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Bernoulli, Johann
But just as much as it is easy to find the differential of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.
Besicovitch, A.S.
A mathematician's reputation rests on the number of bad proofs he has given.
In J. E. Littlewood A Mathematician's Miscellany, Methuen & Co. Ltd., 1953.
Blake
God forbid that Truth should be confined to Mathematical Demonstration!
Notes on Reynold's Discourses, c. 1808.
What is now proved was once only imagin'd.
The Marriage of Heaven and Hell, 1790-3.
Bohr, Niels Henrik David (1885-1962)
An expert is a man who has made all the mistakes, which can be made, in a very narrow field
The Bible
I returned and saw under the sun that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.
Ecclesiastes.
Bolyai, J�os (1802 - 1860)
Out of nothing I have created a strange new universe.
[A reference to the creation of a non-euclidean geometry.]
Bolyai, Wolfgang (1775-1856)
[To son J�os:]
For God's sake, please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life.
[Bolyai's father urging him to give up work on non-Euclidian geometry.]
In P. Davis and R. Hersh The Mathematical Experience , Boston: Houghton Mifflin Co., 1981, p. 220.
Bourbaki
Structures are the weapons of the mathematician.
Bridgman, P. W.
It is the merest truism, evident at once to unsophisticated observation, that mathematics is a human invention.
The Logic of Modern Physics, New York, 1972.
Brown, George Spencer (1923 - )
To arrive at the simplest truth, as Newton knew and practiced, requires years of contemplation. Not activity Not reasoning. Not calculating. Not busy behaviour of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know. And yet those with the courage to tread this path to real discovery are not only offered practically no guidance on how to do so, they are actively discouraged and have to set abut it in secret, pretending meanwhile to be diligently engaged in the frantic diversions and to conform with the deadening personal opinions which are continually being thrust upon them.
The Laws of Form. 1969.