The important thing to remember about mathematics is not to be frightened
Sometimes a good idea comes to you when you are not looking for it. Through an improbable combination of coincidence, naivete and lucky mistakes.
Mathematics-a wonderful science, but it hasn't yet come up with a way to divide one tricycle between three small boys.
The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics.
Many who have never had an opportunity of knowing any more about mathematics confound it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.
Pure mathematics is on the whole distinctly more useful than applied... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.
God exists since mathematics is consistent, and the Devil exists since we cannot prove it.
Mathematics is the purest of the arts, as well as the most misunderstood.
I don't believe in mathematics.
Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the answer.
Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.
One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed.
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
It took the mob only a moment to remove his head; a century will not suffice to reproduce it.
How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasturenothing but years of effort can extract it. You can't hurry the process. Or pass from arithmetic to algebra; you can't shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon.
Young man, in mathematics you don't understand things. You just get used to them.
One merit of mathematics few will deny: it says more in fewer words than any other science. The formula, e^iπ = -1 expressed a world of thought, of truth, of poetry, and of the religious spirit "God eternally geometrizes."
I know that two and two make four - and should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 and 2 into five it would give me much greater pleasure.
I have had my results for a long time: but I do not yet know how I am to arrive at them.
The world is continuous, but the mind is discrete.
In real life, I assure you, there is no such thing as algebra.
You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.
Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.
But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
Mathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and state of present-day mathematics is hardly possible.
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