Take from all things their number and all shall perish.
Isidore of Seville, ca 600
The best material model of a cat is another, or preferably the same, cat.
A. Rosenbluth, Philosophy of Science, 1945
Some of the men stood talking in this room, and at the right of the door a little knot had formed round a small table, the center of which was the mathematics student, who was eagerly talking. He had made the assertion that one could draw through a given point more than one parallel to a straight line; Frau Hagenström had cried out that this was impossible, and he had gone on to prove it so conclusively that his hearers were constrained to behave as though they understood.
Thomas Mann (1875-1955), Little Herr Friedemann
When you have eliminated the impossible, what ever remains, however improbable, must be the truth.
Sir Arthur Conan Doyle (1859-1930), The Sign of Four
A mathematician is a machine for turning coffee into theorems.
When asked what it was like to set about proving something, the mathematician likened proving a theorem to seeing the peak of a mountain and trying to climb to the top. One establishes a base camp and begins scaling the mountain's sheer face, encountering obstacles at every turn, often retracing one's steps and struggling every foot of the journey. Finally when the top is reached, one stands examining the peak, taking in the view of the surrounding countryside and then noting the automobile road up the other side!
Robert J. Kleinhenz
"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."
Lewis Carrol, Through the Looking Glass
It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again... I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.
Karl Friedrich Gauss (1777-1855), Letter to Bolyai
It is here [in mathematics] that the artist has the fullest scope of his imagination.
Havelock Ellis, The Dance of Life
There are many questions which fools can ask that wise men cannot answer.
George Polyá, in H. Eves Return to Mathematical Circles
The real danger is not that computers will begin to think like men, but that men will begin to think like computers.
Sydney Harris, in H. Eves Return to Mathematical Circles
All great theorems were discovered after midnight.
Adrian Mathesis, in H. Eves Return to Mathematical Circles
The infinite! No other question has ever moved so profoundly the spirit of man.
David Hilbert, in J. R. Newman The World of Mathematics
A habit of basing convictions upon evidence, and of giving to them only that degree or certainty which the evidence warrants, would, if it became general, cure most of the ills from which the world suffers.
Bertrand Russell, in G. Simmons Calculus Gems
If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things.
René Descartes (1596-1650), Discours de la Méthode
God made the integers, all else is the work of man.
Leopold Kronecker (1823 - 1891), Jahresberichte der Deutschen Mathematiker Vereinigung
Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
Leonhard Euler (1707-1783), in G. Simmons Calculus Gems
The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight.
[In the margin of his copy of Diophantus' Arithmetica]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)
On two occasions I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.
Charles Babbage (1792-1871)
[On Ramanujan] I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
Godfrey H. Hardy (1877 - 1947), Ramanujan
The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new member of the solar system, and its exact location, were demonstrated with pencil and paper; there was left to observers only the routine task of pointing their telescopes at the spot the mathematicians had marked.
James R. Newman, The World of Mathematics
It is nothing short of a miracle that modern methods of instruction have not yet entirely strangled the holy curiousity of inquiry.
Albert Einstein (1879-1955), in H. Eves Return to Mathematical Circles
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