Archimedes constructing his circle pays with his life for his defective biological adaptation to immediate circumstances.
The mathematician who pursues his studies without clear views of this
matter, must often have the uncomfortable feeling that his paper and pencil
surpass him in intelligence.
"The Economy of Science" in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Like the ski resort full of girls hunting for husbands and husbands hunting
for girls, the situation is not as symmetrical as it might seem.
A Dictionary of Scientific Quotations, Bristol: IOP Publishing, 1991.
Truth ... and if mine eyes
Can bear its blaze, and trace its symmetries,
Measure its distance, and its advent wait,
I am no prophet -- I but calculate.
The Poetical Works of Charles Mackay. 1876.
The concept of number is the obvious distinction between the beast and man. Thanks to number, the cry becomes a song, noise acquires rhythm, the spring is transformed into a dance, force becomes dynamic, and outlines figures.
A great truth is a truth whose opposite is also a great truth.
Essay on Freud. 1937.
I tell them that if they will occupy themselves with the study of mathematics
they will find in it the best remedy against the lusts of the flesh.
The Magic Mountain. 1927.
Some of the men stood talking in this room, and at the right of the door
a little knot had formed round a small table, the center of which was
the mathematics student, who ws eagerly talking. He had made the assertion
that one could draw through a given point more than one parallel to a
straight line; Frau Hagenström had cried out that this was impossible,
and he had gone on to prove it so conclusively that his hearers were constrained
to behave as though they understood.
Little Herr Friedemann.
If your new theorem can be stated with great simplicity, then there will
exist a pathological exception.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
All great theorems were discovered after midnight.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
The greatest unsolved theorem in mathematics is why some people are better
at it than others.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
If you see a formula in the Physical Review that extends over a quarter of a page, forget it. It's wrong. Nature isn't that complicated.
... that, in a few years, all great physical constants will have been approximately
estimated, and that the only occupation which will be left to men of science
will be to carry these measurements to another place of decimals.
Scientific Papers 2, 244, October 1871.
Mathematics began to seem too much like puzzle solving. Physics is puzzle
solving, too, but of puzzles created by nature, not by the mind of man.
J. Dash, Maria Goeppert-Mayer, A Life of One's Own.
Gel'fand amazed me by talking of mathematics as though it were poetry.
He once said about a long paper bristling with formulas that it contained
the vague beginnings of an idea which could only hint at and which he
had never managed to bring out more clearly. I had always thought of
mathematics as being much more straightforward: a formula is a formula,
and an algebra is an algebra, but Gel'fand found hedgehogs lurking in
the rows of his spectral sequences!
Mathematical Notices v. 38, no. 3, March 1991, pp. 185-7.
There are in this world optimists who feel that any symbol that starts
off with an integral sign must necessarily denote something that will
have every property that they should like an integral to possess. This
of course is quite annoying to us rigorous mathematicians; what is even
more annoying is that by doing so they often come up with the right answer.
Bulletin of the American Mathematical Society, v. 69, p. 611, 1963.
It is now quite lawful for a Catholic woman to avoid pregnancy by a resort to mathematics, though she is still forbidden to resort to physics and chemistry.
Notebooks, "Minority Report".
Bridges would not be safer if only people who knew the proper definition
of a real number were allowed to design them.
"Topological Theory of Defects" in Review of Modern Physics, v. 51 no. 3, July 1979.
Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.
From Man or Angel the great Architect
Did wisely to conceal, and not divulge,
His secrets, to be scanned by them who ought
Rather admire. Or, if they list to try
Conjecture, he his fabric of the Heavens
Hath left to their disputes -- perhaps to move
His laughter at their quaint opinions wide
Hereafter, when they come to model Heaven
And calculate the stars: how they will wield
The mighty frame: how build, unbuild, contrive
To save appearances; how gird the Sphere
With Centric and Eccentric scribbled o'er,
Cycle and Epicycle, Orb in Orb.
Paradise Lost.
Chaos umpire sits
And by decision more
embroils the fray
by which he reigns: next
him high arbiter
Chance governs all.
From henceforth, space by itself, and time by itself, have vanished into
the merest shadows and only a kind of blend of the two exists in its own
right.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Logic doesn't apply to the real world.
D. R. Hofstadter and D. C. Dennett (eds.) The Mind's I, 1981.
...She knew only that if she did or said thus-and-so, men would unerringly
respond with the complimentary thus-and-so. It was like a mathematical
formula and no more difficult, for mathematics was the one subject that
had come easy to Scarlett in her schooldays.
Gone With the Wind.
The mathematician's best work is art, a high perfect art, as daring as
the most secret dreams of imagination, clear and limpid. Mathematical
genius and artistic genius touch one another.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Neither you nor I nor anybody else knows what makes a mathematician tick.
It is not a question of cleverness. I know many mathematicians who are
far abler than I am, but they have not been so lucky. An illustration
may be given by considering two miners. One may be an expert geologist,
but he does not find the golden nuggets that the ignorant miner does.
In H. Eves Mathematical Circles Adieu, Boston: Prindle, Weber and Schmidt, 1977.
We lay down a fundamental principle of generalization by abstraction:
"The existence of analogies between central features of various
theories implies the existence of a general theory which underlies the
particular theories and unifies them with respect to those central features...."
In H. Eves Mathematical Circles Revisited, Boston: Prindle, Weber and Schmidt, 1971.
The words figure and fictitious both derive from the same Latin root,
fingere. Beware!
Facts from Figures.
[about Hypatia:]
In an era in which the domain of intellect and politics were almost exclusively
male, Theon [her father] was an unusually liberated person who taught
an unusually gifted daughter and encouraged her to achieve things that,
as far as we know, no woman before her did or perhaps even dreamed of
doing.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.