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I will be sufficiently rewarded if when telling it to others you will
not claim the discovery as your own, but will say it was mine.

In H. Eves *In Mathematical Circles*, Boston: Prindle, Weber and Schmidt, 1969.

Cell and tissue, shell and bone, leaf and flower, are so many portions
of matter, and it is in obedience to the laws of physics that their particles
have been moved, moulded and conformed. They are no exceptions to the
rule that God always geometrizes. Their problems of form are in the first
instance mathematical problems, their problems of growth are essentially
physical problems, and the morphologist is, *ipso facto*, a student of physical
science.

*On Growth and Form*, 1917.

Fourier is a mathematical poem.

He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. The fact which interests us most is the life of the naturalist. The purest science is still biographical.

The story was told that the young Dirichlet had as a constant companion
all his travels, like a devout man with his prayer book, an old, worn
copy of the *Disquisitiones Arithmeticae* of Gauss.

In G. Simmons *Calculus Gems*, New York: McGraw Hill Inc., 1992.

How often might a man, after he had jumbled a set of letters in a bag,
fling them out upon the ground before they would fall into an exact poem,
yea, or so much as make a good discourse in prose. And may not a little
book be as easily made by chance as this great volume of the world.

In J. R. Newman (ed.) *The World of Mathematics*, New York: Simon and Schuster, 1956.

Perhaps the most surprising thing about mathematics is that it is so surprising.
The rules which we make up at the beginning seem ordinary and inevitable,
but it is impossible to foresee their consequences. These have only been
found out by long study, extending over many centuries. Much of our knowledge
is due to a comparatively few great mathematicians such as Newton, Euler,
Gauss, or Riemann; few careers can have been more satisfying than theirs.
They have contributed something to human thought even more lasting than
great literature, since it is independent of language.

In N. Rose *Mathematical Maxims and Minims*, Raleigh NC:Rome Press Inc., 1988.

It can be of no practical use to know that Pi is irrational, but if we
can know, it surely would be intolerable not to know.

In N. Rose *Mathematical Maxims and Minims*, Raleigh NC:Rome Press Inc., 1988.

[Asked whether he would like to see an experimental demonstration of conical
refraction]

No. I have been teaching it all my life, and I do not want
to have my ideas upset.

A modern branch of mathematics, having achieved the art of dealing with
the infinitely small, can now yield solutions in other more complex problems
of motion, which used to appear insoluble. This modern branch of mathematics,
unknown to the ancients, when dealing with problems of motion, admits
the conception of the infinitely small, and so conforms to the chief condition
of motion (absolute continuity) and thereby corrects the inevitable error
which the human mind cannot avoid when dealing with separate elements
of motion instead of examining continuous motion. In seeking the laws
of historical movement just the same thing happens. The movement of humanity,
arising as it does from innumerable human wills, is continuous. To understand
the laws of this continuous movement is the aim of history . Only by
taking an infinitesimally small unit for observation (the differential
of history, that is, the individual tendencies of man) and attaining to
the art of integrating them (that is, finding the sum of these infinitesimals)
can we hope to arrive at the laws of history.

*War and Peace.*

A man is like a fraction whose numerator is what he is and whose denominator
is what he thinks of himself. The larger the denominator the smaller
the fraction.

In H. Eves *Return to Mathematical Circles*, Boston: Prindle, Weber and Schmidt, 1989.

This paper gives wrong solutions to trivial problems. The basic error,however,
is not new.

*Mathematical Reviews* 12, p561.

Whatever a man prays for, he prays for a miracle. Every prayer reduces itself to this: `Great God, grant that twice two be not four'.

Attaching significance to invariants is an effort to recognize what, because
of its form or colour or meaning or otherwise, is important or significant
in what is only trivial or ephemeral. A simple instance of failing in
this is provided by the poll-man at Cambridge, who learned perfectly how
to factorize a^2 - b^2 but was floored because the examiner unkindly asked
for the factors of p^2 - q^2 .

In J. R. Newman (ed.) *The World of Mathematics*, New York: Simon and Schuster, 1956.