Section 3. Outlining. The standard topic outline form. Solving problems.
Today I'm going to talk about some thoughts that psychologists have had on how people go about solving problems. The first point I want to make is that there is no one way of solving all problems.

If you think about it, you will realize the obvious fact that there are many different kinds of problems which have to be solved in different ways.

Let's take two very different examples. A student is sitting in his study, trying to solve a problem in mathematics. After an hour, still unsuccessful, he gives up and goes to bed. The following morning he wakes up and wanders into the study. Suddenly, the solution comes to him.

Now for a very different kind of problem. In the Shakespeare play Hamlet, young Hamlet, prince of Denmark, discovers that his father has been murdered by his uncle. The evidence is based on the appearance of his father's ghost, urging him to revenge his death by killing his uncle. Should he accept the ghost's evidence and kill his uncle?

This is obviously a very different kind of problem. Such moral or emotional problems might have no real solution, or at any rate, no solution that everyone might agree on.

There are many other different types of problems apart from these two. In this talk, I'd like to talk about the first kind of problem, the kind that the student of mathematics was involved with.

The solution to that kind of problem is sometimes called an Ah-ha solution, because the solution comes suddenly out of nowhere as it were. And in English, people sometimes say A-ha when a good idea comes to them like that.

Another, less amusing, name for it is insight. For a long time, the student seems to get nowhere, and then there's a sudden flash of insight and the solution appears.