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
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 (1935-1945) 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