Although IQ is our best measure of intelligence developed so far, it offers only a rough approximation as a measure of this multi-dimensional attribute. A test taken in about one hour reveals a great deal about a person’s ability to think in the abstract, to identify patterns in a sequence of pictures or numbers, and to understand metaphor. However, we might ask whether those who achieve the greatest breakthroughs in mathematics and science are those who perform best on these one-hour IQ tests. There is considerable debate about the link between performance in mathematics competitions and performance in mathematical research. Some argue that contests put excessive emphasis on speed while research allows for deeper, more methodical problem solving over an extended time. For example, Vadim Krutetskii who conducted a comprehensive 12-year study of mathematically gifted students in the former Soviet Union stated: (Krutetskii, Vadim A. 1976. The Psychology of Mathematical Abilities in Schoolchildren. Chicago. Chicago University Press. p. 191.)
Among the most promising pupils in mathematics classes are children who fail regularly in olympiads, where hard problems must be solved in a short time. And at the same time, they can solve much harder problems when they are not limited to any strict deadline.
The eureka! moments (immediate insights) that occur in mathematical competitions have little time for the incubation stage in the discovery process that was described by Poincaré. For a top olympiad competitor, these flashes of insight must come after a few minutes of exploration and reflection. In mathematical research, the incubation period might extend over much longer periods of time. The analogy has been drawn between speed chess, which requires quick intuitive assessments and a fast-and-frugal response, compared with standard chess that allows more time for rumination and rational analysis. If the eureka! moments in competitive problem solving follow the same 4-stage process as in mathematics research, we might expect that winners of competitions would also perform well in mathematical research and conversely.
Many winners of math olympiads go on to perform at the highest level as mathematics or physics researchers. However, many do not. Conversely, some who do not perform exceptionally in mathematics competitions, rise to the highest levels of achievement in their research. The kinds of deep discoveries made by Archimedes, Einstein, and Gödel, clearly require time for incubation, and reflection that is not available in mathematical competitions. However, there are those who excel in both olympiads and in mathematical research and no one defines this category more dramatically than Grigory Perelman. He triumphed in mathematical olympiads and later provided the final piece in his proof of the Poincaré conjecture. (For this achievement, he was awarded the Fields Medal and the $1,000,000 Millennium Prize, which he declined.)
Grisha Perelman is certainly a person of high IQ who has solved some of the most difficult problems in mathematics. Yet, Richard Feynman, reputed to have an IQ of 125, was a brilliant physicist whose accomplishments were also in the stratosphere of great intellectual achievements. It seems that the greatest intellectual breakthroughs are attainable only by those of high IQ (especially in abstract domains), but IQ does not serve well in comparing the intelligence of those in the upper echelons of intellectual ability.
