Plan of action

Once a mathematician has understood the problem, what's the next thing he has to do? The answer is develop a plan of action. This can overlap with the task of understanding the problem. It involves drawing, charting, graphing as the mathematician works out what processes need to be implemented to arrive at a solution. The mathematician may not be able to see the way through the problem at this point, and may decide to undertake the processes that have been identified so far, apply them to the problem and see what it looks like then in it's half solved form. Only then might he be able to map the way forward to a complete solution. One of the most powerful methods of understanding a problem and working out a plan for its solution is to attempt to solve a similar, but simpler problem. "How would I solve an easy problem of this type?" is the question that the mathematician asks. Having discerned a method, then the follow up will be "How can I apply this method to the real problem at hand?"