Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.
An exquisitely complex shape now known as the Mandlebrot set has been called the most complex object in mathematics.
To give emphasis only to beauty makes me think of a mathematics that deals with positive numbers only.
Every child should try everything: sport, music, art, mathematics; they can do it all. Copying and competition are now seen as twin evils, but they are both useful tools.
Mathematics is like music. Neither needs to be useful. It is enough that each gives delight to those who seek delight from it.
Mathematics and art are quite different. We could not publish so many papers that used, repeatedly, the same idea and still command the respect of our colleagues.
Indeed art is fundamental : to science, mathematics and to language. Unfortunately theorists, educators, parents and administrators have not fully understood its importance, relegating it to a secondary role, or that of an add on.
When we cannot use the compass of mathematics or the torch of experience...it is certain we cannot take a single step forward.
Philip Kitcher thinks that mathematics is surprisingly like empirical science. Few mathematicians would agree; philosophers too, from Socrates on, have held the opposite opinion.
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.
Whoever despises the high wisdom of mathematics nourishes himself on delusion and will never still the sophistic sciences whose only product is an eternal uproar.
I read one or two other books which gave me a background in mathematics other than logic.
The laws of Nature are written in the language of mathematics...the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.
Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.
Ada came from Lwów. She was a very good looking girl who was studying mathematics at the University of Geneva. For a few years I had an off-and-on romance with her.
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.
I'm obviously attuned to pick up mathematics whenever I can see it. But in Mozart there is a lot of conscious use of mathematical symbolism and numbers in order to try and give messages.
Emotions are far harder things to understand than algebra and geometry, yet we spend hours in elucidating mathematics and expect such a problem as that of human relationships to solve itself.
Mathematics is one of the most basic -- and most ancient -- types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists.
Mathematics, even in its present and most abstract state, is not detached from life. It is just the ideal handling of the problems of life.
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.
This branch of mathematics [Probability] is the only one, I believe, in which good writers frequently get results which are entirely erroneous.
Mathematics has beauty and romance. It's not a boring place to be, the mathematical world. It's an extraordinary place; it's worth spending time there.
Cryptography shifts the balance of power from those with a monopoly on violence to those who comprehend mathematics and security design.
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.
I still don't like authority exercised without reason. But they laugh at you at Cambridge if you say that sort of thing. For them, the law is a system of rules not that different from mathematics.
We do not know whether there are extra dimensions or multiverse. Let's go forward with the possible ideas that come out of the mathematics. It's hard for us to imagine a universe that would have no time at all.
Aerodynamics is mathematics for those who haven't learned to do calculus. In my case, too, for one who hasn't learned to add or multiply, at least the first time.
If you come from mathematics, as I do, you realize that there are many problems, even classical problems, which cannot be solved by computation alone.
I'm convinced that imagination is at the heart of everything we do - in art, science, even astrophysics and higher mathematics. Imagination leads us to ask, "What if?"
There is an astonishing imagination, even in the science of mathematics. ... We repeat, there was far more imagination in the head of Archimedes than in that of Homer.
Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.
If men had known how to permeate the soul with mathematics in the right way in the arithmetic lessons during these past years, we should not now have Bolshevism in Eastern Europe.
The progress of mathematics can be viewed as progress from the infinite to the finite.
But I quite like the way you can talk about science without necessarily using mathematics, but using metaphors instead.
The temptation to use mathematics is irresistible for economists. It appears to convey the appropriate air of scientific authority and precision to economists' musings.
Math education has changed over the years. In the 19th century, they taught spherical trigonometry because one of the biggest applications of mathematics was navigating the ocean. This is no longer so relevant.
If you think about basic science or coming up with new theories of mathematics, these are not the kinds of things which are necessarily a well-defined market to pay people.
I could never have gone far in any science because on the path of every science the lion Mathematics lies in wait for you.
Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.
I was graduated in 1940 with a degree of Bachelor of Science in Social Science but a major in Mathematics, a paradoxical combination that was prognostic of my future interests.
On the basis of my historical experience, I fully believe that mathematics of the 25th century will be as different from that of today as the latter is from that of the 16th century.
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!
Examples ... which might be multiplied ad libitum, show how difficult it often is for an experimenter to interpret his results without the aid of mathematics.
I had changed from being a mathematician to a practicing scientist. I was increasingly embarassed that I could no longer follow some of the more modern branches of pure mathematics.
As a graduate of the Zsa Zsa Gabor School of Creative mathematics, I honestly do not know how old I am.
Real mathematics must be justified as art if it can be justified at all.
Any impatient student of mathematics or science or engineering who is irked by having algebraic symbolism thrust upon him should try to get along without it for a week.
The basic science is not physics or mathematics but biology -- the study of life. We must learn to think both logically and bio-logically.
I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total.
The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern.
If you go through the list of things that are not possible you're left with a very finite amount of possibilities. The fancy name for this is constraint theory. It's a nonquantitative model, but it's a field of mathematics.
I am not a mathematician, but I was aware that for centuries, mathematics was considered the queen of the sciences because it claimed certainty. It was grounded on some fundamental certainties - axioms - that led to others.
Atheism is the opium of the mathematicians. Atheism is the religion of Mathematics.
a straight line is the shortest possible line between any two points - an axiom equally true in morals as in mathematics.
I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium, and symptoms of schizophrenia.
We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"
I tell them that if they will occupy themselves with the study of mathematics they will find in it the best remedy against the lusts of the flesh.
I was a mathematician by nature, and still am - I just knew I didn't want to be a mathematician. So I decided not to take any mathematics courses.
To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology.
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