Research philosophy



  • If you really think about something, you usually produce something.
                Rudolf E. Kalman

  • Nothing is more practical than a good theory.
                Kurt Lewin

  • One who pursues fame at the risk of losing one's self, is not a scholar.

  • When you write a paper, you are not only reporting what you did but also teaching your readers how to do what you did. The journey, one might say, is part of the result ... Good cooks leave good recipes.
                Malcom D. Shuster

  • Easy reading is damn hard writing.
                Nathaniel Hawthorne

  • "When I use a word", Humpty-Dumpty said, in rather a scornful tone, "it means just what I choose it to mean - neither more, nor less".
                Lewis Caroll

  • Even Hilbert had only a few tricks!
                Gian-Carlo Rota

  • It is not sufficient to know whether there is a river beyond the mountain; it does remain to cross this river!
                Vladimir Arnold

  • Mathematics is not abstract, by which I mean that it isn't a fictional model of something real ... Linear algebra isn't a model of something. It exists in itself, and in that sense it is real, not abstract, in the same way that music is real.
                Bruce Francis

  • By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the "truth" but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity - to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs - you deny them mathematics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes.
               Paul Lockhart

  • I'm often reluctant to go running, but once I do, I enjoy it. And if I don't run for several days, I feel ill. It's the same with people who do great things. They know they'll feel bad if they don't work, and they have enough discipline to get themselves to their desks to start working. But once they get started, interest takes over, and discipline is no longer necessary. Do you think Shakespeare was gritting his teeth and diligently trying to write Great Literature? Of course not. He was having fun. That's why he's so good.

    If you want to do good work, what you need is a great curiosity about a promising question. The critical moment for Einstein was when he looked at Maxwell's equations and said, what the hell is going on here?
                Paul Graham