March 27, 2009
Apparently the jury is still out on this issue but the links below provide some encouragement:
Update: I have just found an interesting follow-up on the Cult of Genius post, The Cult of Theory, at Chad Orzel’s blog.
Update 2: an interesting recent discussion at the Backreaction blog.
Update 3: see this post by Peter Turney and this article
March 12, 2009
Michael Nielsen: Principles of Effective Research
See also his blog for more career advice.
March 10, 2009
Richard Hamming in his famous talk You and Your Research offers superb advice on how to do great science.
Update (via Stephen Kinsella): This talk was also recently published here, so now one has an official reference to cite.
Update 2 (via the Unruled Notebook): the videos of a more recent version of this talk given by Hamming himself in the 90s are available here.
Further advice can be found in the other posts on this blog, e.g. here and here. Also, there are two recent followup papers (On the Process of Becoming a Great Scientist and Ten Simple Rules for Doing Your Best Research, According to Hamming) that could be of some interest.
March 10, 2009
The career advice from Sir Michael Atiyah (see also his lecture containing some bits of career advice (hat tip: N.E.W.)), Béla Bollobás, Alain Connes, Dusa McDuff, and Peter Sarnak is here:
Advice to a Young Mathematician
This is an excerpt from The Princeton Companion to Mathematics. By the way, the most recent errata for PCM are here.
See also great advice from E.W. Dijkstra and J.H. Conway, excellent career advice and writing tips from the blog of Terence Tao, and Six Rules for Rewriting at the Michael Nielsen’s blog.
Finally, here go the interviews containing some nice bits of career advice: Alain Connes, Maxim Kontsevich, Sergey Novikov, Terence Tao (see also his Google buzz page and this blog post).