Life comes with few guarantees, but you can always count on problems. In a long life, you’ll encounter lots and lots of problems, some easy, some hard, but all requiring solutions.
In this regard, George Pólya’s How to Solve It: A New Aspect of Mathematical Method doesn’t simply serve as a guide to tackling math problems but also as a handbook for managing challenges in any area. Polya wisely recommends that we always begin by understanding the problem, followed by carefully devising a solution. Unfortunately, the process does not end there. We still have to do the work to implement the solution.
“To devise a plan, to conceive the idea of the solution is not easy. It takes so much to succeed: formerly acquired knowledge, good mental habits, concentration upon the purpose, and one more thing; good luck. To carry out the plan is much easier, what we need is mainly patience.”
Here, I regretfully disagree with the estimable Polya. Problem solvers certainly need the patience to implement the plan they’ve already devised. But problems on tests like the SAT and ACT require healthy applications of a few other virtues:
If your plan made sense before you started, commit to following it through to the end.
When you do the work, pay attention to every step.
Don’t delay putting in the work on one problem when you have so many more ahead of you.
Those who would solve problems on tests and in life cannot ever be content to simply identify what needs to be done. They have to do the actual work to solve those problems as patiently, carefully, and urgently as possible. Commit to carrying out those grand plans. As Michael Jordan–no stranger himself to the link between effort and results–said, “If you do the work, you get rewarded…”