So any theorem that a human can prove is, ipso facto, utterly trivial.  -- Doron Zeilberger, Opinion 36

A complex system that works is invariably found to have evolved from a simple system that worked. -- John Gall

The infinite is a good approximation of the large finite. -- Laszlo Lovasz

Man muss immer umkehren.  -- CGJ Jacobi

Everybody has plans until they get hit. -- Mike Tyson

Understanding is a poor substitute for convexity. -- NN Taleb, Antifragile

I would rather have today's algorithms on yesterday's computers than vice versa. -- Philippe Toint
  
u"gyeskedhet, nem fog a macska \ egyszerre kint s bent egeret  -- J A, Eszme'let

An economist regarding mathematical research as a product and mathematicians as producers would note that it has a distinctive feature: one's customers are basically the same as one's competitors.

Seeing an astronomer using a telescope to observe a galaxy, no-one will confuse the telescope with the galaxy. Mathematics differs from science in that there is no clear distinction between the tools and the objects of study.

-- David Aldous

I think that it is a relatively good approximation to truth [] that mathematical ideas originate in empirics. [A]s a mathematical discipline travels far from its empirical source it becomes more and more purely aestheticizing, [t]here is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities. [W]henever this stage is reached, the only remedy seems to me to be the rejuvenating return to the source: the re-injection of more or less directly empirical ideas.

-- John von Neumann

Then there is the other secret. There isn't any symbolism. The sea is the sea. The old man is an old man. The boy is a boy and the fish is a fish. The shark are all sharks no better and no worse. 

-- Ernest Hemingway 

In recent decades, many investigators published a great number of mathematical works. Whereas the classics of mathematics regarded the science of mathematics as an objective reflection of reality, many of the new investigators do not share this opinion.

-- Anatoly Karatsuba

 Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap. 
 -- V.I.Arnold
 
The object of mathematical rigour is to sanction and legitimize the conquests of intuition, and there was never any other object for it. 
--Jacques Hadamard

Having impostor syndrome doesn't mean you are not an impostor.
-- Anonymous

I've seen things you people wouldn't believe. Attack ships on fire off the shoulder of Orion. I watched C-beams glitter in the dark near the Tannhauser Gate. All those moments will be lost in time, like tears in rain. Time to die.

-- Batty's monologue in Blade Runner

There are worlds out there where the sky is burning, where the sea's asleep and the rivers dream, people made of smoke and cities made of song. Somewhere there's danger, somewhere there's injustice and somewhere else the tea is getting cold. Come on, Ace, we've got work to do.

-- Dr Who

..Statistical users will be better off if they take note of a two-stage test-of-significance as follows: 
Step 1: Is the difference practically significant? If the answer is NO, don't bother with the next step. 
Step 2: Is the difference statistically significant? 

-- From the book: Sense and Nonsense of Statistical Inference

It's difficult to get a man to understand something when his salary depends on his not understanding it. 

-- Upton Sinclair  

They that can give up essential liberty to purchase a little temporary safety, deserve neither liberty nor safety. 

-- Benjamin Franklin 

Before you can make things better, you have to stop making them worse. 

-- Anonymous

Until you make the unconscious conscious, it will direct your life and you will call it fate. 

-- Carl Jung 

Don't antropomorphise computers, they hate that.

-- Anonymous

There is no such thing as rationality of a belief, there is rationality of action. -- NN Taleb

Of course we have free will. We have no choice! -- C. Hitchens

Madness is rare in individuals -- but in groups, parties, nations, and ages it is the rule. -- Nietzsche

The world as first seen by the child becomes his lifelong standard of excellence, mindless of the fact he is admiring the ruins of his parents. Generation to generation, the natural world decays, the ratchet of perception tightens. Gradually, imperceptibly, big sharks give way to small sharks, small sharks to baitfish, baitfish to jellyfish to slime. On land, the big cats and wolves become feral house cats and coyotes. The wild standard sinks ever lower and becomes ever heavier to raise. Few notice, few care. -- William Stolzenburg, Where the Wild Things Were

The mathematicians then were like mathematicians now, only more so. -- JL Kelley, in [S Krantz: Mathematical Apocrypha]

In the matter of reforming things, as distinct from deforming them, there is one plain and simple principle; a principle which will probably be called a paradox. There exists in such a case a certain institution or law; let us say, for the sake of simplicity, a fence or gate erected across a road. The more modern type of reformer goes gaily up to it and says, "I don't see the use of this; let us clear it away." To which the more intelligent type of reformer will do well to answer: "If you don't see the use of it, I certainly won't let you clear it away. Go away and think. Then, when you can come back and tell me that you do see the use of it, I may allow you to destroy it.
-- GK Chesterton

A billion here, a billion there, pretty soon, you're talking real money. -- Everett Dirksen 

The buck stops with Marcus. -- M. Sugrue, in a lecture on stoicism

All problems in computer science can be solved by another layer of indirection ... except for the problem of too many layers of indirection. -- D Wheeler

Technology [is] an improved means to an unimproved end. -- Thoreau

...the eager pursuit of religious controversy afforded a new occupation to the busy idleness of the metropolis; and we may credit the assertion of an intelligent observer, who describes, with some pleasantry, the effects of their loquacious zeal. "This city," says he, "is full of mechanics and slaves, who are all of them profound theologians; and preach in the shops, and in the streets. If you desire a man to change a piece of silver, he informs you, wherein the Son differs from the Father; if you ask the price of a loaf, you are told by way of reply, that the Son is inferior to the Father; and if you inquire, whether the bath is ready, the answer is, that the Son was made out of nothing."  -- E. Gibbon: .. Decline and Fall of the Roman Empire, Vol. 3.

The ability to play chess is the sign of a gentleman. The ability to play chess well is the sign of a wasted life. -- P Morphy

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk. -- John von Neumann

When art critics get together they talk about Form and Structure and Meaning. When artists get together they talk about where you can buy cheap turpentine. -- P Picasso

Teach a man to fish, and you have a job for a day. Give a man a fish, and you have a job for life. -- Anonymous (?)

I shall not commit the fashionable stupidity of regarding everything I cannot explain as a fraud. -- CG Jung

Communication usually fails, except by accident. -- Wiio

Each karass has two wampeters at any given time, one waxing and one waning. -- Vonnegut: Cat's craddle

If it moves, tax it. If it keeps moving, regulate it. And if it stops moving, subsidize it. -- R Reagan

Q: Who's the greatest father-and-son team in the history of Mathematics?
A: Gauss and his (barrelmaker) father.
    -- from [S Krantz: Mathematical Apocrypha]
    
Wagner's music is much better than it sounds. -- M Twain

I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times. -- Bruce Lee

Before I studied the art, a punch was just a punch, a kick just a kick. After I learned the art, a punch was no longer a punch, a kick no longer a kick. Now that I've understood the art, a punch is just a punch, a kick just a kick. -- Bruce Lee

No wireless. Less space than a nomad. Lame. -- CmdrTaco on Slashdot, commenting on Apple's release of the iPod. 

You can already build such a system yourself quite trivially by getting an FTP account, mounting it locally with curlftpfs, and then using SVN or CVS on the mounted filesystem. -- BrandonM on Hacker News, commenting on the release of Dropbox.

These ambiguities, redundancies and deficiencies remind us of those which doctor Franz Kuhn attributes to a certain Chinese encyclopedia entitled 'Celestial Emporium of Benevolent Knowledge'. In its remote pages it is written that the animals are divided into (a) belonging to the emperor, (b) embalmed, (c) tame, (d) suckling pigs, (e) sirens, (f) fabulous, (g) stray dogs, (h) included in the present classification, (i) trembling as if mad, (j) innumerable, (k) drawn with a very fine camelhair brush, (l) etcetera, (m) having just broken the flower vase, (n) that from a long distance resemble flies. -- JL Borges

I see only one move ahead, but it is always the correct one. -- attributed to JR Capablanca

There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.
   -- Shakespeare: Hamlet
   
Music with dinner is an insult both to the cook and the violinist. -- Chesterton

The door refused to open. It said, "Five cents, please." He searched his pockets. No more coins; nothing. "I'll pay you tomorrow," he told the door. Again he tried the knob. Again it remained locked tight. "What I pay you," he informed it, "is in the nature of a gratuity; I don't have to pay you." "I think otherwise," the door said. "Look in the purchase contract you signed when you bought this conapt." In his desk drawer he found the contract; since signing it he had found it necessary to refer to the document many times. Sure enough; payment to his door for opening and shutting constituted a mandatory fee. Not a tip. "You discover I'm right," the door said. It sounded smug. From the drawer beside the sink Joe Chip got a stainless steel knife; with it he began systematically to unscrew the bolt assembly of his apt's money-gulping door. "I'll sue you," the door said as the first screw fell out. Joe Chip said, "I've never been sued by a door. But I guess I can live through it." -- Philip K. Dick, Ubik 

But that is not my point. I have no point. -- Dave Barry

It is not a case of choosing those [faces] that, to the best of one's judgment, are really the prettiest, nor even those that average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees. -- JM Keynes on the stock market (1936)

If a lion could talk, we could not understand him.  -- L Wittgenstein

Reinventing the flat tire...  -- Alan Kay

That works very well in practice, but how does it work in theory?  -- attributed to various theoreticians

No one can suppose that you can't research for six months without having a paper ready by the end. If everyone wrote a paper every six months the amount of trivial literature would swell beyond all bounds. Given time I shall produce a good paper. But if I hurry it will be ill written and unintelligible and unconvincing. -- Frank P Ramsey

Archduke's death removes danger of European conflict. -- headline in the Vancouver Sun, 29 June 1914.

You can wake up someone who is sleeping, but how do you wake up someone who is hell-bent on pretending to sleep? -- anonymous

Publish and/or perish -- anonymous

More is different -- P W Anderson

The golden age of mathematics -- that was not the age of Euclid, it is ours. -- C J Keyser

You must take your opponent into a deep dark forest where 2+2=5, and the path leading out is only wide enough for one. -- Mikhail Tal

If I have seen less far than others, it was because giants were standing on my shoulders. -- Anonymous (paraphrasing Newton)

There is another legacy of the Sixties which is often neglected: tens of thousands of individuals who won the revolution at least in their own lives. They live within the system but they are not part of it. They organize their work and existences by their own rules, and have achieved a personal independence of thought, action and moral choice which does not require social sanction. They are free men and women and their examples might be the most subversive influences extant today.  -- Walt Crowley: Rites of Passage