Lights All Askew in the Heavens. Men of Science More or Less Agog Over Results of Eclipse Observations.
New York Times headline, Nov. 10, 1919
Cogito Ergo Sum.
Rene Descartes
Why is this a good idea?
Bill Ralph
To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.
Pierre de Fermat (1601?-1665), In the margin of his copy of Diophantus' Arithmetica
God does arithmetic.
Karl Friedrich Gauss (1777-1855)
Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house.
Heinlein, Robert A. in Time Enough for Love.
"The best thing for being sad," replied Merlin, beginning to puff and blow, "is to learn something. That's the only thing that never fails. You may grow old and trembling in your anatomies, you may lie awake at night listening to the disorder of your veins, you may miss your only love, you may see the world about you devastated by evil lunatics, or know your honour trampled in the sewers of baser minds. There is only one thing for it then -- to learn. Learn why the world wags and what wags it. That is the only thing which the mind can never exhaust, never alienate, never be tortured by, never fear or distrust, and never dream of regretting. Learning is the only thing for you. Look what a lot of things there are to learn."
T.H. White, in The Once and Future King.
Neither in the subjective nor in the objective world can we find a criterion for the reality of the number concept, because the first contains no such concept, and the second contains nothing that is free from the concept. How then can we arrive at a criterion? Not by evidence, for the dice of evidence are loaded. Not by logic, for logic has no existence independent of mathematics: it is only one phase of this multiplied necessity that we call mathematics. How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.
Dantzig
Out of nothing I have created a strange new universe.
Bolyai, Janos (1802 - 1860)
The age of chivalry is gone. That of sophisters, economists and calculators has succeeded.
Edmund Burke, in Reflections on the Revolution in France.
Things should be made as simple as possible, but no simpler.
I don't believe in mathematics.
Imagination is more important than knowledge.
The most beautiful thing we can experience is the mysterious. It is the source of all true art and science.
Common sense is the collection of prejudices acquired by age eighteen.
God does not care about our mathematical difficulties. He integrates empirically.
How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?
Nature hides her secrets because of her essential loftiness, but not by means of ruse.
Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.
Do not worry about your difficulties in mathematics, I assure you that mine are greater.
The truth of a theory is in your mind, not in your eyes.
Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone.
Science without religion is lame; religion without science is blind.
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.
The City of God.
The good Christian should beware of mathematicians, and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.
DeGenesi ad Litteram, Book II, xviii, 37 [Note: mathematician = astrologer]
If I am given a formula, and I am ignorant of its meaning, it cannot teach me anything, but if I already know it what does the formula teach me?
De Magistro ch X, 23.
Can you do addition? the White Queen asked. What's one and one and one and one and one and one and one and one and one and one? I don't know, said Alice. I lost count.
in Through the Looking Glass.
When I use a word, Humpty Dumpty said, in a rather scornful tone, it means just what I choose it to mean - neither more nor less. The question is, said Alice, whether you can make words mean so many different things. The question is, said Humpty Dumpty, which is to be master - that's all.
in Through the Looking Glass.
Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.
The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.
in A Mathematician's Apology (1941)
Detection is, or ought to be, an exact sciences and should be treated in the same cold and unemotional manner. You have attempted to tinge it with romanticism, which produces much the same effect as if you worked a love story or an elopement into the fifth proposition of Euclid.
in The Sign of Four.
When you have eliminated the impossible, what ever remains, however improbable must be the truth.
in The Sign of Four.
From a drop of water a logician could predict an Atlantic or a Niagara.
in A study in Scarlet (1929).
For thy sweet love remembr'd
such wealth brings
that then I scorn to change my state with kings.(I forget where it's from)