Logic is invincible, because in order to combat logic it is necessary to use logic.
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
Though this be madness, yet there is method in't.
Statistics: the mathematical theory of ignorance.
Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.
Pure mathematics, may it never be of any use to anyone.
A painting is more than the sum of its parts
It would be better for the true physics if there were no mathematicians on earth.
Mathematics is the science which uses easy words for hard ideas.
A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence.
God does not care about our mathematical difficulties. He integrates empirically.
When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.
Mathematics is like draughts in being suitable for the young, not too difficult, amusing, and without peril to the state.
Six is a number perfect in itself, and not because God created the world in six days; rather the contrary is true. God created the world in six days because this number is perfect, and it would remain perfect, even if the work of the six days did not exist.
Poets do not go mad; but chess-players do. Mathematicians go mad, and cashiers; but creative artists very seldom. I am not, as will be seen, in any sense attacking logic: I only say that this danger does lie in logic, not in imagination.
The real danger is not that computers will begin to think like men, but that men will begin to think like computers.
The whole is more than the sum of its parts.
Errors using inadequate data are much less than those using no data at all.
I had a feeling once about mathematics - that I saw it all... but it was after dinner and I let it go.
I know that two and two make four - and should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 and 2 into five it would give me much greater pleasure.
Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic.
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
There are three kinds of people: those who can count, and those who cannot.
Perfect numbers like perfect men are very rare.
Perhaps the most surprising thing about mathematics is that it is so surprising.
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