I advise my students to listen carefully the moment they decide to take no more mathematics courses. They might be able to hear the sound of closing doors.
Everybody a mathematician?,CAIP Quarterly 2 (Fall, 1989).
To throw in a fair game at Hazards only three-spots, when something great
is at stake, or some business is the hazard, is a natural occurrence and
deserves to be so deemed; and even when they come up the same way for
a second time if the throw be repeated. If the third and fourth plays
are the same, surely there is occasion for suspicion on the part of a
prudent man.
De Vita Propria Liber.
It is a mathematical fact that the casting of this pebble from my hand
alters the centre of gravity of the universe.
Sartor Resartus III.
Teaching school is but another word for sure and not very slow destruction.
In H. Eves In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.
A witty statesman said, you might prove anything by figures.
Chartism.
What I tell you three times is true.
The Hunting of the Snark.
The different branches of Arithmetic -- Ambition, Distraction, Uglification,
and Derision.
Alice in Wonderland.
"Can you do addition?" the White Queen asked. "What's one and one and
one and one and one and one and one and one and one and one?" "I don't
know," said Alice. "I lost count."
Through the Looking Glass.
"Alice laughed: "There's no use trying," she said; "one can't believe
impossible things."
"I daresay you haven't had much practice," said the Queen. "When I was
younger, I always did it for half an hour a day. Why, sometimes I've
believed as many as six impossible things before breakfast."
Alice in Wonderland.
"Then you should say what you mean," the March Hare went on.
"I do, " Alice hastily replied; "at least I mean what I say, that's
the same thing, you know."
"Not the same thing a bit!" said the Hatter. "Why, you might just as
well say that "I see what I eat" is the same thing as "I eat what I see!"
Alice in Wonderland.
"It's very good jam," said the Queen.
"Well, I don't want any to-day, at any rate."
"You couldn't have it if you did want it," the Queen said. "The rule
is jam tomorrow and jam yesterday but never jam to-day."
"It must come sometimes to "jam to-day,""Alice objected.
"No it can't," said the Queen. "It's jam every other day; to-day isn't
any other day, you know."
"I don't understand you," said Alice. "It's dreadfully confusing."
Through the Looking Glass.
"When I use a word," Humpty Dumpty said, in a rather scornful tone, "it
means just what I choose it to mean - neither more nor less."
"The question is," said Alice, "whether you can make words mean so many
different things."
"The question is," said Humpty Dumpty, "which is to be master - that's all."
Through the Looking Glass.
Entre le pénis et les mathématiques... il n'existe rien. Rien! C'est le vide.
Voyage au bout de la nuit. Paris: Gallimard.
A thing is obvious mathematically after you see it.
In N. Rose (ed.) Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
Men pass away, but their deeds abide.
[His last words (?)]
In H. Eves Mathematical Circles Revisted, Boston: Prindle, Weber and Schmidt, 1971.
As for everything else, so for a mathematical theory: beauty can be
perceived but not explained.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Projective geometry is all geometry.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
...treat Nature by the sphere, the cylinder and the cone...
To isolate mathematics from the practical demands of the sciences is
to invite the sterility of a cow shut away from the bulls.
In G. Simmons, Calculus Gems, New York: Mcgraw Hill, Inc., 1992, page 198.
There is no national science just as there is no national multiplication
table; what is national is no longer science.
In V. P. Ponomarev Mysli o nauke Kishinev, 1973.
Poets do not go mad; but chess-players do. Mathematicians go mad, and cashiers; but creative artists very seldom. I am not, as will be seen, in any sense attacking logic: I only say that this danger does lie in logic, not in imagination.
Orthodoxy ch. 2.
You can only find truth with logic if you have already found truth without
it.
The Man who was Orthodox. 1963.
It isn't that they can't see the solution. It is that they can't see
the problem.
The Point of a Pin in The Scandal of Father Brown.
"I think you're begging the question," said Haydock, "and I can see looming
ahead one of those terrible exercises in probability where six men have
white hats and six men have black hats and you have to work it out by
mathematics how likely it is that the hats will get mixed up and in what
proportion. If you start thinking about things like that, you would go
round the bend. Let me assure you of that!"
The Mirror Crack'd. Toronto: Bantam Books, 1962.
I continued to do arithmetic with my father, passing proudly through fractions
to decimals. I eventually arrived at the point where so many cows ate
so much grass, and tanks filled with water in so many hoursI found it
quite enthralling.
An Autobiography.
It is a good thing from an uneducated man to read books of quotations.
Roving Commission in My Early Life. 1930.
I had a feeling once about Mathematics - that I saw it all. Depth beyond
depth was revealed to me - the Byss and Abyss. I saw - as one might see the
transit of Venus or even the Lord Mayor's Show - a quantity passing through
infinity and changing its sign from plus to minus. I saw exactly why
it happened and why the tergiversation was inevitable but it was after
dinner and I let it go.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
The measure of our intellectual capacity is the capacity to feel less
and less satisfied with our answers to better and better problems.
In J.E. Littlewood A Mathematician's Miscellany. Methuen and Co., Ltd.
1953.
The composer opens the cage door for arithmetic, the draftsman gives geometry its freedom.
...from the time of Kepler to that of Newton, and from Newton to Hartley,
not only all things in external nature, but the subtlest mysteries of
life and organization, and even of the intellect and moral being, were
conjured within the magic circle of mathematical formulae.
The Theory of Life.
C'este donc par l'étude des mathématiques, et seulement par elle,
que l'on peut se faire une idée juste et approfondie de ce que c'est
qu'une science.
Quoted by T. H. Huxley in Fortnightly Review, Vol. II, N.S. 5.
Don't talk to me of your Archimedes' lever. He was an absentminded person
with a mathematical imagination. Mathematics commands all my respect,
but I have no use for engines. Give me the right word and the right accent
and I will move the world.
Preface to A Personal Record.
[Upon proving that the best betting strategy for "Gambler's Ruin" was
to bet all on the first trial.]
It is true that a man who does this is
a fool. I have only proved that a man who does anything else is an even
bigger fool.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
Mathematics is written for mathematicians.
De Revolutionibus.
In my experience most mathematicians are intellectually lazy and especially
dislike reading experimental papers. He (René Thom) seemed to have
very strong biological intuitions but unfortunately of negative sign.
What Mad Pursuit. London: Weidenfeld and Nicolson, 1988.
Revolutions never occur in mathematics.
Historia Mathematica. 1975.