The whole thing that makes a mathematician’s life worthwhile is that he gets the grudging admiration of three or four colleagues.
Donald KnuthScience is what we understand well enough to explain to a computer. Art is everything else we do.
Donald Knuth...methods are more important than facts. The educational value of a problem given to a student depends mostly on how often the thought processes that are invoked to solve it will be helpful in later situations. It has little to do with how useful the answer to the problem may be. On the other hand, a good problem must also motivate the students; they should be interested in seeing the answer. Since students differ so greatly, I cannot expect everyone to like the problems that please me.
Donald Knuth