This student works only in the highest realms of mathematics.  The mathematical madness dominates this boy.  I think it would be best for him if his parents would allow him to study nothing but this.  Otherwise he is wasting his time here and does nothing but torment his teachers and overwhelm himself with punishments.

xⁿ+yⁿ=zⁿ: No Solutions
I have discovered a truly remarkable proof of this, but I can't write it now because my train is coming.
    --Found spray-painted on the New York Eighth Street subway station.

A problem worthy of attack, Proves its worth by fighting back.
    --Piet Hein

An expert problem solver must be endowed with two incompatible qualities-- a restless imagination and a patient pertinacity.
    --Howard W. Eves

Mathematics is one of the purest and most profound of intellectual disciplines.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean. 
    --G. H. Hardy

An astronomer, a physicist, and a mathematician were holidaying in Scotland.  Glancing from a train window, they observed a black sheep in the middle of a field.  “How interesting,” observed the astronomer, “all Scottish sheep are black!”  To which the physicist responded, “No, no!  Some Scottish sheep are black!”  The mathematician then gazed heavenward in supplication, and then intoned, “In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black.”

"Young men should prove theorems, old men should write books." 
    --G. H. Hardy

"...mathematicians simply hate to make a false statement."

"As far as the laws of mathematics refer to reality, they are not certain, 
and as far as they are certain, they do not refer to reality."
     --Albert Einstein

Pascal, the mathematician stated, "the excitement that a gambler feels when making a bet is equal to the amount he might win multiplied by the probability of winning it."  He then argued that the possible prize of eternal happiness has an infinite value and that the probability of entering heaven by leading a virtuous life, no matter how small, is certainly finite.  Therefore, according to Pascal's definition, religion was a game of infinite excitement and one worth playing.

Simon Flagg and the Devil:

The Devil asks Simon Flagg to set him a question. If the Devil succeeds in answering it within twenty-four hours then he takes Simon’s soul, but if he fails then he must give Simon $100,000.  Simon poses the question: “Is Fermat’s Last Theorem correct?”  The evil disappears and whizzes around the world to absorb every piece of mathematics that has ever been created in order to prove the Last Theorem.  The following day he returns and admits defeat:  “You win, Simon,” he said, almost in a whisper, eyeing him with ungrudging respect.  “Not even I can learn enough mathematics in such a short time for so difficult a problem.  The more I get into it the worse it became.  Non-unique factoring, ideals—Bah! Do you know,” the Devil confided, “not even the best mathematicians on other planets—all far ahead of yours—have solved it? Why, there’s a chap on Saturn—he looks something like a mushroom on stilts—who solves partial differential equations mentally; and even he’s given up.”

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost.  Rigor should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.   
    W. S. Anglin

Mathematics takes us into the region of absolute necessity, to which not only the actual world, but every possible world, must conform.
    Bertrand Russell

If you happen to know the author of one of the quotes currently missing one, feel free to enlighten me: quotemaster