Mathematical Quotations -- B

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Babbage, Charles (1792-1871)

Errors using inadequate data are much less than those using no data at all.

I wish to God these calculations had been executed by steam.
In H. Eves In Mathematical Circles,, Boston: Prindle, Weber and Schmidt, 1969.

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 kindof confusion of ideas that could provoke such a question.

Bacon, Sir Francis (1561-1626)

And as for Mixed Mathematics, I may only make this prediction, that there cannot fail to be more kinds of them, as nature grows further disclosed.
Advancement of Learning book 2; De Augmentis book 3.

Bacon, Roger

For the things of this world cannot be made known without a knowledge of mathematics.
Opus Majus part 4 Distinctia Prima cap 1, 1267.

In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures; so in the mathematics, that use which is collateral and intervenient is no less worthy than that which is principal and intended.
John Fauvel and Jeremy Gray (eds.) A History of Mathematics: A Reader, Sheridan House, 1987.

Baker, H. F.

[On the concept of group:]
... what a wealth, what a grandeur of thought may spring from what slight beginnings.
Florian Cajori, A History of Mathematics, New York, 1919, p 283.

Bagehot, Walter

Life is a school of probability.
Quoted in J. R. Newman (ed.) The World of Mathematics, Simon and Schuster, New York, 1956, p. 1360.

Balzac, Honore de (1799 - 1850)

Numbers are intellectual witnesses that belong only to mankind.

Banville, John

Throughout the 1960s and 1970s devoted Beckett readers greeted each successively shorter volume from the master with a mixture of awe and apprehensiveness; it was like watching a great mathematician wielding an infinitesimal calculus, his equations approaching nearer and still nearer to the null point.
Quoted in a review of Samuel Beckett's Nohow On: I11 Seen I11 Said, Worstward Ho, in The New York Review of Books, August 13, 1992.

Bell, Eric Temple (1883-1960)

Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.
In H. Eves Return to Mathematical Circles., Boston: Prindle, Weber and Schmidt, 1988.

Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.
Mathematics, Queen and Servant of Science, New York, 1951, p 164.

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.

The Handmaiden of the Sciences.
[Book by that title.]

Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.

"Obvious" is the most dangerous word in mathematics.

The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular.
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.

Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956, p. 308.

The longer mathematics lives the more abstract -- and therefore, possibly also the more practical -- it becomes.
In The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991.

The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry.
In R Crayshaw-Williams The Search For Truth, p. 191.

If "Number rules the universe" as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number.
In H. Eves Mathematical Circles Revisited, Boston: Prindle, Weber and Schmidt, 1971.

I have always hated machinery, and the only machine I ever understood was a wheelbarrow, and that but imperfectly.
In H. Eves Mathematical Circles Adieu, Boston: Prindle, Weber and Schmidt, 1977.

Belloc, Hillaire (1870-1953)

Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death.
The Silence of the Sea

Bentham, Jeremy (1748-1832)

O Logic: born gatekeeper to the Temple of Science, victim of capricious destiny: doomed hitherto to be the drudge of pedants: come to the aid of thy master, Legislation.
In J. Browning (ed.) Works.

Bernoulli, Daniel would be better for the true physics if there were no mathematicians on earth.
In The Mathematical Intelligencer, v. 13, no. 1, Winter 1991.

Bernoulli, Jacques (Jakob?) (1654-1705)

I recognize the lion by his paw.
[After reading an anonymous solution to a problem that he realized was Newton's solution.]
In G. Simmons, Calculus Gems, New York: McGraw Hill, 1992, p. 136.

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.


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.

Bolyai, János (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 János:]
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.


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.

Browne, Sir Thomas (1605-1682)

God is like a skilful Geometrician.
Religio Medici I, 16.

All things began in Order, so shall they end, and so shall they begin again, according to the Ordainer of Order, and the mystical mathematicks of the City of Heaven.
Hydriotaphia, Urn-burial and the Garden of Cyrus, 1896.

...indeed what reason may not go to Schoole to the wisdome of Bees, Aunts, and Spiders? what wise hand teacheth them to doe what reason cannot teach us? ruder heads stand amazed at those prodigious pieces of nature, Whales, Elephants, Dromidaries and Camels; these I confesse, are the Colossus and Majestick pieces of her hand; but in these narrow Engines there is more curious Mathematicks, and the civilitie of these little Citizens more neatly sets forth the wisedome of their Maker.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956, p. 1001.

Buck, Pearl S. (1892 - 1973)

No one really understood music unless he was a scientist, her father had declared, and not just a scientist, either, oh, no, only the real ones, the theoreticians, whose language mathematics. She had not understood mathematics until he had explained to her that it was the symbolic language of relationships. "And relationships," he had told her, "contained the essential meaning of life."
The Goddess Abides, Pt. I, 1972.

Burke, Edmund

The age of chivalry is gone. That of sophisters, economists and calculators has succeeded.
Reflections on the Revolution in France.

Butler, Bishop

To us probability is the very guide of life.
Preface to Analogy.

Butler, Samuel (1835 - 1902)

... There can be no doubt about faith and not reason being the ultima ratio. Even Euclid, who has laid himself as little open to the charge of credulity as any writer who ever lived, cannot get beyond this. He has no demonstrable first premise. He requires postulates and axioms which transcend demonstration, and without which he can do nothing. His superstructure indeed is demonstration, but his ground his faith. Nor again can he get further than telling a man he is a fool if he persists in differing from him. He says "which is absurd," and declines to discuss the matter further. Faith and authority, therefore, prove to be as necessary for him as for anyone else.
The Way of All Flesh.


When Newton saw an apple fall, he found ...
A mode of proving that the earth turnd round
In a most natural whirl, called gravitation;
And thus is the sole mortal who could grapple
Since Adam, with a fall or with an apple.

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