My first program taught me a lot about the errors that I was going to be making in the future, and also about how to find errors. That's sort of the story of my life, making errors and trying to recover from them. I try to get things correct. I probably obsess about not making too many mistakes.

Science is what we understand well enough to explain to a computer. Art is everything else we do.

...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.

We should continually be striving to transform every art into a science: in the process, we advance the art.

I'm obsessively detail-oriented.

AI has by now succeeded in doing essentially everything that requires 'thinking' but has failed to do most of what people and animals do 'without thinking'-that, somehow, is much harder.

The best programs are written so that computing machines can perform them quickly and so that human beings can understand them clearly. A programmer is ideally an essayist who works with traditional aesthetic and literary forms as well as mathematical concepts, to communicate the way that an algorithm works and to convince a reader that the results will be correct.