On Doing Mathematics Research

Tips

  • Guess! Invent. Imagine. Dream.
  • Don't be afraid to make mistakes.
  • Did you make a mistake? What did you learn from it?
  • Don't be discouraged if you can't solve a problem immediately.
    • Try a different approach.
    • Try a slightly different problem.
    • Try a special case.
    • Try a more general problem.
    • Study examples.
    • Look for counter-examples.
  • Have more than one problem to study. When you've momentarily run out of ideas to try on one problem, work on another problem for a while.
  • Write down your thoughts in a notebook (problems, questions, ideas, guesses, examples, mathematical soliloquies, what you'd like to be able to show, sketches of proofs, etc.).
  • It helps to explain your ideas to someone.
  • Ask for help when you need it; offer your help when others need it.
  • Work with a group.
  • Take breaks.
  • Don't wait until you're at a desk to work. Archimedes made his discovery in his bath!
    • Carry some mini-problems around in your head to think about when you have time, here and there.
  • Have fun!

Participant Testimonials