Research philosophy
Lectures
Quotes
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.
Zuangzi
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
Do not confuse "elementary" with "easy": a proof can certainly be elementary without being easy. In fact, there are many examples of theorems for which a little sophistication makes the proof easy to understand and brings out the underlying ideas, whereas an elementary treatment that avoids sophisticated notions hides what is going on.
Peter Sarnak
"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
It is stupid to claim that birds are better than frogs because they see farther, or that frogs are better than birds because they see deeper. The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it.
Freeman Dyson
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
The great thing about tenure is that it means your research can be driven by your actual interests instead of the ever-changing winds of fashion. The problem is, by the time many people get tenure, they've become such slaves of fashion that they no longer know what it means to follow their own interests. They've spent the best years of their life trying to keep up with the Joneses instead of developing their own personal style! So, bear in mind that getting tenure is only half the battle: getting tenure while keeping your soul is the really hard part.
To do this, you have to make sure you never lose that raw naive curiosity that got you interested in science in the first place. Don't get too wrapped up seriousness. The universe is a cool place; exploring it is fun! ...
So: keep playing around with all sorts of ideas, techniques and tools. Read voraciously. Don't be scared of experts and their jargon. Become one yourself, but then give the game away by explaining things in simple language whenever possible. Talk to lots of people! Teach them; learn from them; don't worry too much about impressing them. Don't be scared to ask basic questions -- and don't be surprised when nobody knows the answers. The simplest questions are the last to be answered.
John Baez
If somebody said what advice would I give to a young person - they always ask that funny kind of a question - I think one of the things that would sort of come first to me is this idea of, don't just believe that because something is trendy, that it's good. I'd probably go the other extreme where if I find too many people adopting a certain idea I'd probably think it's wrong or if, you know, if my work had become too popular I probably would think I had to change. This is, of course, ridiculous but I see the other side of it too often where people will do something against their own gut instincts because they think the community wants them to do it that way, so people will work on a certain subject even though they aren't terribly interested in it because they think that they'll get more prestige by working on it.
I think you get more prestige by doing good science than by doing popular science because if you go with what you really think is important then it's a higher chance that it really is important in the long run and it's the long run which has the most benefit to the world.
Donald Knuth
