About Solving Problems Now we've seen a problem and worked out a solution, however rough, let's look at the whole business of problem solving. There is no way that at the first reading i can expect you to grasp all the infinite subtleties of the following discussion. So read it a couple of times and move on. But do come back to it from time to time. Hopefully you'll make more sense of it all as time goes on. Holton's Analysis of solving problems a. First take one problem . Problem solving differs in only one or two respects to mathematical research. The difference is simply that most problems are precisely stated and there is a definite answer (which is known to someone else at the outset). All the steps in between problem and solution are common to both problem solving and research. The extra skill of a research mathematician is learning to pose problems precisely. Of course he/she has more mathematical techniques to hand too. b. Read and understand . It is often nec...