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Polya, George (1887-1985)
Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.
One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.
How to Solve It. Princeton: Princeton University Press. 1945.
Polya, George (1887-1985)
In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.
How to Solve It. Princeton: Princeton University Press. 1945.
Pope, Alexander (1688-1744)
[Epitaph on Newton:]
Nature and Nature's law lay hid in night:
God said, "Let Newton be!," and all was light.

[Added by Sir John Collings Squire:]
It did not last: the Devil shouting "Ho.
Let Einstein be," restored the status quo.

[Aaron Hill's version:]
O'er Nature's laws God cast the veil of night,
Out blaz'd a Newton's soul and all was light.
unknown
Pope, Alexander (1688-1744)
Order is Heaven's first law.
An Essay on Man IV.
Pope, Alexander (1688-1744)
See skulking Truth to her old cavern fled,
Mountains of Casuistry heap'd o'er her head!
Philosophy, that lean'd on Heav'n before,
Shrinks to her second cause, and is no more.
Physic of Metaphysic begs defence,
And Metaphysic calls for aid on Sense!
See Mystery to Mathematics fly!
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Pordage, Matthew
One of the endearing things about mathematicians is the extent to which they will go to avoid doing any real work.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
Proclus Diadochus (412 - 485)
It is well known that the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled. And so the guilty man, who fortuitously touched on and revealed this aspect of living things, was taken to the place where he began and there is for ever beaten by the waves.
Scholium to Book X of Euclid V.
Purcell, E. and Varberg
The Mean Value Theorem is the midwife of calculus -- not very important or glamorous by itself, but often helping to delivery other theorems that are of major significance.
Calculus with Analytic Geometry, 5th edition, Englewood Cliffs, NJ: Prentice Hall, 1987.
Pushkin, Aleksandr Sergeyevich (1799 - 1837)
Inspiration is needed in geometry, just as much as in poetry.
Likhtenshtein

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