On: Dealing with Hard Problems (2015)

[joshe]

Polya's little "How to solve it" booklet has great advice.

It's great because it's addressed to math classes but based on the practices of a research mathematician. So it's not just solving the problems in the book, it's also about solving new unsolved problems. It's specific to math, but really useful for so many other questions.

There is much more to the book but one of my favorite parts is the Heuristics and their simple explanations. Wikipedia has a good table of them

  Analogy         Can you find a problem analogous to your problem and solve that?
  Generalization  Can you find a problem more general than your problem?
  Induction       Can you solve your problem by deriving a generalization from some examples?
  Specialization  Can you find a problem more specialized?
  Draw a Figure   Can you draw a picture of the problem?
  ...

https://en.wikipedia.org/wiki/How_to_Solve_It

The calm, deliberate attitude of the book is infectious, it's great for getting unstuck from tough problems. So do read the book itself in addition to the wikipedia article.

[ascar → joshe]

Thanks for sharing this! The steps in Wikipedia are so clear and concise in describing how I attempted to track down different bugs.

I'll definitely also read the book and use it as a guideline on what to try next instead of randomly asking myself "what else can I try?".