particular computer could, therefore, simulate this output and thus behave (externally) in the same way as a human mathematician-whatever the Godel argument might appear to tell us to the contrary?

While this is presumably true, it ignores the essential issue, which is how we (or computers) know which mathematical statements are true and which are false. (In any case, the mere storage of mathematical statements is something that could be achieved by a system much less sophisticated than a general purpose computer, e.g. photographically.) The way that the computer is being employed in Q7 totally ignores the critical issue of truth judgment. One could equally well envisage computers that contain nothing but lists of totally false mathematical 'theorems', or lists containing random jumbles of truths and falsehoods. How are we to tell which computer to trust? The arguments that I am trying to make here do not say that an effective simulation of the output of conscious human activity (here mathematics) is impossible, since purely by chance the computer might 'happen' to get it right-even without any understanding whatsoever. But the odds against this are absurdly enormous, and the issues that are being addressed here, namel ~ Roger Penrose

James Edward Oliver might have been one of the great mathematicians of his time had he not been absolutely wanting in the power of continuous work. ~ Simon Newcomb

It is not the job of mathematicians ... to do correct arithmetical operations. It is the job of bank accountants. ~ Samuil Shatunovsky

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. ~ Bill Gaede

Mathematics is fun if you don't let mathematicians push you around when you are doing it. ~ Jack Edmonds

As we have seen with reference to the experiences of Gauss and Poincare, the mathematicians also discovered the fact that our representations are "ordered" before we become aware of them. B.L. van der Waerden, who cites many examples of essential mathematical insights arising from the unconscious, concludes: " ... the unconscious is not only able to associate and combine, but even to judge. The judgment of the unconscious is an intuitive one, but it is under favorable circumstances completely sure. ~ C. G. Jung

Work/Loaf Ratio" ... I have spent fourteen years perfecting ... I won't bore you with a long-winded explanation of the "W/LR" save to say that it is an algebraic formula of such complex numeric subtlety that it can be understood only by mathematicians and hobos. ~ Gary Reilly

[I can] scarcely write upon mathematics or mathematicians. Oh for words to express my abomination of the science. ~ Thomas B. Macaulay

The only reason psychology students don't have to do more and harder mathematics than physics students is because the mathematicians haven't yet discovered ways of dealing with problems as hard as those in psychology. ~ John G. Kemeny

Nature is probably quite indifferent to the aesthetic preferences of mathematicians. ~ Alfred North Whitehead

The calendar is intolerable to all wisdom, the horror of all astronomy, and a laughing stock from a mathematician's point of view. ~ Roger Bacon

This is the time for obscure Italian mathematicians ~ Gail Carriger

When I told my mother that I have to give a talk, and was debating what could I possibly say to non-mathematicians, she said: "You got what to wear?". ~ Richard A. Falk

I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia. ~ John Forbes Nash

The legendary inscription above the Academy's door speaks loudly about Plato's attitude toward mathematics. In fact, most of the significant mathematical research of the fourth century BC was carried out by people associated in one way or another with the Academy. Yet Plato himself was not a mathematician of great technical dexterity, and his direct contributions to mathematical knowledge were probably minimal. Rather, he was an enthusiastic spectator, a motivating source of challenge, an intelligent critic, an an inspiring guide. The first century philosopher and historian Philodemus paints a clear picture: "At that time great progress was seen in mathematics, with Plato serving as the general architect setting out problems, and the mathematicians investigating them earnestly." To which the Neoplatonic philosopher and mathematician Proclus adds: "Plato...greatly advanced mathematics in general and geometry in particular because of his zeal for these studies. It is well known that his writings are thickly sprinkled with mathematical terms and that he everywhere tries to arouse admiration for mathematics among students of philosophy." In other words, Plato, whose mathematical knowledge was broadly up to date, could converse with the mathematicians as an equal and as a problem presenter, even though his personal mathematical achievements were not significant. ~ Mario Livio

What is causing this mysterious perpetual air of inconvenience to slowly engulf the evening. It is not merely emptiness but an awakening in itself about nothingness.
Leave behind what was never yours and accept the fact that momentary pleasures and hideous treasures will perish too soon; so will your pride be snatched away by nothing. Mathematicians often say an instance tends to infinity. But, in actual sense, is anything even close to infinity?
Nullify yourself and disappear into zero, for that is what we call the beginning; the beginning of the end. ~ Ranjani Ramachandran

As there are so many who talk prose without knowing it, or, again, who syllogize without having the least idea what a syllogism is, so economists have long been mathematicians without being aware of the fact. ~ William Stanley Jevons

I am not interested in what today's mathematicians find interesting. ~ Richard P. Feynman

All musicians are subconsciously mathematicians. ~ Thelonious Monk

The perceiving of mathematical truth can be achieved in very many different ways. There can be little doubt that whatever detailed physical activity it is that takes place when a person perceives the truth of some mathematical statement, this physical activity must differ very substantially from individual to individual, even though they are perceiving precisely the same mathematical truth. Thus, if mathematicians just use computational algorithms to form their unassailable mathematical truth judgments, these very algorithms are likely to differ in their detailed construction, from individual to individual. Yet, in some clear sense, the algorithms would have to be equivalent to one another. ~ Roger Penrose

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers. ~ Hans Reichenbach

I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future. ~ Andrew Wiles

The best description of this book is found within the title. The full title of this book is:

"This is the story my great-grandfather told my father, who then told my grandfather, who then told me about how The Mythical Mr. Boo, Charles Manseur Fizzlebush Grissham III, better known as Mr. Fizzlebush, and Orafoura are all in fact me and Dora J. Arod, who sometimes shares my pen, paper, thoughts, mind, body, and soul, because Dora J. Arod is my pseudonym, as he/it incorporates both my first and middle name, and is also a palindrome that can be read forwards or backwards no matter if you are an upright man in the eyes of God or you are upside down in a tank of water wearing purple goggles and grape jelly discussing how best to spread your time between your work, your wife, and the toasted bread being eaten by the man you are talking to who goes by the name of Dendrite McDowell, who is only wearing a towel on his head and has an hourglass obscuring his "time machine"--or the thing that he says can keep him young forever by producing young versions of himself the way I avert disaster in that I ramble and bumble like a bee until I pollinate my way through flowery situations that might otherwise have ended up being more than less than, but not equal to two short parallel lines stacked on top of each other that mathematicians use to balance equations like a tightrope walker running on a wire stretched between two white stretched limos parked on a long cloud that looks like ~ Jarod Kintz

I am first affrighted and confounded with that forelorn solitude, in which I am plac'd in my philosophy, and fancy myself some strange uncouth monster, who not being able to mingle and unite in society, has been expell'd all human commerce, and left utterly abandon'd and disconsolate. Fain wou'd I run into the crowd for shelter and warmth; but cannot prevail with myself to mix with such deformity. I call upon others to join me, in order to make a company apart; but no one will hearken to me. Every one keeps at a distance, and dreads that storm, which beats upon me from every side. I have expos'd myself to the enmity of all metaphysicians, logicians, mathematicians, and even theologians; and can I wonder at the insults I must suffer? I have declar'd my disapprobation of their systems; and can I be surpriz'd, if they shou'd express a hatred of mine and of my person? When I look abroad, I foresee on every side, dispute, contradiction, anger, calumny and detraction. When I turn my eye inward, I find nothing but doubt and ignorance. All the world conspires to oppose and contradict me; tho' such is my weakness, that I feel all my opinions loosen and fall of themselves, when unsupported by the approbation of others. Every step I take is with hesitation, and every new reflection makes me dread an error and absurdity in my reasoning.
For with what confidence can I venture upon such bold enterprises, when beside those numberless infirmities peculiar to myself, I find so many which ~ David Hume

When I told my son that I had to give a talk about my work to non-mathematicians, he warned me that regular people don't think like mathematicians. ~ Richard A. Falk

Artists realise that mathematicians have a way of looking at the world that can make them see things differently. ~ Marcus Du Sautoy

Land surveyors can spend as much time reading legislation, bylaws, and engineering documents as we spend in front of an instrument in the field or calculating coordinates for a subdivision. We are mathematicians, historians, project managers, advocates, engineers, and even chainsaw operators! ~ Mark Mason