How to Think Like a Mathematician

CHAPTER 5

How to solve problems

It isn’t that they can’t see the solution. It is that they can’t see the problem.

G.K. Chesterton, The Scandal of Father Brown – ‘The Point of a Pin’

Solving mathematical problems is hard and there is no magic formula which solves all problems. If there were, anyone could do it, and employers would not be so keen to hire problem-solving mathematicians. However, in this chapter we will try to provide at least some ideas on how to solve problems.

Let us first distinguish between an exercise and a problem. An exercise ...