Others have already pointed this out, but it’s worth highlighting.
Terence Tao – recent winner of the Field’s medal (a sort of Nobel prize for mathematics) – has written some really interesting career advice. It’s aimed at mathematicians, but lots of it is more generally applicable, and certainly lots of strikes a chord with academic philosophy. It’s also not just for graduates: e.g. I’m a recent-graduate, and I’m sure there’s lots there that I’m not doing, which it’s good to be reminded of.
The advice to “use the wastebasket” is going to be more difficult now that the University of Leeds has decided to remove all wastebackets from our offices…
HT: Shawn Standefer, Richard Zach
p.s. here’s one thing that struck me as particularly transferable:
“Don’t prematurely obsess on a single “big problem” or “big theory”. This is a particularly dangerous occupational hazard in this subject – that one becomes focused, to the exclusion of other mathematical activity, on a single really difficult problem in a field (or on some grand unifying theory) before one is really ready (both in terms of mathematical preparation, and also in terms of one career) to devote so much of one’s research time to such a project. When one begins to neglect other tasks (such as writing and publishing one’s “lesser” results), hoping to use the eventual “big payoff” of solving a major problem or establishing a revolutionary new theory to make up for lack of progress in all other areas of one’s career, then this is a strong warning sign that one should rebalance one’s priorities. While it is true that several major problems have been solved, and several important theories introduced, by precisely such an obsessive approach, this has only worked out well when the mathematician involved (a) has a proven track record of reliably producing significant papers in the area already, and (b) has a secure career (e.g. a tenured position). If you do not yet have both (a) and (b), and if your ideas on how to solve a big problem still have a significant speculative component (or if your grand theory does not yet have a definite and striking application), I would strongly advocate a more balanced approach instead: keep the big problems and theories in mind, and tinker with them occasionally, but spend most of your time on more feasible “low-hanging fruit”, which will build up your experience, mathematical power, and credibility for when you are ready to tackle the more ambitious projects. “