Quotes About Mathematics

The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities.

Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.

People think that mathematics is complicated. Mathematics is the simple bit, it’s the stuff we CAN understand. It’s cats that are complicated.

The most rewarding part of my work is the "Aha" moment, the excitement of discovery and enjoyment of understanding something new - the feeling of being on top of a hill and having a clear view. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight. I find discussing mathematics with colleagues of different backgrounds one of the most productive ways of making progress.

Philosophically, mathematics is not a part of science. Mathematics studies patterns, science studies nature

When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, "one at least of our nobler impulses can best escape from the dreary exile of the actual world."

In mathematics we find the primitive source of rationality; and to mathematics must the biologists resort for means to carry out their researches.

A Noah's Ark of mathematicians, their lives, loves, hard times, and madnesses, Loving and Hating Mathematics shows our community with all its warts as well as its triumphs. I especially liked the chapter on much-hated school mathematics, 'Almost All Children Left Behind.'

Except in mathematics, the shortest distance between point A and point B is seldom a straight line. I don't believe in mathematics.

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.

I tell you that studying humanities in high school is more important than mathematics - mathematics is too sharp an instrument, no good for kids.

Mathematics is one of the surest ways for a man to feel the power of thought and the magic of the spirit. Mathematics is one of the eternal truths and, as such, raises the spirit to the same level on which we feel the presence of God.

[P]olitical and social and scientific values ... should be correlated in some relation of movement that could be expressed in mathematics, nor did one care in the least that all the world said it could not be done, or that one knew not enough mathematics even to figure a formula beyond the schoolboy s=(1/2)gt2. If Kepler and Newton could take liberties with the sun and moon, an obscure person ... could take liberties with Congress, and venture to multiply its attraction into the square of its time. He had only to find a value, even infinitesimal, for its attraction.

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.

I am ever more intrigued by the correspondence between mathematics and physical facts. The adaptability of mathematics to the description of physical phenomena is uncanny.

The problem is that modern fundamental physics is so far from you and me. The mathematics has become so much more complicated that you need at least 10 years to understand it. Fundamental physics has advanced so far from the understanding of most people that there is really a big disconnect.

Mathematics is written for mathematicians.

That is, you can have nothingness, absolute nothingness for maybe a tiny fraction of a second, if a second can be defined in that arena, but then it falls apart into a something and an anti-something. And that something is then what we call the universe. But can we really understand that or put rigorous mathematics or testable experiments against that? Not yet. So one of the big holy grail of physics is to understand why there is something rather than nothing.

I went to Princeton from Amherst, where I split my interests between mathematics and philosophy.

One can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are methematical figures.

... we should not be disappointed that everyday language does not work any longer at the apex of our little theory. It is natural; like poetry, the very reason for the existence of mathematics is that it expresses thoughts and feelings which we cannot express in mundane everyday language.

This splendid subject [mathematics], queen of all exact sciences, and the ideal and norm of all careful thinking.

Poetry is a form of mathematics, a highly rigorous relationship with words.

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

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.

Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?

My occupation is an open question. I was once an assistant professor of mathematics. Since then, I have spent time living in the woods of Montana.

[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.

In my schooling through high school, I excelled mainly in chemistry, physics and mathematics.

The Advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation.

We have these amazing gifts of music and mathematics and painting and Olympic running. I mean, we're the animal that is best of all the animals at long-distance running. Why? It is quite amazing. Superfluous gifts you don't really need to survive.

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.

Regarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.

As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from other contexts, so as to develop a sense of the structure, not just familiarity with a particular tour through the structure.

You can only hear clearly when you sit quietly, when you give your attention. Nor can you have order if you are not free to watch, if you are not free to listen, if you are not free to be considerate. This problem of freedom and order is one of the most difficult and urgent problems in life. It is a very complex problem. It needs to be thought over much more than mathematics, geography, or history.

Anyone who believes a growth rate in excess of 15% per annum over the long term is attainable should pursue a career in sales, but avoid one in mathematics.

When we cannot use the compass of mathematics or the torch of experience...it is certain we cannot take a single step forward.

Mathematics allows for no hypocrisy and no vagueness.

It may be more important in the mathematics class how you teach than what you teach.

As regards authority I so proceed. Boetius says in the second prologue to his Arithmetic, 'If an inquirer lacks the four parts of mathematics, he has very little ability to discover truth.' And again, 'Without this theory no one can have a correct insight into truth.' And he says also, 'I warn the man who spurns these paths of knowledge that he cannot philosophize correctly.' And Again, 'It is clear that whosoever passes these by, has lost the knowledge of all learning.'

I fly in dreams, I know it is my privilege, I do not recall a single situation in dreams when I was unable to fly. To execute every sort of curve and angle with a light impulse, a flying mathematics - that is so distinct a happiness that it has permanently suffused my basic sense of happiness.

As an exercise of the reasoning faculties, pure mathematics is an admirable exercise, because it consists of reasoning alone and does not encumber the student with any exercise of judgment.

The language that nature speaks is the same language that we invented for mathematics. That's just an amazing piece of luck, which we don't understand.

How happy is the lot of the mathematician! He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve. No cashier writes a letter to the press complaining about the incomprehensibility of Modern Mathematics and comparing it unfavorably with the good old days when mathematicians were content to paper irregularly shaped rooms and fill bathtubs without closing the waste pipe.

The advance and perfecting of mathematics are closely joined to the prosperity of the nation.

No price is too high to pay to try to make the financial system go on a little bit longer. But ultimately it can't be saved, because of the mathematics that are involved.