Lesson Five: You don’t have to be a genius to do creative work.
Lesson Six:You must measure up to a very high level of performance.
Lesson Three: By and large, “knowing how” matters more than “knowing what.”
and, occasionally even surprising:
Students join forces on the problem sets, and some students benefit more than others from these weekly collective efforts. The most brilliant students will invariably work out all the problems and let other students copy, and I pretend to be annoyed when I learn that this has happened. But I know that by making the effort to understand the solution of a truly difficult problem discovered by one of their peers, students learn more than they would by working out some less demanding exercise.
I am often asked why there are so few applied mathematicians in the department at MIT. The reason is that all of MIT is one huge applied mathematics department; you can find applied mathematicians in practicially every department at MIT except mathematics.
Take a look!