Quotes about math

God made the integers all the rest is the work of Man.

The Professor never really seemed to care whether we figured out the right answer to a problem. He preferred our wild, desperate guesses to silence, and he was even more delighted when those guesses led to new problems that took us beyond the original one. He had a special feeling for what he called the "correct miscalculation," for he believed that mistakes were often as revealing as the right answers.

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?

Another mistaken notion connected with the law of large numbers is the idea that an event is more or less likely to occur because it has or has not happened recently. The idea that the odds of an event with a fixed probability increase or decrease depending on recent occurrences of the event is called the gambler's fallacy. For example, if Kerrich landed, say, 44 heads in the first 100 tosses, the coin would not develop a bias towards the tails in order to catch up! That's what is at the root of

The ocean is a Turing machine, the sand is its tape; the water reads the marks in the sand and sometimes erases them and sometimes carves new ones with tiny currents that are themselves a response to the marks.

I do not think that G. H. Hardy was talking nonsense when he insisted that the mathematician was discovering rather than creating... The world for me is a necessary system, and in the degree to which the thinker can surrender his thought to that system and follow it, he is in a sense participating in that which is timeless or eternal.

All the truths of mathematics are linked to each other, and all means of discovering them are equally admissible.

The deep study of nature is the most fruitful source of mathematical discoveries. By offering to research a definite end, this study has the advantage of excluding vague questions and useless calculations; besides it is a sure means of forming analysis itself and of discovering the elements which it most concerns us to know, and which natural science ought always to conserve.

With me, everything turns into mathematics.

Some people believe in imaginary friends. I believe in imaginary numbers.

The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to no

I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go.

I did the math. (I presume Americans don't pluralise mathematics because they only plan to do it once.)

We’ll start with an easy one, shall we? What is the secant of three pi?” The troll asked. “Pie?” Toru felt suddenly hungry. “What are you talking about, man, have you gone senile? A sea camp? You mean like the floating city?

Man had been given a brain that could think in numbers, and it could not be coincidence that the world was unlocked by that very tool. To understand any aspect of the cosmos was to look on the face of God: not directly, but by a species of triangulation, because to think mathematically was to feel the action of God in oneself.

Eternal truths are ultimately invisible, and you won't find them in material things or natural phenomena, or even in human emotions. Mathematics, however, can illuminate them, can give them expression - in fact, nothing can prevent it from doing so.

Really, there was only one problem with Mr. Davis, as far as Gregory was concerned; He taught math.

REAL MATHEMATICS is not about just computing but it is about figuring out…Figuring out the truthfulness, reasoning behind specific event, patterns, determinism in chaotic processes etc.

You’re probably better at math than I am, because pretty much everyone’s better at math than I am, but it’s okay, I’m fine with it. See, I excel at other, more important things—guitar, sex, and consistently disappointing my dad, to name a few. By the way, it's apparently true that you'll never use it in the real world. Math, I mean.

Math is a very peculiar thing, for in it all numbers have a double but not all have halves.

Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence.

Math is my Passion. Engineering is my Profession.

Where there is no mathematics, there is no freedom.

This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.

For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.

The first successes were such that one might suppose all the difficulties of science overcome in advance, and believe that the mathematician, without being longer occupied in the elaboration of pure mathematics, could turn his thoughts exclusively to the study of natural laws.

Mathematics is the science which draws necessary conclusions.

Littlewood, on Hardy's own estimate, is the finest mathematician he has ever known. He was the man most likely to storm and smash a really deep and formidable problem; there was no one else who could command such a combination of insight, technique and power.

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficultie

[Benjamin Peirce's] lectures were not easy to follow. They were never carefully prepared. The work with which he rapidly covered the blackboard was very illegible, marred with frequent erasures, and not infrequent mistakes (he worked too fast for accuracy). He was always ready to digress from the straight path and explore some sidetrack that had suddenly attracted his attention, but which was likely to have led nowhere when the college bell announced the close of the hour and we filed out, leavi

He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication were discovered. Algebra was invented and provided an interesting diversion for a minute or two. And then he felt the fog of numbers drift away, and looked up and saw the sparkling, distant mountains of calculus.

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.

I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind.(Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.)

Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds.

Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.

How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.

[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.

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.

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

I entered Princeton University as a graduate student in 1959, when the Department of Mathematics was housed in the old Fine Hall. This legendary facility was marvellous in stimulating interaction among the graduate students and between the graduate students and the faculty. The faculty offered few formal courses, and essentially none of them were at the beginning graduate level. Instead the students were expected to learn the necessary background material by reading books and papers and by organ

Tengo's lectures took on uncommon warmth, and the students found themselves swept up in his eloquence. He taught them how to practically and effectively solve mathematical problems while simultaneously presenting a spectacular display of the romance concealed in the questions it posed. Tengo saw admiration in the eyes of several of his female students, and he realized that he was seducing these seventeen- or eighteen-year-olds through mathematics. His eloquence was a kind of intellectual forepla

A term meant to convey a person's inability to make sense of the numbers that run their lives.

Anything you try to quantify can be divided into any number of "anythings," or become the thing - the unit - itself. And what is any number, itself, but just another unit of measurement? What is a 'six' but two 'threes', or three 'twos'...half a 'twelve', or just six 'ones' - which are what? (attrib: F.L. Vanderson)

As a teacher, Tengo pounded into his students' heads how voraciously mathematics demanded logic. Here things that could not be proven had no meaning, but once you had succeeded in proving something, the world's riddles settled into the palm of your hand like a tender oyster.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.

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

The language of categories is affectionately known as "abstract nonsense," so named by Norman Steenrod. This term is essentially accurate and not necessarily derogatory: categories refer to "nonsense" in the sense that they are all about the "structure," and not about the "meaning," of what they represent.

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.

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 unaffect

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.

Believe me, if Archimedes ever had the grand entrance of a girl as pretty as Gloria to look forward to, he would never have spent so much time calculating the value of Pi. He would have been baking her a Pie! If Euclid had ever beheld a vision of loveliness like the one I see walking into my anti-math class, he would have forgotten all the geometry of lines and planes, and concentrated on the sweet simplicity of soft curves. If Pythagoras had ever had a girl look at him the way Gloria's eyes fix

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

I am the rain, when I'm on math I make the day horrible that's why the day is horrible, that's why I don't go outside.

Yes," I continued, "I discovered this model recently and her style never fails to be mathematically perfect. She seems to come by it naturally. As if she were born resonant. I notice Japanese models tend to do this. Like I said, they seem to have resonance somewhere deep in their culture. But Yuri Nakagawa, she's the best I've ever seen. The best model, with the most powerful resonance. I need her to probe deeper into this profound mathematical instinct, which I call resonance.

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

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.

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.

The sky is where mathematics and magic become one.

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.

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.

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 outs

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'.

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

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.

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.

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 r

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

It can only be our familiarity with soap bubbles from our earliest recollections, causing us to accept their existence as a matter of course, that prevents most of us from being seriously puzzled as to why they can be blown at all.

It baffled me how people could resist math's gorgeousness, but people did, and people do. The fine of its purity drives them away, the purity of the fine, unmixed with the heaviness of unnecessitated being.

Infinity...is used in physics simply as a shorthand for "a very big number.

Everyone now agrees that a physics lacking all connection with mathematics ... would only be an historical amusement, fitter for entertaining the idle than for occupying the mind of a philosopher.

A mathematician may say anything he pleases, but a physicist must be at least partially sane.

[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation.

There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, ... the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the

I do not think the division of the subject into two parts - into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics will neither sufficiently discipline the mind or sufficiently extend our knowledge in a subject like physics.

I studied calculus for the first time, which to me was an amazingly empowering experience which I could really see how you could understand all sorts of things, and I decided that chemistry and biology just had too much memory for me to be interested. Physics was very easy.

...Pff... there is always a reason for everything if you go deeper and deeper under the sea you will die in the same time, even you will drown however you will find the reason. It's about 50 out of 100 which will mean 50% chance you have to live and 50% there is a chance to die.

Math is a Chaos and it doesn't have order <--- what's the purpose of it?

Math teaches us chaos or order, for god sake?

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 ma

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.

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

The philosophers make still another objection: "What you gain in rigour," they say, "you lose in objectivity. You can rise toward your logical ideal only by cutting the bonds which attach you to reality. Your science is infallible, but it can only remain so by imprisoning itself in an ivory tower and renouncing all relation with the external world. From this seclusion it must go out when it would attempt the slightest application.

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

Human beings are more or less formulas. Pun intended. We are not any one thing that is mathematically provable. We are more or less than we are anything. We are more or less kind, or more or less not. More or less selfish, happy, wise, lonely.

I will never listen to ocean waves or view a beautiful sunset in quite the same way again. That is perhaps the greatest gift one can gain by delving into calculus: It is a whole new way of looking at the world, accessible only through the realm of mathematics.

If there is anything that can bind the mind of man to this dreary exile of our earthly home and can reconcile us with our fate so that one can enjoy living,—then it is verily the enjoyment of the mathematical sciences and astronomy.

But twice-two-makes-four is for all that a most insupportable thing. Twice-two-makes-four is, in my humble opinion, nothing but a piece of impudence. Twice-two-makes-four is a farcical, dressed-up fellow who stands across your path with arms akimbo and spits at you.

Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.

For the first time in his life, he decided to focus on his math homework.

Somehow life had become a story problem, and William was horrible at math.

We often hear that mathematics consists mainly of 'proving theorems.' Is a writer's job mainly that of 'writing sentences?

Why do you have such a crappy attitude about math?""I don't. I have a crappy attitude about everything.

Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.

It is the story that matters not just the ending.

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.

This success permits us to hope that after thirty or forty years of observation on the new Planet [Neptune], we may employ it, in its turn, for the discovery of the one following it in its order of distances from the Sun. Thus, at least, we should unhappily soon fall among bodies invisible by reason of their immense distance, but whose orbits might yet be traced in a succession of ages, with the greatest exactness, by the theory of Secular Inequal

Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner, published in the Annalen der Physik in 1905 five papers on entirely different subjects. Three of them were among the greatest in the history of physics. One, very simple, gave the quantum explanation of the photoelectric effect—it was this work for which, sixteen years later, he was awarded the Nobel prize. Another dealt with the phenomenon of Brownian motion, the apparently erratic movement of t

Further, the same Arguments which explode the Notion of Luck, may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design to be, as it were, in Competition with each other, for the production of some sorts of Events, and many calculate what Probability there is, that those Events should be rather be owing to the one than to the other.