Learn from the masters

People who have solved unsolved problems are the best source. So, do not take the webpage you currently look at too seriously.

Creativity takes time

Thinking about a problem can take all your time. Try a putnam exam problem. It can sometimes occupy you for a day.

Learn by doing

The best books about creativity offer problems which illustrate its mechanisms. Exclusive abstractly reading about creativity alone is worthless.

Trying is valuable

Even trying unsuccessfully to solve a problem is valuable practice. If you can solve a problem immediately, it was either too easy or a pattern was known to you already.

Reflect about problem solving

Collect templates. What mechanisms do work for you? How did the breakthrough happen? What exterior conditions were favorable? Join the socienty for creativity and innovation.

Work alone

If somebody else solves the problem for you, there is almost no benefit. There is a fine line between beneficial collaboration and just following somebody else.

Brainstorm with someone

Solving problems with other people can give you helpful insight how to think and teach things on the meta level.

Avoid tip lists

Including this tasty one ... Make your own list. Be creative!
Added Nov 1, 2012: Tricki Added Nov 23, 2017: A talk of Gellmann: mentions 3 steps of Helmholtz: "saturation", "incubation" and "illumination", to which Poincar'e added "verification" Gram Wallace had already listed these 4 stages. A slide from that talk of Gellmann from 2007:

Oliver Knill, Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA. SciCenter 432 Tel: (617) 495 5549, Email: knill@math.harvard.edu Quantum calculus blog, Twitter, Youtube, Vimeo, Linkedin, Scholar Harvard, Academia, Google plus, Google Scholar, ResearchGate, Slashdot, Ello, Webcam, Spring 2018 office hours: Mon-Fri 4-5 PM and by appointment.