Letters to a Young Mathematician (Art of Mentoring)

by Ian Stewart

Because the lectures progress through set topics, one step at a time, it is easy for students to think that this is how to learn the material. It is not a bad idea to work systematically through the book, but there are other tactics you can use if you get stuck. Many students believe that if you get stuck, you should stop. Go back, read the offending passage again; repeat until light dawns—either in your mind or outside the library window. This is almost always fatal. I always tell my students that the first thing to do is read on. Remember that you encountered a difficulty, don’t try to pretend that all is sweetness and light, but continue. Often the next sentence, or the next paragraph, will resolve your problem.

It takes a certain insight into your own thought processes as well as a certain discipline to pinpoint exactly what you don’t understand and relate it to your immediate difficulty.

definitive refutation has never been a match for fervent belief.