Math Quotes

Play with your dolls for not more than half an hour, no more than fifteen minutes, no more than a second, a millisecond. If you learned math as fast as you ran outside to play, then you might be a genius. But you do not and you are not. You're a hole where knowledge goes to sleep.

~ Weike Wang

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 Poincaré

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.

~ George Boole

The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.

~ Eric Temple Bell

Science attempts to find logic and simplicity in nature. Mathematics attempts to establish order and simplicity in human thought.

~ Edward Teller

One must acknowledge with cryptography no amount of violence will ever solve a math problem.

~ Jacob Appelbaum

The mathematical giant [Gauss], who from his lofty heights embraces in one view the stars and the abysses …

~ Farkas Bolyai

Math anxiety is worst than a regular check up at the dentist.

~ Charmaine J. Forde

It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing.

~ Sofia Kovalevskaya

I don't see how it's doing society any good to have it's members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them.

~ Paul Lockhart

There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

~ George Pólya

Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.

~ Edward Griffith Begle

Being kidnapped and abused by the undead was worse than calculus, but not by a wide margin.

~ Thomm Quackenbush

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

~ George Pólya

... I succeeded at math, at least by the usual evaluation criteria: grades. Yet while I might have earned top marks in geometry and algebra, I was merely following memorized rules, plugging in numbers and dutifully crunching out answers by rote, with no real grasp of the significance of what I was doing or its usefulness in solving real-world problems. Worse, I knew the depth of my own ignorance, and I lived in fear that my lack of comprehension would be discovered and I would be exposed as an academic fraud -- psychologists call this imposter syndrome.

~ Jennifer Ouellette

We're all born with curiosity, but at some point, school usually manages to knock that out of us.

~ Max Tegmark

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.

~ G.h. Hardy

So what were your favorite subjects in school?School? He leaned back in his chair as though he needed the extra space to think about it. Probably math. It always made sense. Unlike English, economics, and girls.And exactly how do you plan on taking over the free world if you don't understand economics?I'll hire advisers. I'll hire you, in fact.Okay. Let me know when your army of junior high zombies is ready.

~ Janette Rallison

What I like??I like how people solve the problems, the way they think aND THEIR aspects!

~ Deyth Banger

Math is made for idiots, here is what is the proccess in math class. The teacher show you few exercises, show you the formula, show you the way, say everything about the exercises and then she tell you to solve problems. So as for me the proccess is REPEAT!

~ Deyth Banger

A goal of this book has been to tear down in some small part these barriers to understanding by attempting to shatter the “divinity of arithmetic,” through showing that even the methods, which we now take most for granted, were not given to us from on high, but were actually the result of centuries of scientific efforts on the part of our predecessors. p. 269

~ G. Arnell Williams

A person's value is attached to a variable exponent.

~ David Bajo

. . . I still wouldn't be able to control myself around him, and I'm math geek enough to know that equation doesn't work out.

~ Robin Brande

It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematics, its motivations and goals and the ideas that must bind divergent interests together.

~ Richard Courant

Infinity exist unfortnately what will happen if we accept it??After all numbers are taken what happens??We will start with Omega+1 Then Omega+Omega+1... Think on this, this is the infinitive road, I gave it to you but what you will do?

~ Deyth Banger

The sky is where mathematics and magic become one.

~ Tony Abbott

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

Whereas Nature does not admit of more than three dimensions ... it may justly seem very improper to talk of a solid ... drawn into a fourth, fifth, sixth, or further dimension.

~ John Wallis

Like Molière’s M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole’s 'The Mathematical Analysis of Logic'.

~ Ernest Nagel

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well constructed theory is in some respects undoubtedly an artistic production. A fine example is the famous Kinetic Theory of Maxwell. ... The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art.

~ Ernest Rutherford

Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems—general and specific statements—can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.

~ Christopher Zeeman

Mathematics had never had more than a secondary interest for him [her husband, George Boole]; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to give rest had no tendency to prove them.

~ Mary Everest Boole

If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.

~ Alfred Tarski

Logic, it is often said, is the study of valid arguments. It is a systematic attempt to distinguish valid arguments from invalid arguments.

~ W.h. Newton-Smith

Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don't like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russel pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russel replied immediately that 'if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1'! A contradictory statement is the ultimate Trojan horse.

~ John D. Barrow

If my path is right, let it be your path; if your path is right, let it be my path!

~ Mehmet Murat Ildan

The appearance of Professor Benjamin Peirce, whose long gray hair, straggling grizzled beard and unusually bright eyes sparkling under a soft felt hat, as he walked briskly but rather ungracefully across the college yard, fitted very well with the opinion current among us that we were looking upon a real live genius, who had a touch of the prophet in his make-up.

~ William Elwood Byerly

Music was not so very different from mathematics. It was all just patterns and sequences. The only difference was that they hung in the air instead of on a piece of paper. Dancing was a grand equation. One side was sound, the other movement. The dancer's job was to make them equal.

~ Julia Quinn

Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to say to a student 'Your feelings and ideas are suspect. You need to think and speak our way.

~ Paul Lockhart

Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity

~ G.h. Hardy