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Expert heuristics for problem solving - George Polya's "How To Solve It"

It is characteristic of an expert to have a systematic approach to problem solving.

A very good example of this is George Polya's How To Solve It, subtitled "A new aspect of the mathematical method". In it he prepares the math student for a problem solving approach, not so much by the memorization of zillions of dry facts, but an approach and a set of heuristics (read "methods", "rules", or even "hacks") for dealing with a broad range of mathematical questions, discovery and invention.

The core of How To Solve It is a structured approach to problem solving, and a dictionary of techniques which can be applied to this structure.

First. You have to understand the problem.
Second. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.
Third. Carry out your plan.
Fourth. Examine the solution obtained.

The dictionary of heuristic follows with short pithy entries on technique, questions like "What is the unknown?" and strategies like "Decomposing and recombining".

This book is a math book, but more than that it's a way of thinking about things - and as such, I've found it useful to refer to whenever I embark on a new project to help me understand what I'm after and the sorts of things I need to learn along the way to get to a satisfactory answer. It is as well a brilliant example of how to distill expertise into a handbook which can carry on teaching long after the expert is gone.

Become an expert by collecting other experts in your field or other fields

How do you become an expert in a field? By writing about that field, repeatedly, until you have mastered it to the level which people find you easily and draw on your expertise.

A big part of being able to write about something twice a day is to have a ready collection of other people to call on for ideas or to ask for details or referrals. By being ready to tap into other people's expertise, you figure out what you need to know fast.

Here from Anne Lamott's Bird by Bird:

There are an enormous number of people out there with invaluable information to share with you, and all you have to do is pick up the phone. They love it when you do, just as you love it when people ask if they can pick your brain about something you happen to know a great deal about -- or, as in my case, have a number of impassioned opinions on.

This is part of the "blogger's secret" series.

The blogger's secret: how to be an expert about anything

You can be an expert with the blogger's secret:

1. Pick a topic.
2. Write about it twice a day.
3. At the end of six months, you will be an expert.

Note well: choose carefully what you want to be an expert about! It's mighty hard to be an expert about more than one thing this way, just because it consumes so much time.