I enjoy a well-phrased idea as much as the next nerd. Here are some of my favourite quotations, loosely categorised by topic. Currently these are: mathematics, science and computer science. I've tried to link to the source of the quote whenever I've been able to find it.
Mathematical wisdom, if not forgotten, lives as an invariant of all its (re)presentations in a permanently self–renewing discourse.
– Yuri Manin (source)
Mathematics is the art of giving the same name to different things.
— Jules Henri Poincare (cf. Poetry is the art of giving different names to the same thing)
A mathematician who is not also something of a poet will never be a complete mathematician.
— Karl Weierstrass
Fundamental progress has to do with the reinterpretation of basic ideas.
— Alfred North Whitehead
In mathematics you don't understand things, you just get used to them.
— John von Neumann
Suppose someone says that X is true. Here is a simple test to see if this statement has any meaning. Think of not X: if this statement is obviously false or is obviously true, then X is meaningless.
— Rich Lipton (source)
The proofs have been carried out to an excruciating level of detail … The reader may feel that we have given long, tedious proofs of obvious assertions. However, what he has not seen are the many equally obvious assertions that we discovered to be wrong only by trying to write similarly long, tedious proofs.
— Leslie Lamport (source, via John D. Cook)
Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
— Nikola Tesla
The important thing is not to stop questioning. Curiosity has its own reason for existing. One cannot help but be in awe when he contemplates the mysteries of eternity, of life, of the marvelous structure of reality. It is enough if one tries merely to comprehend a little of this mystery every day. Never lose a holy curiosity.
— Albert Einstein
I have no special talents. I am only passionately curious.
— Albert Einstein
Any technology not distinguishable from magic is insufficiently advanced.
— Barry Gehm's Corollary to Clarke's Third Law
If you ‘understand’ something in only one way, then you scarcely understand it at all—because when you get stuck, you’ll have nowhere to go. But if you represent something in several ways, then when you get frustrated enough, you can switch among different points of view, until you find one that works for you!
— Marvin Minsky, [The Emotion Machine](http://www.amazon.com/Emotion-Machine-Commonsense-Artificial-Intelligence/dp/0743276647/ref=edoe_p/)_
It is the business of the future to be dangerous; and it amongst the merits of science that it equips the future for its duties
— Alfred North Whitehead (via DJ Spooky's [Riddim Warfare](http://en.wikipedia.org/wiki/RiddimWarfare)_)
The movement of historical, and philosophical, criticism of detached questions, which on the whole has dominated the last two centuries, has done its work, and requires to be supplemented by a more sustained effort of constructive thought.
— Alfred North Whitehead (in [Process and Reality](http://en.wikipedia.org/wiki/Processand_Reality)_)
The first time you do something, it's Science. The second , it's Engineering. The third time, it's Technology. I'm a scientist -- once I do something I want to do something else.
— Clifford Stoll (in his TED talk)
Seen from this perspective, the technology for coping with large-scale computer systems merges with the technology for building new computer languages, and computer science itself becomes no more (and no less) than the discipline of constructing appropriate descriptive languages.
— Abelson and Sussman ([Structure and Interpretation of Computer Programs](http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-25.html#%chap_4)_)
The purpose of computation is insight, not numbers.
— Richard Hamming
Computing is full of second-rate physicists.
— Richard Hamming
People fear computers becoming smarter and taking over the world, but currently computers are not very smart and they already have taken over the world!
— Pedro Domingos (via Luis von Ahn's post Some Tough Questions)