The very term 'combinatorial methods' has an oxymoronic character.
In order to solve this differential equation you look at it until a solution occurs to you.
It is clear that the chief end of mathematical study must be to make the students think.
It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.
Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity
The Good Lord made all the integers; the rest is man's doing.
The moving power of mathematical invention is not reasoning but imagination.
If only I had the Theorems! Then I should find the proofs easily enough.
We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years.
It should seem that it is easier to square the circle than to get round a mathematician.
As long as algebra is taught in school, there will be prayer in school.
Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.
In one word he told me the secret of success in mathematics: plagiarize; only be sure always to call it . . . research.
Mathematics is concerned with "all possible worlds."
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 remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways."
Mathematics began to seem too much like puzzle solving. Physics is puzzle solving, too, but of puzzles created by nature, not by the mind of man.
Mathematics is the art of giving the same name to different things. [As opposed to the quotation: Poetry is the art of giving different names to the same thing].
Yet what are all such gaieties to me whose thoughts are full of indices and surds?
It is not of the essence of mathematics to be conversant with the ideas of number and quantity.
The purpose of computing is insight, not numbers.
Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.
Nixon's motto was, if two wrongs don't make a right, try three.
Mathematics are well and good but Nature keeps dragging us around by the nose.
A mathematician who is not also something of a poet will never be a complete mathematician.
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