- "There is no royal road to geometry." Attributed to Euclid.
- "I had no need of that hypothesis." Pierre Simon de Laplace.
- "It is not possible to feel satisfied at having said the last word about some theory as long as it cannot be explained in a few words to any passer-by encountered in the street." Joseph D. Gergonne.
- "Mathematics is the art of giving the same name to different objects." Henri Poincare.
- "The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics."
- Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game. G. H. Hardy, (1941) A Mathematician's Apology.
- "Hence a wealth of information creates a poverty of attention and a need to allocate that attention efficiently among the overabundance of information sources that might consume it." Herbert A. Simon, (1971).
- "Essentially, all models are wrong, but some are useful." George E.P. Box & Norman R. Draper (1987), Empirical Model-Building and Response Surfaces.
- "The best of ideas is hurt by uncritical acceptance and thrives on critical examination." George Polya (1956), How to Solve It.
- As a joke I said, "What is the purpose of Life? Proof and conjecture, and keep the SF's score low." Paul Erdos, N is a Number: A Portrait of Paul Erdos.
- "Three o'clock is always too late or too early for anything you want to do." Jean-Paul Sartre.
- "Karl Marx asked all the good questions. But he did give no good answers to them." Douglas C. North.
- "Anyone who believes in indefinite growth in anything physical, on a physically finite planet is either mad, or an economist." Kenneth E. Boulding.
- "The first principle is that you must not fool yourself — and you are the easiest person to fool."
- "No problem is too small or too trivial if we can really do something about it." Richard P. Feynman.
- If you keep proving stuff that others have done, getting confidence, increasing the complexities of your solutions- for the fun of it - then one day you'll turn around and discover that nobody actually did that one! And that is the way to become a computer scientist. - Richard P. Feynman - (Feynman Lectures on Computation).
- "I suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail." Abraham Maslow.
- "I had to leave my country to remain a physicist." Abdus Salam (2004), One Hundred Reasons to Be a Scientist.
- "Good artists copy, great artists steal." attributed to Pablo Picasso (1989) but he might have stolen it.
- "There is a general principle that a stupid man can ask such questions to which one hundred wise men would not be able to answer. In accordance with this principle I shall formulate some problems." V.I. Arnold.
- "A paper in Economics which is not rejected should not be published". Ariel Rubinstein.
- "When you work on a mathematical problem, you put together all the ingredients and you mix and mix and mix ... you wait until there is a chemical reaction between the ideas: Bump! Ah, it all come together in the good way." Cedric Villani.
- "I think the mathematics of the 20th century is best presented around programs, not problems." Yuri I. Manin.
- "Name one theory in all of the social sciences which is both true and nontrivial?" Stanislaw Ulam.
- "In economics we believe that demand and supply meet. In mathematics we believe that inconsistencies are unsustainable." - N.U-
- "Until the 20'th century probability existed within the law of large numbers, but since then this relation is reversed." - N.U.-
- "Ярьдаг юмныхаа эсрэгийг хийж буй хүн нэн өрөвдөлтэй харагддаг." -Н.У-
- Most scientists try to make jumps while most of science is reluctant to discontinuous progresses. - N.U.-
- Category theory is the place for LAZY mathematics, whereas complex analysis is a FREEDOM. - N.U.-
- In academic world all the interesting discussions happen during the process of publication, behind the scene, so that once our works get published there remains very little interest. - N.U.-
- "..., though it may be said, in any country at any time, one is usually both ambitious and poor at the beginning of one's career." - Goro Shumira-.