Albert Einstein, genius that he was, reportedly commented that, if he only had one hour to solve a problem, he would spend 55 minutes defining the problem and the remaining 5 minutes solving it. No matter that this quote is most likely apocryphal; the brilliance and truthfulness of it transcends its false origins. Any great mind can recognize how much work goes into understanding a problem before actually solving it.
George Pólya certainly understood the reality of problem solving. This highly influential Hungarian mathematician is well-known for his contributions to complex analysis, mathematical physics, probability theory, geometry, and combinatorics. However, he most distinguished himself to the masses through his work on heuristics, which is to say problem solving.
In 1945, Pólya wrote How to Solve It: A New Aspect of Mathematical Method, a small book with a large impact. This volume describes his four principles of problem solving, steps so powerful yet elegant in their simplicity that anyone can understand them. No wonder this book has sold over a million copies and inspired generations of scientists and mathematicians.
What are Pólya’s four principles of problem solving?
First, we have to understand the problem; we have to see clearly what is required.
Second, we have to see how the various items are connected, how the unknown is linked to the data, in order to obtain the idea of the solution, to make a plan.
Third, we carry out our plan.
Fourth, we look back at the completed solution, we review and discuss it.
Easy, right? Yet this process holds the key to the toughest problems found in school, on standardized tests, and perhaps even throughout life. Anyone tackling the SAT, ACT, GRE, or any other math exam will find How to Solve It as useful as any other prep resource. Even better, find a test prep program (like ours) that stresses fundamental heuristics over rote memorization and basic calculation.
Pólya, like Einstein, was a genius. You can harness a little of that intellectual firepower by absorbing the enduring lessons of How to Solve It. After all, problems aren’t just confined to math tests, are they?
Mike Bergin