Advice to a Young Scientist by Edsger W. Dijkstra

Excerpted from:
http://www.cs.utexas.edu/users/EWD/transcriptions/EWD10xx/EWD1055A.html
another one
http://math.ucr.edu/home/baez/advice.html

Raise your standards as high as you can live with, avoid wasting your time on routine problems, and always try to work as closely as possible at the boundary of your abilities. Do this because it is the only way of discovering how that boundary should be moved forward.

We all like our work to be socially relevant and scientifically sound. If we can find a topic satisfying both desires, we are lucky; if the two targets are in conflict with each other, let the requirement of scientific soundness prevail.

Never tackle a problem of which you can be pretty sure that (now or in the near future) it will be tackled by others who are, in relation to that problem, at least as competent and well-equipped as you are.

Write as if your work is going to be studied by a thousand people.

Don't get enamored with the complexities you have learned to live with (be they of your own making or imported). The lurking suspicion that something could be simplified is the world's richest source of rewarding challenges.

Before embarking on an ambitious project, try to kill it.

Remember that research with a big R is rarely mission-oriented and plan in terms of decades, not years. Resist all pressure --be it financial or cultural-- to do work that is of ephemeral significance at best.

Don't strive for recognition (in whatever form): recognition should not be your goal, but a symptom that your work has been worthwhile.

Avoid involvement in projects so vague that their failure could remain invisible: such involvement tends to corrupt one's scientific integrity.

Striving for perfection is ultimately the only justification for the academic enterprise; if you don't feel comfortable with this goal --e.g. because you think it too presumptuous--, stay out!

another one
http://math.ucr.edu/home/baez/advice.html

John Baez
March 25, 2007
I have reached the stage where young mathematicians and physicists sometimes ask me for advice. Here is my advice. Most of it applies to grad students and postdocs in any branch of science who seek an academic career involving research. The stuff on giving good talks will be helpful to almost all scientists, since most give pretty bad talks. Near the end I have a section on a more specialized question that vexes many students who email me: should I go into math or physics?
On Keeping Your Soul
Some Practical Tips
Go to the most prestigious school and work with the best possible advisor. A good advisor will give you a hot topic to work on where you can get results that people will find interesting. A good advisor will be so famous that merely being their student will cause people to be interested in you. A good advisor will go to bat for you when it comes time for you to get a job. A good advisor will be politically well-connected and lubricate your way straight to the holy groves of academe. A good advisor will also work your butt off and scare the crap out of you by expecting you to know about millions of things - don't let that put you off.
Publish. Publish papers that get definitive results on fashionable subjects, so they'll get cited. Publish papers that open up promising new lines of investigation. Publish papers that people can actually read - but don't tell anyone else this trick, or everyone will start doing it, and then where will you be? Publish papers that show you have your own research program. Publish papers that create a shock wave the moment they hit the archive! But most importantly: publish.
Go to conferences. There's an infinite number of conferences, and you should go to them. Give lots of talks, chat with lots of people, make connections, find out where the jobs are, find out what people are working on, find out what people will be working on. Have fun and be friendly. And most of all: give good talks!