Advice is what we ask for when we already know the answer but wish we didn’t. (Erica Jong)
- Graduate level
- It is important to work hard, and work professionally. But it is also important to enjoy your work.
- Think ahead to understand the way forward; ask yourself dumb questions to understand the way before.
- Attend talks and conferences, even those not directly related to your own work.
- Talk to your advisor, but also take the initiative.
- Don’t prematurely obsess on a single “big problem” or “big theory”.
- Write down what you’ve done, and make your work available. In this regard, I have some advice on how to write and submit papers.
- Postdoctoral level
- Learn and relearn your field, but don’t be afraid to learn things outside your field.
- Learn the limitations of your tools, but also learn the power of other mathematician’s tools. In particular, you should continually aim just beyond your current range.
- In your research, be both flexible and patient.
- You should definitely travel and present your research if given the opportunity. But be considerate of your audience; talks are not the same as papers.
- Be sceptical of your own work, and don’t be afraid touse the wastebasket.
I am also (slowly) in the process of gathering my thoughts on time management from the perspective of a research mathematician.
- Here are some general thoughts on this topic.
- Batch low-intensity tasks together to take advantage of economies of scale and to reduce distraction.
- John Baez’s page on career advice.
- Po Bronson’s article on the relative importance of innate intelligence versus effort.
- Fan Chung’s advice for graduate students.
- Lance Fortnow’s “Graduate Student Guide“.
- Oded Goldreich’s “On our duties as scientists“.
- Richard Hamming’s “A stroke of genius: striving for greatness in all you do“.
- Matt Might’s “Illustrated guide to a Ph.D.“
- Gian-Carlo Rota’s “Ten lessons I wish I had been taught”.
- J. Michael Steele’s “Advice for Graduate Students in Statistics.”
- Ian Stewart’s “Letters to a Young Mathematician“.
- Ravi Vakil’s “For potential students“.
- The Princeton Companion to Mathematics‘ section on advice to younger mathematicians, with contributions bySir Michael Atiyah, Béla Bollobás, Alain Connes, Dusa McDuff, and Peter Sarnak.
- AMS advice page for new PhDs
- AMS graduate student blog
- The Mathematics Stack Exchange has a number of questions and answers on career development (and one can ask further questions that have not already been posed on that site). MathOverflow similarly hasquestions and answers on careers. Finally, theAcademia Stack Exchange has a large number of questions and answers on all academic matters, including career issues.
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