One of the most important differences I’ve observed between those who are great problem solvers and those who are not, resides in their attitude. This seems strange, because IQ is crucial to strong problem solving ability.
The greatest problem solvers approach a problem with the belief that they will be able to solve it. Fermat’s proposition was a conjecture that had lasted for 350 years and its proof had eluded the greatest mathematicians during those centuries. Some in the mathematics community thought it might be an undecidable proposition and pursuing a proof was thought by many to be a waste of time. Then, a young British mathematician, named Andrew, decided to dedicate his life to its solution. He tried and failed countless times, working in secret, lest the mathematical community dismiss him as following a “pipe dream”. Then, in the mid 1990’s, as he reached 40 years of age, this relentless problem solver, Andrew Wiles, announced that he had found a proof of Fermat’s conjecture. The mathematics community exploded in a flurry of excitement, scouring the proof to ensure it was valid. Eventually, an error was found and the proof collapsed into nothing. He had failed miserably.
Disheartened, but not discouraged, Wiles told his wife that she would not see much of him in the next while, because he had to put his life on hold while searching for a way to repair the proof. Many months later, Wiles found a way around the obstacle, and after another year of checking by colleagues in his field, it was determined that his new proof was valid. Fermat’s famous conjecture became Fermat’s Last Theorem and Andrew became “Sir Andrew Wiles.”
The story of Andrew Wiles reflects the unrelenting self-assurance and tolerance for failure that is a vital part of great problem solving ability. Certainly, a high IQ is essential for solving arcane and abstruse problems, but a positive attitude is also a necessary condition. Deep problems, such as those solved by mathematicians like Wiles or Perelman, or physicists like Albert Einstein or Stephen Hawking require deep long-term reflection. Much of the solution comes from our subconscious activity as we sleep. But all problem solving whether mathematical, scientific or military comes from considering options, possible scenarios and an unrelenting tolerance for failure. Failure causes poor problem solvers to become discouraged, but it causes the elite problem solvers to double their efforts.
During a career spanning education, academe and business, I have seen many potentially capable people surrender too quickly when attempting to solve a problem, master a skill or learn a computer programming language. If I were training someone to be a top problem solver, I would give them sets of easily-solved problems, helping them enjoy the addictive eureka! sensation that comes with success. Then, I would gradually increase the problem difficulty, causing them to fail more often, helping them to build a tolerance for failure. At the end of the process, their attitude toward a tough problem would be, “Let me have a go at it; I think I can solve it.” This is the process that Sergei Rukshin, coach of the Soviet math Olympiad team, used in training super problem-solvers like Perelman.
Everyone with high or low IQ must approach problem solving slowly and deliberately, but most importantly with an expectation of short-term failure and long-term success.
