Quotes of All Topics . Occasions . Authors
Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers.
Many of the proofs in mathematics are very long and intricate. Others, though not long, are very ingeniously constructed.
My specific goal is to revolutionize the future of the species. Mathematics is just another way of predicting the future.
The science of mathematics performs more than it promises, but the science of metaphysics promises more than it performs.
Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem.
Mathematics is so much easier than words mathematics makes things clear that words merely muddle and confuse and mess up.
Mathematics is, as it were, a sensuous logic, and relates to philosophy as do the arts, music, and plastic art to poetry.
In mathematics, our freedom lies in the questions we ask — and in how we pursue them — but not in the answers awaiting us.
We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry.
No Victor, you got it backwards, you should evaluate these integrals non-rigorously if you can, and rigorously if you must.
I think the term "Kantian constructivism" as an oxymoron. Kant was a constructivist about mathematics, but not about ethics.
Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
In my family, as in most middle-class Indian families I knew when I was growing up, science and mathematics were held in awe.
Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.
I have to admit that he was not bad at combinatorial analysis - a branch, however, that even then I considered to be dried up.
Mathematics is like music. Neither needs to be useful. It is enough that each gives delight to those who seek delight from it.
Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.
It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.
Over the centuries, monumental upheavals in science have emerged time and again from following the leads set out by mathematics.
The only time a question should be asked is when all other possibilities of finding the answer for yourself have been eliminated.
Mathematicians are a bit like the laconic Vermonter who, when asked if he's lived in the state his whole life, replies, "Not yet."
The pendulum of mathematics swings back and forth towards abstraction and away from it with a timing that remains to be estimated.
A felicitous but unproved conjecture may be of much more consequence for mathematics than the proof of many a respectable theorem.
What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else.
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.
There is no smallest among the small and no largest among the large, but always something still smaller and something still larger.
If everybody who was in the Forbes 400 said they were going to create 10,000 jobs, by my mathematics, that would be 4 million jobs.
... a result once generally accepted by mathematicians is seldom retracted, and then only with great pangs. The Nature of Mathematics
MacPherson told me that my theorem can be viewed as blah blah blah Grothendieck blah blah blah, which makes it much more respectable.
Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.
This attitude [the abstract method in mathematics] can be encapsulated in the following slogan: a mathematical object is what it does.
Physicists are more like avant-garde composers, willing to bend traditional rules... Mathematicians are more like classical composers.
It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed.
As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
James Brown is important because he decorates the clock correctly and he's good with lower mathematics. Don't get me wrong - he's good.
In some parts of life, like mathematics and science, yeah, I was a genius. I would top all the top scores you could ever measure it by.
The economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.
Have you ever observed that we pay much more attention to a wise passage when it is quoted, than when we read it in the original author?
For centuries, everything was taught through music. History was taught through music; language and mathematics were taught through music.
The standard model gives us an accuracy of ten decimal digits, this is an amazing success that has never been achieved before in science.
Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.
All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.
[Adams] supposed that, except musicians, everyone thought Beethoven a bore, as every one except mathematicians thought mathematics a bore.
The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'.
Some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation.
So, naturalists observe, a flea; Hath smaller fleas that on him prey; And these have smaller fleas to bite 'em, And so proceed ad infinitum.
Mathematics was hard, dull work, I thought; geography pleased me more. For my other studies, as well as for dancing, I was quite enthusiastic.