Mathematical musings: On mathematical research, individual level

• Ability is overrated: raw mathematical talent is only the third most important factor for a satisfying career in mathematics. The most important factor is intellectual curiousity; the second most important factor is intellectual discipline.

  Commentary. Intellectual curiousity is self-explanatory. Intellectual discipline is harder to pin down. One aspect is avoiding various extremes such as
  (i) starting lots of projects but never completing any
  (ii) only attempting do-able problems -- the next problem that suggests itself.
  Another aspect is being able to formulate your own views on what is important and interesting while being aware of other people's views.

• No-one ever got famous from their second 100 papers.

  Commentary. I know you can think of counter-examples, but it's a generality, OK? My conclusion is that at age 45, say, you should reflect on what you want to achieve in the seond half of your career, not just continue on auto-pilot.

• A young mathematician naturally seeks approval from established older mathematicians, but after age 45 it is wiser to pay more attention to what younger people think of your work.

  Commentary. Because they'll be around longer.

• If an author doesn't judge his work important enough to make it easily accessible in electronic form, why should I judge it important enough to cite?

  Commentary. Why indeed.

• Conferences and the arXiv are great places to find out what clever and energetic people are working on. But where do you go to to find out what clever and energetic people are NOT working on?

  Commentary. Reminiscnt of a great quote from Don Knuth: email is great if you want to stay on top of things; But I want to get to the bottom of things!.