As I often update old posts instead of writing new ones , below is the (possibly incomplete) list of most recent updates:

• Career advice from the Fields medalists and some other mathematicians (last update: November 7, 2009)
• How to Write a Really Good Research Paper (last update: October 29, 2009)
• How to Choose a Research Topic (last update:  October 29, 2009)
• Hunting Down the Old References (last update: June 22, 2009)
• Academic Networking: on the Network and beyond (last update: June 22, 2009)
• Academia or Industry? (last update: June 6, 2009)
• How to Maximize Citations (last update: June 1, 2009)

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I have found (hat tip: Yuri Kryakin)  a great interview in Russian with Ivan Panin, where he reminesces, inter alia, about his teacher, a prominent mathematician Andrei Suslin and the way he works.  The whole text is pretty long and very interesting but it is quite difficult to find reasonably self-contained excerpts to translate into English for those who don’t speak Russian, so let me give you just one bit as a teaser:

Suslin tackled the problems roughly as follows: first we see [the problem or the result to prove -- S.R.], then we believe [that we can solve it or that we can prove the result -- S.R.], and then we prove it. Because if you don’t believe, you will not have your vision materialized.

According to Sir Michael Atiyah, the most important quality for a working mathematician is the ability to maintain concentration for a long time.  Via Konstantin Zuev (original post in Russian).

Israel Gelfand (September 2, 1913 — October 5, 2009). R.I.P.

To learn more about him, see e.g. the excellent post by Terence Tao.

While writing the research papers one quite often needs to get back to the full texts of old (pre-Internet or at least pre-arXiv) references. Of course, having access to a good library and/or the interlibrary loan usually solves the problem but can be somewhat time- and cost-consuming.

It is not that well known, however, that there is a fair chance to find the old paper or preprint you need online for free. Of course, the first thing to try is Google or perhaps another search engine of your choosing. However, if this does not work, you still have a fighting chance, at least as far physics and mathematics are concerned. The places to try are:

• the KISS preprint server (you can also try the umbrella interface at SPIRES)  allows you to search in (and get to the full text of) a huge database of scanned preprints  going back to the 1970s at least. The database covers mostly high-energy physics and related areas, including a fair share of mathematical physics and mathematics. For instance, you can find there a number of preprints by Richard Feynman, including the unpublished ones.
• the Digital Mathematics Library
• NUMDAM and CEDRAM (French mathematical journals)
• The Project Euclid
• MathNet.Ru (Russian mathematical journals)

All items but KISS are purely mathematical databases (to be precise, MathNet.Ru includes several physics, mechanics and mathematical physics journals as well).

If you know of other similar databases (be it in physics, mathematics, life sciences,…), please feel free to drop a comment with the relevant link(s).

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This great lecture by a prominent physicist can be found here (hat tip: Biocurious)

This very interesting and very controversial issue is discussed here, here and here. The discussion was triggered by this post at the YFS blog on the all not-too-nice kinds of people one encounters in science and on losing one’s illusions down the road into the academe (see also here for a related post at the RS blog); for a kind of alternative point of view see here.

See this article from the Science Careers (hat tip: ZapperZ)

Update: on the broader issue of leaving academia see also here, here, here, and here. There also is a fair number of blogs and web sites addressing this issue, for instance:

• Alternative Scientist
• Leaving Academia
• Beyond Academe (primarily for historians leaving the academia)
• Beyond the Ivory Tower and Moving to a Nonacademic Career series at The Chronicle of Higher Education

Choosing a research problem to work on is a tough decision to make, and the relevant advice is rather scarce.

So far I have found only a handful of reasonably looking tips:

• work on important problems (R. Hamming, You and Your Research)
• go for the messes, i.e., for the areas far from being crystal clear
  (S. Weinberg, Scientist: Four golden lessons)
• look for an unoccupied niche that has potential (this and some other good tips can be found in the paper Picking a research problem — the critical decision which is primarily addressed to the researchers in biology and medicine but can be of interest to the other scientists too)
• try to move beyond the subject of your Ph.D. thesis (if you have already defended one, indeed) or your postodoc (or your postdoctoral mentor, for that matter); more broadly, beyond your current area of research (see e.g. this post of Terence Tao). This has an extra benefit of reducing the risk of being scooped as discussed here.
• do something you will enjoy doing and what you feel you can do
• your work should rather open the way to new breakthroughs than close the whole subject down

The last three tips are somewhat of a common wisdom and can be found in a number of places; see e.g. the article Choosing a research topic by Richard Reis, which contains some further interesting thoughts on the subject.

See also:

• Uri Alon: How to choose a good scientific problem
• Michael Nielsen: Principles of Effective Research
• this post of Terence Tao

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