Colorless green ideas sleep furiously.
Noam Chomsky in his first book, Syntactic Structures (1957)

Never be afraid to tackle a difficult problem, however difficult it may appear. You may not solve it, but it could lead you to something else.
J. E. Littlewood

A mathematician confided
That a M÷bius strip is one-sided.
    And you'll get quite a laugh
    If you cut one in half,
For it stays in one piece when divided.

Spaceship: An imaginary aircraft of the future for interplanetary travel outside the earth's atmosphere.
Webster's New Collegiate Dictionary (1959), the one I took to college.

Bitte vergisz was du auf der Schule gelernt hast, denn du hast es nicht gelernt.
    Edmund Landau, Grundlagen der Analysis, 1930.

Lawrence Sluter Benson, a tireless disseminator of unsound mathematical doctrines, died at Newark, N. J., January 27.
American Mathematical Monthly, vol. 10 (1903), p. 85

Military people who saw no use in mathematics were like "two footed moles and toads, whom destiny and nature hath ordained to crawl within the earth and suck upon the much."
Thomas Diggs, 1751
Quoted in Arts of Calculation edited by
David Glimp and Michelle R. Warren, p. 151

Neil de Grassa Tyson, director of the Hayden Planetarium in Manhattan "has a gift for putting the fizz in physics and taking the sigh out of science.''
Clyde Haberman, New York Times, March 11, 2013, p. A 18.

"In mathematics as in war, it should be made a principle, not to advance, while anything is left unconquered behind."
                                          Jeremiah Day, An Introduction to Algebra (1814), p. 4.

"Leap like a knight of faith into the arms of Peano, Leibniz, Hilbert, L'H˘pital. You will be lifted up. Fourier, Gauss, LaPlace, Rickey. Borne up. Never let fall. Wiener, Reimann, Frege, Green."
Infinite Jest (1996), by David Foster Wallace. pp. 1071-1072.

"On Aug 22 [2012], the US population hit 100 million times pi."
John A. Mellman (biostatistician)
September 27, 2012 on the EXLIBRIS-L list

“I cannot live without books.”
Thomas Jefferson to John Adams, 1815.

“Whether or not we can appreciate them individually, it is important to realize that every name matters. Each name on a map helps provide context for the rest. History is a richly colorful mosaic; remove bits here and there, and the full picture begins to fade.”
Larry Perez, Miami
From the Washington Post

"Mathemata mathematicis scribuntur" (Mathematics are written for mathematicians).
Nicolaus Copernicus, De revolutionibus orbium coelestium, 1543.

“Technology is changing. To look something up we used to have to walk over to the computer. Now we can just use the IPhone.”
                                                                                                                                            T. J. Rickey (age 10), 2011.

“Undoubtedly a willing and perseverant reader can learn a lot from this book, but the reviewer would fail in his duty if he were to recommend it for general bedtime reading.”
                                                      J. Lambek, in a review of Anthony Morse,
                                                      A Theory of Sets, in the Canadian
                                                       Mathematical Bulletin, 1968, pp. 354-355.
A poem in symbols:

    ((12 + 144 + 20 + (3 * 4^(1/2))) / 7) +  (5 * 11)  =  9^2 + 0

and in English:

    A dozen, a gross, and a score,
    Plus three times the square root of four,
    divided by seven,
    plus five times eleven,
    equals nine squared and not a bit more.
                                                                                                                       John Saxton

“Because of general confusion and an abundance of errors, the paper is without value.”
W. V. Quine in a review of a paper by L. O. Kattsoff in the
first volume of the Journal of Symbolic Logic, 1936, p. 43.

“In many colleges, it is possible for a boy to win 12 letters without learning how to write one.”
Robert Maynard Hutchins,  President of the University of Chicago
in The Saturday Evening Post  (1939?) as quoted in the
New York Times, 17 September 2011, p. D1.

“Religion divides people, logic brings them together.”
Alfred Tarski as quoted by Henry Hiż.

“Only beautiful works will persist for ages and exert their influence on the following generations.”
Jan Łukasiewicz, “O nauce” (On Science), 1915.

Bertrand Russell [in a lecture to the “Heretics” society] said that the Ten Commandments were like the customary rubric for a ten-question examination paper: ‘Only six need be attempted.’
Quoted in  John Haffenden, William Empson, vol. 1, p . 108.