When a student comes and asks, "Should I become a mathematician?" the answer should be no. If you have to ask, you shouldn't even ask.
It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.
... the student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us a faculty that can pass our Master's exams."
Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick.
A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to reason better.
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