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

No plan of operations extends with any certainty beyond the first contact with the main hostile force. -- Moltke the Elder

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.

The war situation has developed not necessarily to Japan's advantage. -- Emperor Hirohito in the radio broadcast announcing Japan's surrender in 1945

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)

You can fool some of the people all the time, and those are the ones you want to concentrate on. -- Anonymous (paraphrasing Lincoln) 

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


If you want to be read in the future, make sure you would have been read in the past. -- NN Taleb

It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of light, it was the season of darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way -- in short, the period was so far like the present period that some of its noisiest authorities insisted on its being received, for good or for evil, in the superlative degree of comparison only. -- Dickens: A Tale of Two Cities

A barometric low hung over the Atlantic. It moved eastward toward a high-pressure area over Russia without as yet showing any inclination to bypass this high in a northerly direction. The isotherms and isotheres were functioning as they should. The air temperature was appropriate relative to the annual mean temperature and to the aperiodic monthly fluctuations of the temperature. The rising and setting of the sun, the moon, the phases of the moon, of Venus, of the rings of Saturn, and many other significant phenomena were all in accordance with the forecasts in the astronomical yearbooks. The water vapor in the air was at its maximal state of tension, while the humidity was minimal. In a word that characterizes the facts fairly accurately, even if it is a bit old-fashioned: It was a fine day in August 1913. -- Musil: The Man Without Qualities

Sphinx of black quartz, judge my vow. (an almost perfect pangram)

Two roads diverged in a wood, and I,
I took the one less traveled by, 
And that has made all the difference. -- Robert Frost

These are the good old days. (anonymous)

The old man the boat. (garden-path sentence)

If I have made myself clear, you must have misunderstood me. -- Alan Greenspan

It says here in this history book that luckily, the good guys have won every single war. What are the odds? -- Norm MacDonald

Any technology distinguishable from magic is insufficiently advanced. -- contrapositive of Arthur C Clarke's law. 

The only thing we have to fear is fear itself -- FDR

There are only two ways of telling the complete truth--anonymously and posthumously -- T Sowell

Turning and turning in the widening gyre 
The falcon cannot hear the falconer; 
Things fall apart; the centre cannot hold; 
Mere anarchy is loosed upon the world. -- Yeats

When one teaches, two learn. -- Robert Heinlein

I don't see any god up here. -- Y. Gagarin 

The first gulp from the glass of natural sciences will turn you into an atheist, but at the bottom of the glass God is waiting for you. -- W. Heisenberg

If only there were evil people somewhere insidiously committing evil deeds, and it were necessary only to separate them from the rest of us and destroy them. But the line dividing good and evil cuts through the heart of every human being. -- Solzhenitsyn

Censorship is telling a man he can't have a steak just because a baby can't chew it. -- Mark Twain 

No group of professionals meets except to conspire against the public at large. -- Mark Twain

When I was a boy of 14, my father was so ignorant I could hardly stand to have the old man around. But when I got to be 21, I was astonished at how much the old man had learned in seven years -- Mark Twain

The purpose of a system is what it does. -- S Beer

I took a speed-reading course and read War and Peace in twenty minutes. It involves Russia. -- Woody Allen

Yet it is not these gifts, nor the most determined ambition combined with irresistible will-power, that enables one to surmount the "invisible yet formidable boundaries" that encircle our universe. Only innocence can surmount them, which mere knowledge doesn't even take into account, in those moments when we find ourselves able to listen to things, totally and intensely absorbed in child's play. -- Grothendieck

Algebra is to the geometer what you might call the "Faustian Offer". [..] The devil says: "I will give you this powerful machine, and it will answer any question you like. All you need to do is give me your soul; give up geometry and you will have this marvellous machine." Of course we like to have things both ways: we would probably cheat on the devil, pretend we are selling our soul, and not give it away. 
Nevertheless the danger to our soul is there, because when you pass over into algebraic calculation, essentially you stop thinking; you stop thinking geometrically, you stop thinking about the meaning. -- M Atiyah
 
After all, all he did was string together a lot of old, well-known quotations.	-- HL Mencken on Shakespeare

The biggest lesson that can be read from 70 years of AI research is that general methods that leverage computation are ultimately the most effective, and by a large margin. -- R Sutton: The Bitter Lesson

We made the wrong mistake. -- Yogi Berra

There are four sorts of countries: developed, underdeveloped, Japan, and Argentina. -- S Kuznets

Silicate chemistry is second nature to us geochemists, so it's easy to forget that the average person probably only knows the formulas for olivine and one or two feldspars, and of course quartz. -- xkcd

I strongly feel that this is an insult to life itself. -- H. Miyazaki after being shown AI-generated art in 2016. 

Git gets easier once you understand branches are homeomorphic endofunctors mapping submanifolds of a Hilbert space. -- I. Wolkerstorfer

There's never enough time to do it right, but somehow, there's always enough time to do it over. There is never a single right solution. There are always multiple wrong ones, though. In nature, the optimum is almost always in the middle somewhere. Distrust assertions that the optimum is at an extreme point. (Akin's Laws)

A well written paper has clear components: skeleton, muscles, etc. The skeleton is an acyclic digraph of basic definitions and statements, with cross-references. The meat consists of proofs (muscles) each separately verifiable by competent graduate students having to read no other parts but statements and definitions cited. Intuitive comments, examples and other comfort items are fat and skin: a lack or excess will not make the paper pretty. Proper scholarly references constitute clothing, no paper should ever appear in public without! Trains of thought which led to the discovery are blood and guts: keep them hidden. Metaphors for other vital parts, like open problems, I skip out of modesty. -- L Levin

Measure with a micrometer, mark with a chalk, cut with an axe. -- Anonymous

In an information-rich world, the wealth of information means a dearth of something else: a scarcity of whatever it is that information consumes. What information consumes is rather obvious: it consumes the attention of its recipients. Hence a wealth of information creates a poverty of attention. -- H. Simon, 1971

There's no sense in being precise when you don't even know what you're talking about. -- J v Neumann 

The world of finance hails the invention of the wheel over and over again, often in a slightly more unstable version. All financial innovation involves in one form or another, the creation of debt secured in greater or lesser adequacy by real assets. -- JK Galbraith

This is an unfair thing about war: victory is claimed by all, failure to one alone. -- Tacitus

When a tenant marries the landlord, the national income shrinks. -- Anonymous

Anything that can't go on forever eventually stops. -- H. Stein 

Profits are on paper, losses are in cash. -- Bombieri's Law of Finance

In measure theory you have to say "almost everywhere" almost everywhere.
-- K Friedrichs

And so, these are my five ideas about technological change. First, that we always pay a price for technology; the greater the technology, the greater the price. Second, that there are always winners and losers, and that the winners always try to persuade the losers that they are really winners. Third, that there is embedded in every great technology an epistemological, political or social prejudice. Sometimes that bias is greatly to our advantage. Sometimes it is not. The printing press annihilated the oral tradition; telegraphy annihilated space; television has humiliated the word; the computer, perhaps, will degrade community life. And so on. Fourth, technological change is not additive; it is ecological, which means, it changes everything [..] and fifth, technology tends to become mythic; that is, perceived as part of the natural order of things, and therefore tends to control more of our lives than is good for us. -- Neil Postman

Thank you for sending me a copy of your book - I'll waste no time reading it. -- M Hadas 

It is sometimes of great use for a man to pretend he is deceiv'd; for when we let a subtile fellow see that we are sensible of his tricks, it gives him occasion to be more refin'd. -- A Boyer, 1702 

Blasphemy is a victimless crime. -- Anonymous (T-Shirt)  

It's taken me all my life to learn what not to play. -- Dizzy Gilespie

What this country needs is a really good five-cent cigar. -- TR Marshall, US vice-president

After all, the whole purpose of science is not technology -- God knows we have gadgets enough already. -- ET Bell (1937)

They misunderestimated me. -- GW Bush

How did you go bankrupt? Two ways. Gradually, then suddenly.  -- Hemingway