In an examination those who do not wish to know ask questions of those
who cannot tell.
Some Thoughts on Examinations.
To avoide the tediouse repetition of these woordes: is equalle to: I
will settle as I doe often in woorke use, a paire of paralleles, or gemowe
[twin] lines of one lengthe: =, bicause noe .2. thynges, can be moare
equalle.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.
It is the invaluable merit of the great Basle mathematician Leonard Euler,
to have freed the analytical calculus from all geometric bounds, and thus
to have established analysis as an independent science, which from his
time on has maintained an unchallenged leadership in the field of mathematics.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
The simplest schoolboy is now familiar with facts for which Archimedes
would have sacrificed his life.
Souvenirs d'enfance et de jeunesse.
If I feel unhappy, I do mathematics to become happy. If I am happy, I
do mathematics to keep happy.
P. Turán, "The Work of Alfréd Rényi", Matematikai Lapok 21, 1970,
pp 199 - 210.
Another advantage of a mathematical statement is that it is so definite
that it might be definitely wrong; and if it is found to be wrong, there
is a plenteous choice of amendments ready in the mathematicians' stock
of formulae. Some verbal statements have not this merit; they are so
vague that they could hardly be wrong, and are correspondingly useless.
Mathematics of War and Foreign Politics.
The magic words are squeamish ossifrage
[This sentence is the result when a coded message in Martin Gardner's column
about factoring the famous number RSA-129 is decoded. See the article whose title is the above sentence by Barry Cipra, SIAM News July 1994, 1, 12-13.]
it was by just such a hazard, as if a man should let fall a handful of
sand upon a table and the particles of it should be so ranged that we
could read distinctly on it a whole page of Virgil's Aenead.
Traité de Physique, Paris, 1671.
[with Norbert Wiener]
The best material model of a cat is another, or preferably the same, cat.
Philosophy of Science 1945.
You know we all became mathematicians for the same reason: we were lazy.
Hugo Rossi
In the fall of 1972 President Nixon announced that the rate of increase
of inflation was decreasing. This was the first time a sitting president
used the third derivative to advance his case for reelection.
Mathematics Is an Edifice, Not a Toolbox, Notices of the AMS,
v. 43, no. 10, October 1996.
We often hear that mathematics consists mainly of "proving theorems."
Is a writer's job mainly that of "writing sentences?"
In preface to P. Davis and R. Hersh The Mathematical Experience, Boston: Birkhäuser, 1981.
How dare we speak of the laws of chance? Is not chance the antithesis
of all law?
Calcul des probabilités.
Mathematics takes us into the region of absolute necessity, to which
not only the actual word, but every possible word, must conform.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Although this may seem a paradox, all exact science is dominated by the
idea of approximation.
W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.
At the age of eleven, I began Euclid, with my brother as my tutor. This
was one of the great events of my life, as dazzling as first love. I
had not imagined there was anything so delicious in the world. From that
moment until I was thirty-eight, mathematics was my chief interest and
my chief source of happiness.
The Autobiography of Bertrand Russell .
A good notation has a subtlety and suggestiveness which at times make
it almost seem like a live teacher.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
If I were a medical man, I should prescribe a holiday to any patient who
considered his work important.
The Autobiography of Bertrand Russell .
Ordinary language is totally unsuited for expressing what physics really
asserts, since the words of everyday life are not sufficiently abstract.
Only mathematics and mathematical logic can say as little as the physicist
means to say.
The Scientific Outlook, 1931.
With equal passion I have sought knowledge. I have wished to understand
the hearts of men. I have wished to know why the stars shine. And I
have tried to apprehend the Pythagorean power by which number holds sway
about the flux. A little of this, but not much, I have achieved.
The Autobiography of Bertrand Russell .
At first it seems obvious, but the more you think about it the stranger
the deductions from this axiom seem to become; in the end you cease to
understand what is meant by it.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Calculus required continuity, and continuity was supposed to require the
infinitely little; but nobody could discover what the infinitely little
might be.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
The fact that all Mathematics is Symbolic Logic is one of the greatest
discoveries of our age; and when this fact has been established, the remainder
of the principles of mathematics consists in the analysis of Symbolic
Logic itself.
Principles of Mathematics. 1903.
A habit of basing convictions upon evidence, and of giving to them only
that degree or certainty which the evidence warrants, would, if it became
general, cure most of the ills from which the world suffers.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.
The method of "postulating" what we want has many advantages; they are
the same as the advantages of theft over honest toil.
Introduction to
Mathematical Philosophy, New York and London, 1919, p 71.
Aristotle maintained that women have fewer teeth than men; although he
was twice married, it never occurred to him to verify this statement by
examining his wives' mouths.
The Impact of Science on Society, 1952.
[Upon hearing via Littlewood an exposition on the theory of relativity:]
To think I have spent my life on absolute muck.
J.E. Littlewood, A Mathematician's Miscellany, Methuen and Co. ltd., 1953.
"But," you might say, "none of this shakes my belief that 2 and 2 are
4." You are quite right, except in marginal cases -- and it is only in
marginal cases that you are doubtful whether a certain animal is a dog
or a certain length is less than a meter. Two must be two of something,
and the proposition "2 and 2 are 4" is useless unless it can be applied.
Two dogs and two dogs are certainly four dogs, but cases arise in which
you are doubtful whether two of them are dogs. "Well, at any rate there
are four animals," you may say. But there are microorganisms concerning
which it is doubtful whether they are animals or plants. "Well, then
living organisms," you say. But there are things of which it is doubtful
whether they are living organisms or not. You will be driven into saying:
"Two entities and two entities are four entities." When you have told
me what you mean by "entity," we will resume the argument.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
I wanted certainty in the kind of way in which people want religious faith.
I thought that certainty is more likely to be found in mathematics than
elsewhere. But I discovered that many mathematical demonstrations, which
my teachers expected me to accept, were full of fallacies, and that, if
certainty were indeed discoverable in mathematics, it would be in a new
field of mathematics, with more solid foundations than those that had
hitherto been thought secure. But as the work proceeded, I was continually
reminded of the fable about the elephant and the tortoise. having constructed
an elephant upon which the mathematical world could rest, I found the
elephant tottering, and proceeded to construct a tortoise to keep the
elephant from falling. But the tortoise was no more secure than the elephant,
and after some twenty years of very arduous toil, I came to the conclusion
that there was nothing more that I could do in the way of making mathematical
knowledge indubitable.
Portraits from Memory.
Men who are unhappy, like men who sleep badly, are always proud of the
fact.
W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.
Work is of two kinds: first, altering the position of matter at or near the earth's surface relatively to other such matter; second, telling other people to do so. The first kind is unpleasant and ill paid; the second is pleasant and highly paid.
A sense of duty is useful in work but offensive in personal relations.
Certain characteristics of the subject are clear. To begin with, we do
not, in this subject, deal with particular things or particular properties:
we deal formally with what can be said about "any" thing or "any" property.
We are prepared to say that one and one are two, but not that Socrates
and Plato are two, because, in our capacity of logicians or pure mathematicians,
we have never heard of Socrates or Plato. A world in which there were
no such individuals would still be a world in which one and one are two.
It is not open to us, as pure mathematicians or logicians, to mention
anything at all, because, if we do so we introduce something irrelevant
and not formal.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
The desire to understand the world and the desire to reform it are the
two great engines of progress.
Marriage and Morals.
It can be shown that a mathematical web of some kind can be woven about
any universe containing several objects. The fact that our universe lends
itself to mathematical treatment is not a fact of any great philosophical
significance.
W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.
If your experiment needs statistics, you ought to have done a better experiment.
In N. T. J. Bailey the Mathematical Approach to Biology and Medicine, New York: Wiley, 1967.