How Did Claude Shannon Simplify Hard Problems?

David Senra, reading the chapter Constructive Dissatisfaction in Jimmy Soni and Rob Goodman's A Mind at Play, says Claude Shannon simplified hard problems before he tried to solve them. Shannon proposed six strategies. The first, which he stated outright, is to start by simplifying. Almost every problem is befuddled with extraneous data, and bringing it down to the main issues shows what you are trying to do. Simplification cuts away everything except what makes the problem interesting.

The rest follow the same idea. Encircle the problem with answers to similar questions and see what those answers share. Senra calls that ingenious incrementalism. Shannon put it this way: it seems much easier to make two small jumps than one big jump in any kind of mental thinking. Then restate the question. Change the words and the viewpoint, and do not get trapped by the work already spent. Someone new to the problem sometimes solves it on the first try because old biases are not in the way. Then break an overwhelming problem into small pieces. Shannon pointed out that a proof often starts with results that seem to lead nowhere and reaches the solution by the back door.

Then invert. If the premises will not prove the conclusion, imagine the conclusion is already true and try to prove the premises instead. Last, give the result time and generalize it yourself before someone else does.