Math Quotes

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.

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.

It is strange a difference comes from a subtraction.

Mathematicians enjoy thinking about the simplest possible things, and the simplestpossible things are imaginary.

From the age of 13, I was attracted to physics and mathematics. My interest in these subjects derived mostly from popular science books that I read avidly. Early on I was fascinated by theoretical physics and determined to become a theoretical physicist. I had no real idea what that meant, but it seemed incredibly exciting to spend one's life attempting to find the secrets of the universe by using one's mind.

Division isn't just a math's problem.It's also humanities!

Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.

Just as I had long suspected, a person didn't really need math for anything anyway. Maybe some people did. Some limited people.

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

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than their, it is because they are made with ideas.

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.

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

If I wanted you to understand, I would have explained it better ~ Aarush Kashyap

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.

No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence--a duty and a duty alone--and no hint of magic or beauty of the subject might be allowed to come through.

Mom actually said that?" Cassie's face shown with happiness. "She always hated my math!""Nah," Martin said. "She was just being that way for you. She thought it was what you needed to hear. If parents told us what they really think about stuff, we could figure them out like regular people.

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.

One might suppose that reality must be held to at all costs. However, though that may be the moral thing to do, it is not necessarily the most useful thing to do. The Greeks themselves chose the ideal over the real in their geometry and demonstrated very well that far more could be achieved by consideration of abstract line and form than by a study of the real lines and forms of the world; the greater understanding achieved through abstraction could be applied most usefully to the very reality that was ignored in the process of gaining knowledge.

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.

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.

Conventional wisdom nor scientific, mathematical prove of randomness in life could do nothing to deter human's curiosity for the unknown, however small the chance of a positive outcome maybe.

Je me rends parfaitement compte du desagreable effet que produit sur la majorite de l'humanité, tout ce qui se rapporte, même au plus faible dègré, á des calculs ou raisonnements mathematiques.I am well aware of the disagreeable effect produced on the majority of humanity, by whatever relates, even at the slightest degree to calculations or mathematical reasonings.

Here is an equation worth remembering: Five dollars earned minus seven dollars spent = Unhappy Life." (Life Hacks, p.51)

[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, leaving him abstractedly staring at his work, still with chalk and eraser in his hands, entirely oblivious of his departing class.

Making mathematics accessible to the educated layman, while keeping high scientific standards, has always been considered a treacherous navigation between the Scylla of professional contempt and the Charybdis of public misunderstanding.

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

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

Business, to be successful, must be based on science, for demand and supply are matters of mathematics, not guesswork.

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.

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 foreplay. Mathematical functions stroked their backs; theorems sent warm breath into their ears.

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?

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.

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.

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.

If I were king, I would redress an abuse which cuts back, as it were, one half of human kind. I would have women participate in all human rights, especially those of the mind.

[About Pierre de Fermat] It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For my part, however, I have always been taught to take a broad overview of things, in order to be able to deduce from them general rules, which might be applicable elsewhere.

The consequence model, the logical one, the amoral one, the one which refuses any divine intervention, is a problem really for just the (hypothetical) logician. You see, towards God I would rather be grateful for Heaven (which I do not deserve) than angry about Hell (which I do deserve). By this the logician within must choose either atheism or theism, but he cannot possibly through good reason choose anti-theism. For his friend in this case is not at all mathematical law: the law in that 'this equation, this path will consequently direct me to a specific point'; over the alternative and the one he denies, 'God will send me wherever and do it strictly for his own sovereign amusement.' The consequence model, the former, seeks the absence of God, which orders he cannot save one from one's inevitable consequences; hence the angry anti-theist within, 'the logical one', the one who wants to be master of his own fate, can only contradict himself - I do not think it wise to be angry at math.

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.

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 organising seminars among themselves. It was a stimulating environment but not an easy one for a student like me, who had come with only a spotty background. Fortunately I had an excellent group of classmates, and in retrospect I think the "Princeton method" of that period was quite effective.

Education makes your maths better, not necessarily your manners.

Math has proven the existence of God, because it is absolute and without contradiction; but the devil must exist as well, because we cannot prove it