Advice to a Young Mathematician [pdf]

Ha, Sir Michael Atiyah's advice to a young mathematician includes a great anecdote: ""J. E. Littlewood is reported to have set each of his research students to work on a disguised version of the Riemann hypothesis, letting them know what he had done only after six months. He argued that the student would not have the confidence to attack such a famous problem directly, but might make progress if not told of the fame of his opponent! The policy may not have led to a proof of the Riemann hypothesis, but it certainly led to resilient and battle-hardened students"".

What a great story — sounds like it just leapt off the pages of the McSweeny's list "Zen Parable or Just Someone Being Cruel?".

"If you keep asking yourself such questions when reading a paper or listening to a lecture, then sooner or later a glimmer of an answer will emerge—some possible route to investigate. When this happens to me I always take time out to pursue the idea to see where it leads or whether it will stand up to scrutiny. Nine times out of ten it turns out to be a blind alley, but occasionally one strikes gold. The difficulty is in knowing when an idea that is initially promising is in fact going nowhere. At this stage one has to cut one’s losses and return to the main road. Often the decision is not clear-cut, and in fact I frequently return to a previously discarded idea and give it another try"

'Don't become a scientist!': http://wuphys.wustl.edu/~katz/scientist.html 'Women in science': http://philip.greenspun.com/careers/women-in-science

The career for pure mathematicians(which is more like the humanities, and specific knowledge quite untransferrable) in academia, being better or worse, is open for discussion.