Quotes About Mathematics

Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.

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.

A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful-"important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.

The fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune.

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

What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?

I do not remember having felt, as a boy, any passion for mathematics, and such notions as I may have had of the career of a mathematician were far from noble. I thought of mathematics in terms of examinations and scholarships: I wanted to beat other boys, and this seemed to be the way in which I could do so most decisively.

... the word "theory" ... was originally an Orphic word, which Cornford interprets as "passionate sympathetic contemplation" ... For Pythagoras, the "passionate sympathetic contemplation" was intellectual, and issued in mathematical knowledge ... To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural.

You have this world of mathematics, which is very real and which contains all kinds of wonderful stuff. And then we also have the world of nature, which is real, too. And that, by some miracle, 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.

The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.

I was fortunate to find an extraordinary mathematics and applied mathematics program in Toronto.

For me, rhythm is a type of divine mathematics in a way. No matter where you're from, we can all understand the mathematics of rhythm. I try to apply this mathematical thinking to my playing.

Mathematics is really an art, not a science. You could say science also is an art. So I would say the difference is something you can't really describe - you can only recognize. You hear somebody playing the violin, and it was Fritz Kreisler or it was somebody else, and you can tell the difference. It is so in almost every art. We just don't understand why it is that there are just a few people who are just completely off the scale and the rest of them are just mediocre. And we don't know why. But I say it's certainly true of mathematics.

It seems that every practitioner of physics has had to wonder at some point why mathematics and physics have come to be so closely entwined. Opinions vary on the answer. ..Bertrand Russell acknowledged..'Physics is mathematical not because we know so much about the physical world, but because we know so little.' ..Mathematics may be indispensable to physics, but it obviously does not constitute physics.

Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.

General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly generalized constructions of pure mathematics and the specific theories of the specialized disciplines. Mathematics attempts to organize highly general relationships into a coherent system, a system however which does not have any necessary connections with the "real" world around us. It studies all thinkable relationships abstracted from any concrete situation or body of empirical knowledge.

If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.

Mathematics is the surest way to immortality. If you make a big discovery in mathematics, you will be remembered after everyone else will be forgotten

The research reported on in our book "A=B", has moved a whole active field of mathematics from the province of human thought to the realm of computer-fodder. It is quite exciting to think about what other fields of pure mathematics, hitherto thought to be reserved to human intelligence, might be moved to that realm next. The goal is to put ourselves out of business completely, and the work is well underway.

The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics.

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.

A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?

Mathematics is a language. We want scientists to be able to read it, speak it, and write it. But we are are not training them to be grammarians.

God exists since mathematics is consistent, and the Devil exists since we cannot prove it.

Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.

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

You can not apply mathematics as long as words still becloud reality.

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.

I doubt not, but from self-evident Propositions, by necessary Consequences, as incontestable as those in Mathematics, the measures of right and wrong might be made out.

Mathematics is the art of giving the same name to different things.

Beauty means a lot of different things to a lot of different people. A lot of different ways in which things can be beautiful. But this really has a very specific meaning and which is more along the lines of elegance which is that we say an idea is beautiful or elegant in mathematics or physics if a very simple principle or a very simple idea, or simple set of ideas, turns out to be very powerful and leads to all sort of unexpected structure and unexpected predictions.

The importance of the "New Mathematics" lies mainly in the fact that it has taught us the difference between the disc and the circle.

I have long admired Ron Whitehead. He is crazy as nine loons, and his poetry is a dazzling mix of folk wisdom and pure mathematics

But I simply can't stand a view limited to this earth, I feel life is so small unless it has windows into other worlds...I like mathematics largely because it is not human.

In high school I was good at math and everybody wanted me to do something with that - mathematics or engineering - which was a nightmare scenario for me. Meeting other artists and going to punk rock shows at that age, there was a feeling of freedom and community that I wanted to partake in.

My brain doesn't work very well, in terms of mathematics. I'm not one of those people who can just spout off numbers for things, if numbers are thrown at me.

If mathematics is to be understood widely, we need to emphasise its elegance and its applications. Sometimes it seems that universities want to emphasise how difficult it is!

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience

I merely say that all reading for pleasure is escape, whether it be Greek, mathematics, astronomy, Benedetto Croce, or The Diary of the Forgotten Man. To say otherwise is to be an intellectual snob, and a juvenile at the art of living.

I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his precious time.

One thing that definitely did calculate properly for me was the mathematics that makes sense every day, no matter how I look at it, I can't get around it. I try to get around it, I keep trying to find one plus one is not two, somehow. I can't. People can talk about string theory, parallel realities, different dimensions, it's still one plus one is two, baby.

Cryptography shifts the balance of power from those with a monopoly on violence to those who comprehend mathematics and security design.

Each generation has its few great mathematicians, and mathematics would not even notice the absence of the others. They are useful as teachers, and their research harms no one, but it is of no importance at all. A mathematician is great or he is nothing.

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

Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs.

[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.

The science of mathematics performs more than it promises, but the science of metaphysics promises more than it performs.