Leonhard Euler

• [upon losing his right eye's sight] Now I will have less distraction.

Isaac Newton

• If I have been able to see further, it was only because I stood on the shoulders of giants. [Letter to Robert Hooke]
• I will not define time, space, place and motion, as being well known to all. [Principia Mathematica]

Albert Einstein

• If we knew what it was we were doing, it would not be called research, would it ?
• The search for truth is more precious than its possession.
• God does not play dice.
• Imagination is more important than knowledge.
• No, this trick won't work...How on earth are you ever going to explain in terms of chemistry and physics so important a biological phenomenon as first love?
• Only two things are infinite, the universe and human stupidity, and I'm not sure about the former

Carl Friedrich Gauss

• When a philosopher says something is true then it is trivial. When he says something is not trivial then it is false.

Archimedes

• Give me a place to stand and I will move the earth. [On the lever in Pappus Synagoge]

David Hilbert

• No one shall expel us from the paradise that Cantor has created for us.
• Sometimes it happens that a man's circle of horizon becomes smaller and smaller, and as the radius approaches zero it concentrates on one point. And then that becomes his point of view.

Alan Turing

• We can only see a short distance ahead, but we can see plenty there that needs to be done.

Paul Erdos

• There'll be plenty of time to rest in the grave.

Niels H. Abel

• [A reply to a question about how he got his expertise:] By studying the masters and not their pupils.

Edmonds (1966)

• The classes of problems which are respectively known and not known to have good algorithms are of great theoretical interest ... I conjecture that there is no good algorithm for the traveling salesman problem. My reasons are the same as for any mathematical conjecture: (1) it is a legitimate mathematical possibility; and (2) I do not know.

G. H. Hardy

• Beauty is the first test: there is no permanent place in the world for ugly Mathematics.

Augustus De Morgan

• [When asked about his age.] I was x years old in the year x^2.

Rene Descartes

• It is not enough to have a good mind. The main thing is to use it well.

Benjamin Disradeli

• There are three kinds of lies: lies, damned lies, and statistics.

Herman Minkowski

• 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.

Doron Zeiberger

• [Upon receiving his Steel Prize (with H. Wilf) in 1998] He also thanked all his collaborators and mentioned his main influencers some of whom are: Devorah Segev, his seventh grade math teacher, Joe Gillis, who in his early teens first made him into a mathematician through his 'Gilyonot le Matematika', his advisor Harry Dym who initiated him into research, his god-advisor *** Duffin who discretized him, Leon Ehrenpreis who dualized him, Gian-Carlo Rota who umbralized him, *** Askey who hypergeometrized him, George Andrews who q-fied him, Herb Wilf who combinatorized him, and Dominique Foata who bijectified him.

• The future belongs to those who believe in the beauty of their dreams.

Gandhi

• Hesitating to act because the whole vision might not be achieved, or because others do not yet share it, is an attitude that only hinders progress.

Donald E. Knuth

• I was surprised to learn that the writing of programs for TeX and for METAFONT proved to be much more difficult than all the other things I had done (like proving theorems or writing books). The creation of good software demands a significantly higher standard of accuracy than those other things do, and it requires a longer attention span than other intellectual tasks.
• My work on typography has made me so conscious of the low-level details of printing that I can no longer read any books without being intensely aware of the shapes and spacing of all the individual letters. When I sit down in a restaurant and look at the menu, I subconsciously study the fonts of type so carefully that it sometimes takes me five minutes before I realize that the menu is about food.

Leslie Lamport

• Mathematicians tend to be conservative, and many are unwilling to consider that there might be a better way of writing proofs. But, I am told that mathematicians are embarrassed to learn that they published incorrect theorems, so they are motivated to avoid errors. I believe they will like structured proofs if they can be persuaded to try them.
• Computer scientists are more willing to explore unconventional proof styles. Unfortunately, I have found that few of them care whether they have published incorrect results. They often seem glad that an error was not caught by the referees, since that would have meant one fewer publication. I fear that few computer scientists will be motivated to use a proof style that is likely to reveal their mistakes.

Vasek Chvatal
[Linear Programming, page 252]

• Do not try to visualize n-dimensional objects for n>=4. Such an effort is not only doomed to failure - it may be dangerous to your mental health. (If you do succeed, then you are in trouble.)
  

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• Ho.c nhu+ nghi.ch thu?y ha`nh cha^u, ba^'t tie^'n ta^'t thoa'i\.
  Ta^m nhu+ bi`nh nguye^n mu.c ma~, di. pho'ng nan truy\.

Harold Belson and Gerald Jay Sussman
[From the "Structure and Interpretation of Computer Programs"]

• It is better to have 100 functions operate on one data structure than to have 10 functions operate on 10 data structures
• Computer language is not just a way of getting a computer to perform operations but rather that it is a novel formal medium for expressing ideas about methodology. Thus, programs must be written for people to read, and only incidentally for machines to execute.
• "Computer Science" is not a science that its significance has little to do with computers. The computer revolution is a revolution in the way we think and in the way we express what we think
• Mathematics provides a framework for dealing precisely with notions of "what is." Computation provides a framework for dealing precisely with notions of "how to".
• We do not know who produced the Chinese edition, but we consider it an honor to have been selected as the subject of an "unauthorized" translation.

Aldous Huxley

• The charm of history and its enigmatic lesson consist in the fact that, from age to age, nothing changes and yet everything is completely different.

Alexander Graham Bell

• When one door closes another door opens; but we so often look so long and so regretfully upon the closed door, that we do not see the ones which open for us.

Anatole France

• The whole art of teaching is only the art of awakening the natural curiosity of young minds for the purpose of satisfying it afterwards.