Quotes About Mathematics

Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.

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.

Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.

Men are constantly attracted and deluded by two opposite charms: the charm of competence which is engendered by mathematics and everything akin to mathematics, and the charm of humble awe, which is engendered by meditation on the human soul and its experiences. Philosophy is characterized by the gentle, if firm, refusal to succumb to either charm.

Mathematics is the queen of science, and arithmetic the queen of mathematics.

Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?

Mathematics and logic have been proved to be one; a fact from which it seems to follow that mathematics may successfully deal with non-quantitative problems in a much broader sense than was suspected to be possible.

Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.

Theology, Mr. Fortune found, is a more accommodating subject than mathematics; its technique of exposition allows greater latitude. For instance when you are gravelled for matter there is always the moral to fall back upon. Comparisons too may be drawn, leading cases cited, types and antetypes analysed and anecdotes introduced. Except for Archimedes mathematics is singularly naked of anecdotes.

Mathematics is ordinarily considered as producing precise and dependable results; but in the stock market the more elaborate and abstruse the mathematics the more uncertain and speculative are the conclusions we draw there from. Whenever calculus is brought in, or higher algebra, you could take it as a warning that the operator was trying to substitute theory for experience, and usually also to give to speculation the deceptive guise of investment.

I'm not the sort of person who does my mathematics writing on paper. I do that at the last stage of the game. I do my mathematics in my head. I sit down for a hard day's work and I write nothing all day. I just think. And I walk up and down because that helps keep me awake, it keeps the blood circulating, and I think and think.

The product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new.

I think math is a hugely creative field, because there are some very well-defined operations that you have to work within. You are, in a sense, straightjacketed by the rules of the mathematics. But within that constrained environment, it's up to you what you do with the symbols.

Strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.

If all of mathematics disappeared, physics would be set back by exactly one week.

To give emphasis only to beauty makes me think of a mathematics that deals with positive numbers only.

The idea here, of course, is, you know, mathematics is the language of science, it's the way that we understand the natural world. And there's definitely been a push to sort of study advanced math and kind of reawaken the love of advanced math.

Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.

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

If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither "number" nor "size", but always form. And among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other and continues to fascinate me, is the structure hidden in mathematical things.

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

Mathematical study and research are very suggestive of mountaineering. Whymper made several efforts before he climbed the Matterhorn in the 1860's and even then it cost the life of four of his party. Now, however, any tourist can be hauled up for a small cost, and perhaps does not appreciate the difficulty of the original ascent. So in mathematics, it may be found hard to realise the great initial difficulty of making a little step which now seems so natural and obvious, and it may not be surprising if such a step has been found and lost again.

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.

Mathematics is the abstract key which turns the lock of the physical universe.

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.

All of mathematics is a tale about groups.

The indispensability argument says (roughly) that if you have ample reason to accept an empirical scientific theory that makes indispensable use of mathematics, and that theory entails that numbers exist, then you have ample reason to accept that numbers exist. The argument affirms the antecedent of this conditional, and concludes that you have ample reason to believe that numbers exist. What is striking about this argument is that it seems to show that the empirical reasons that suffice for accepting a scientific theory also suffice for accepting a metaphysical claim.

It is insufficient to protect ourselves with laws; we need to protect ourselves with mathematics.

Why does mathematics describe nature. That's a deeper question than most.

Modern economics is sick. Economics has increasingly become an intellectual game played for its own sake and not for its practical consequences for understanding the economic world. Economists have converted the subject into a sort of social mathematics in which analytical rigour is everything and practical relevance is nothing.

It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.

And silence. She liked the silence most of all. The silence in which the body, senses, the instincts, are more alert, more powerful, more sensitized, live a more richly perfumed and intoxication life, instead of transmuting into thoughts, words, into exquisite abstractions, mathematics of emotion in place of violent impact, the volcanic eruptions of fever, lust and delight.

It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.

Perfection is crucial in building an aircraft, a bridge, or a high-speed train. The code and mathematics residing just below the surface of the Internet is also this way. Things are either perfectly right or they will not work. So much of the world we work and live in is based upon being correct, being perfect.

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

Why don't we want our children to learn to do mathematics? Is it that we don't trust them, that we think it's too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon. Why not about triangles?

Even when I was studying mathematics, physics, and computer science, it always seemed that the problem of consciousness was about the most interesting problem out there for science to come to grips with.

If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.

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.

Mathematics is not a separate entity. It owes a great deal of its power and its beauty to other disciplines.

Things like the financial markets - a proper grounding in mathematics could help the common man. I believe that if people are more familiar with mathematical concepts... it can help deal with modern life, which is increasingly complex.

Mathematics directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars.

Our future rates of gain will fall far short of those achieved in the past. Berkshire's capital base is now simply too large to allow us to earn truly outsized returns. If you believe otherwise, you should consider a career in sales but avoid one in mathematics.

The truth is that you can divide your heart in all sorts of interesting ways - a little here, a little there, most banked at home, some of it coined out for a flutter. But love cleaves through the mind's mathematics. Love's lengthways splits the heart in two - the heart where you are, the heart where you want to be. How will you heal your heart when love has split it in two?

When I was done with high school, I knew that music was really important to me and I knew I didn't want to be a cellist, but I wasn't really sure if I wanted to be a composer, or think about - I was just interested in the ideas behind music, I was interested in mathematics.

Mathematics is a world created by the mind of men, and mathematicians are people who devote their lives to what seems to me a wonderful kind of play!

I want to get young girls excited in science, tech, engineering mathematics, art, design - and how they come together. We've got this Choose Science campaign. Once women are there, though, we have to retain them. When I look at universities, it's not enough to have role models, we need to have champions. We need to have more women in senior leadership positions. There are issues about work-life balance. Women go to have children and then who keeps the lab running? There are many challenges.

There are few humanities that could surpass in discipline, in beauty, in emotional and aesthetic satisfaction, those humanities which are called mathematics, and the natural sciences.