Nixon's motto was, if two wrongs don't make a right, try three.
I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because, like Spinoza's God, it won't love us in return.
It will be another million years, at least, before we understand the primes.
All mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.
...it is the greatest achievement of a teacher to enable his students to surpass him.
The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, refuge from the goading urgency of contingent happenings, and the sort of beauty changeless mountains present to senses tried by the present day kaleidoscope of events.
The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede.
He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side.
To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.
But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.
Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof.
Geometry existed before creation.
The merit of painting lies in the exactness of reproduction. Painting is a science and all sciences are based on mathematics. No human inquiry can be a science unless it pursues its path through mathematical exposition and demonstration.
With me, everything turns into mathematics.
I have discovered a truly marvelous proof of this, which however the margin is not large enough to contain.
In the fall of 1972, President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a president used the third derivative to advance his case for reelection.
A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence.
A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to learn something new, I make it my first job to build one.
Now I feel as if I should succeed in doing something in mathematics, although I cannot see why it is so very important. . . The knowledge doesn't make life any sweeter or happier, does it?
If equations are trains threading the landscape of numbers, then no train stops at pi.
It is clear that economics, if it is to be a science at all, must be a mathematical science.
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
Perhaps the greatest paradox of all is that there are paradoxes in mathematics.
Why are numbers beautiful? It’s like asking why is Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.
Questions are creative acts of intelligence.
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