The moving power of mathematical invention is not reasoning but imagination.
The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede.
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.
There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.
Medicine makes people ill, mathematics make them sad and theology makes them sinful.
There are three kinds of lies: lies, damned lies, and statistics.
Beauty in mathematics is seeing the truth without effort.
An individual understands a concept, skill, theory, or domain of knowledge to the extent that he or she can apply it appropriately in a new situation.
Mathematics may be compared to a mill of exquisite workmanship, which grinds your stuff to any degree of fineness.
A mathematician is a device for turning coffee into theorems.
Mathematics is the art of giving the same name to different things.
God created everything by number, weight and measure.
Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven't. You get the feeling that the result you have discovered is forever, because it's concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don't get a feeling of having done an honest day's work. Don't get the wrong idea - combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.
Mathematics is the only good metaphysics.
Music is the pleasure the human mind experiences from counting without being aware that it is counting.
The purpose of computing is insight, not numbers.
Small deeds done are better than great deeds planned.
The laws of nature are but the mathematical thoughts of God.
Mathematics is the gate and key to science.
But mathematics is the sister, as well as the servant, of the arts and is touched with the same madness and genius.
There's no reason to stereotype yourself. Doing math is like going to the gym - it's a workout for your brain and it makes you smarter.
The shortest path between two truths in the real domain passes through the complex domain.
Standard mathematics has recently been rendered obsolete by the discovery that for years we have been writing the numeral five backward. This has led to reevaluation of counting as a method of getting from one to ten. Students are taught advanced concepts of Boolean algebra, and formerly unsolvable equations are dealt with by threats of reprisals.
Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.
God exists since mathematics is consistent, and the Devil exists since we cannot prove it.
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