The science of pure mathematics ... may claim to be the most original creation of the human spirit.

The study of mathematics is apt to commence in disappointment....We are told
that by its aid the stars are weighed and the billions of molecules in a drop of
water are counted. Yet, like the ghost of Hamlet's father, this greatest science
eludes the efforts of our mental weapons to grasp it.*An Introduction to
Mathematics*

Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.

So far as the mere imparting of information is concerned, no university has
had any justification for existence since the popularization of printing in the
fifteenth century. *The Aims of Education*.

No Roman ever died in contemplation over a geometrical diagram.

[A
reference to the death of Archimedes.]

Quoted in H Eves *Mathematical
Circles Squared* (Boston 1972).

Life is an offensive, directed against the repetitious mechanism of the
Universe.*Adventures of Ideas*, 1933.

There is no nature at an instant.

Let us grant that the pursuit of mathematics is a divine madness of the human
spirit, a refuge from the goading urgency of contingent happenings.

Quoted
in N Rose *Mathematical Maxims and Minims* (Raleigh N C 1988).

There is a tradition of opposition between adherents of induction and of
deduction. In my view it would be just as sensible for the two ends of a worm to
quarrel.

Quoted in N Rose *Mathematical Maxims and Minims* (Raleigh N C
1988).

It is a profoundly erroneous truism, repeated by all copy books and by
eminent people when they are making speeches, that we should cultivate the habit
of thinking of what we are doing. The precise opposite is the case. Civilization
advances by extending the number of important operations which we can perform
without thinking about them. *An Introduction to Mathematics.*

Our minds are finite, and yet even in these circumstances of finitude we are
surrounded by possibilities that are infinite, and the purpose of life is to
grasp as much as we can out of that infinitude.

Quoted in N Rose
*Mathematical Maxims and Minims* (Raleigh N C 1988).

In modern times the belief that the ultimate explanation of all things was to
be found in Newtonian mechanics was an adumbration of the truth that all
science, as it grows towards perfection, becomes mathematical in its
ideas.

Quoted in N Rose *Mathematical Maxims and Minims* (Raleigh N C
1988).

Algebra reverses the relative importance of the factors in ordinary language.
It is essentially a written language, and it endeavors to exemplify in its
written structures the patterns which it is its purpose to convey. The pattern
of the marks on paper is a particular instance of the pattern to be conveyed to
thought. The algebraic method is our best approach to the expression of
necessity, by reason of its reduction of accident to the ghostlike character of
the real variable.

Quoted in W H Auden and L Kronenberger *The Viking Book
of Aphorisms* (New York 1966).

By relieving the brain of all unnecessary work, a good notation sets it free
to concentrate on more advanced problems, and, in effect, increases the mental
power of the race.

Quoted in P Davis and R Hersh *The Mathematical
Experience* (Boston 1981).

Everything of importance has been said before by somebody who did not
discover it.

Quoted in J R Newman, *The World of Mathematics* (New York
1956).

Seek simplicity, and distrust it.

Quoted in W H Auden and L Kronenberger
*The Viking Book of Aphorisms* (New York 1966).

Fundamental progress has to do with the reinterpretation of basic
ideas.

Quoted in W H Auden and L Kronenberger *The Viking Book of
Aphorisms* (New York 1966).

We think in generalities, but we live in details.

Quoted in W H Auden and
L Kronenberger *The Viking Book of Aphorisms* (New York 1966).

Apart from blunt truth, our lives sink decadently amid the perfume of hints
and suggestions.

Quoted in W H Auden and L Kronenberger *The Viking Book of
Aphorisms* (New York 1966).

"Necessity is the mother of invention" is a silly proverb. "Necessity is the
mother of futile dodges" is much nearer the truth.

Quoted in W H Auden and L
Kronenberger *The Viking Book of Aphorisms* (New York 1966).

It is more important that a proposition be interesting than that it be true.
This statement is almost a tautology. For the energy of operation of a
proposition in an occasion of experience is its interest and is its importance.
But of course a true proposition is more apt to be interesting than a false
one.

Quoted in W H Auden and L Kronenberger *The Viking Book of
Aphorisms* (New York 1966).

War can protect; it cannot create.

Quoted in W H Auden and L Kronenberger
*The Viking Book of Aphorisms* (New York 1966).

The progress of Science consists in observing interconnections and in showing
with a patient ingenuity that the events of this ever-shifting world are but
examples of a few general relations, called laws. To see what is general in what
is particular, and what is permanent in what is transitory, is the aim of
scientific thought.*An Introduction to Mathematics.*

Through and through the world is infested with quantity: To talk sense is to
talk quantities. It is not use saying the nation is large .. How large? It is no
use saying the radium is scarce ... How scarce? You cannot evade quantity. You
may fly to poetry and music, and quantity and number will face you in your
rhythms and your octaves.

Quoted in J R Newman, *The World of
Mathematics* (New York 1956).

"One and one make two" assumes that the changes in the shift of circumstance
are unimportant. But it is impossible for us to analyze this notion of
unimportant change.

Quoted in W H Auden and L Kronenberger *The Viking Book
of Aphorisms* (New York 1966).

I will not go so far as to say that to construct a history of thought without
profound study of the mathematical ideas of successive epochs is like omitting
Hamlet from the play which is named after him. That would be claiming too much.
But it is certainly analogous to cutting out the part of Ophelia. This simile is
singularly exact. For Ophelia is quite essential to the play, she is very
charming ... and a little mad.

Quoted in W H Auden and L Kronenberger *The
Viking Book of Aphorisms* (New York 1966).

In the study of ideas, it is necessary to remember that insistence on
hard-headed clarity issues from sentimental feeling, as it were a mist, cloaking
the perplexities of fact. Insistence on clarity at all costs is based on sheer
superstition as to the mode in which human intelligence functions. Our
reasonings grasp at straws for premises and float on gossamers for
deductions.

Quoted in J R Newman, *The World of Mathematics* (New York
1956).

Familiar things happen, and mankind does not bother about them. It requires a
very unusual mind to undertake the analysis of the obvious.*Science and
the Modern World.*

It is a safe rule to apply that, when a mathematical or philosophical author writes with a misty profundity, he is talking nonsense.

The race that does not value trained intelligence is doomed.

Let us grant that the pusuit of mathematics is a divine madness of the human spirit.

A Unitarian is a person who believes in at most one God.

Quoted in D
MacHale, *Comic Sections *(Dublin 1993)

... to be an abstraction does not mean that an entity is nothing. It merely
means that its existence is only a factor of a more concrete element of
nature.*The Concept of Nature*

... algebra is the intellectual instrument which has been created for
rendering clear the quantitative aspects of the world.*The Organisation of
Thought*

The point of mathematics is that in it we have always got rid of the
particular instance, and even of any particular sorts of entities. So that for
example, no mathematical truths apply merely to fish, or merely to stones, or
merely to colours. So long as you are dealing with pure mathematics, you are in
the realm of complete and absolute abstraction. ... Mathematics is thought
moving in the sphere of complete abstraction from any particular instance of
what it is talking about.*Science and the Modern World*

But in the prevalent discussion of classes, there are illegitimate
transitions to the notions of a 'nexus' and of a 'proposition'. The appeal to a
class to perform the services of a proper entity is exactly analogous to an
appeal to an imaginary terrier to kill a real rat.*Process and Reality*

Now in creative thought common sense is a bad master. Its sole criterion for
judgement is that the new ideas shall look like the old ones. In other words it
can only work by suppressing originality.*An Introduction to
Mathematics*

I regret that it has been necessary for me in this lecture to administer a
large dose of four-dimensional geometry. I do not apologise, because I am realyy
not responsible for the fact that nature in its most fundamental aspect is
four-dimensional. Things are what they are ...*The Concept of Nature*

Mathematics, in its widest significance, is the development of all types of
formal, necessary, deductive reasoning.*A treatise on universal
algebra* (New York, 1960).

The utmost abstractions are the true weapons with which to combat our thought
of concrete fact.

Quoted in M Kline, *Mathematics in Western culture*
(New York, 1953).

Order is not sufficient. What is required, is something much more complex. It is order entering upon novelty; so that the massiveness of order does not degenerate into mere repetition; and so that the novelty is always reflected upon a background of system.

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