Yesterday, I provided an answer to the question, “What Kind Of Mindset Or Skills Do You Need To Succeed In The Putnam Competition If You’re Not Naturally Inclined To Prove Things?” In that post, I profiled one of the multiple gold medal winners in the Putnam competitions, summarized the outstanding qualifications of that person and attempted to explain the remarkable gifts of people at this high level of performance. The main “takeaway” message of that post is that these winners of math Olympiads are intellectually gifted. They all work extremely hard, so that people who are less gifted are unlikely to be able to succeed at the highest levels of mathematical accomplishment by merely working harder.
However, some may have the misconception that if they are not good at math competitions, then they cannot be great mathematicians. While a high level of innate problem-solving ability is necessary for a person to excel in these contests, there are people of extremely high problem-solving ability who do not perform well in a timed competition, yet solve some of the most difficult problems in mathematics. Similarly the best chess players are not always those who are the best at speed chess. Some people solve deep problems by ruminating over them during an extended period of time.
