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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.

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.

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.

[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.

Life is a school of probability.

Quoted in J. R. Newman (ed.) *The World of Mathematics*, Simon and Schuster, New York, 1956, p. 1360.

Numbers are intellectual witnesses that belong only to mankind.

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.

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.

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

*The Silence of the Sea
*

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*.

...it would be better for the true physics if there were no mathematicians
on earth.

In *The Mathematical Intelligencer*, v. 13, no. 1, Winter 1991.

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.

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.

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.

An expert is a man who has made all the mistakes, which can be made, in
a very narrow field.

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.*

Out of nothing I have created a strange new universe.

[A reference to the creation of a non-euclidean geometry.]

[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.

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.

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.

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.

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.

The age of chivalry is gone. That of sophisters, economists and calculators
has succeeded.

*Reflections on the Revolution in France*.

To us probability is the very guide of life.

Preface to *Analogy*.

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.