Intelligence is a characteristic spanning several cognitive dimensions, including neural efficiency, memory, intuition, creativity, capacity for abstraction and power of visualization, among others. Although the IQ test provides the best measure of intelligence that we have, it addresses only some of these dimensions. For that reason, it is correlated to intelligence rather than providing a precise measure of it.
To give an example of a cognitive dimension that is not captured by an IQ test, we examine the ability to solve deep mathematical problems. An IQ test taken over a period of 45 minutes or more is a brief snapshot of a person’s ability to see patterns, make quick connections and do simple problem solving. However, the ability to solve deep problems in subjects such as mathematics or physics that are worthy of a Fields medal or Nobel Prize is not measurable on an IQ test.
This fact emerges in the debate about the link between performance in mathematics competitions and performance in mathematical research. Some argue that mathematics olympiads put excessive emphasis on speed while research allows for deeper, more methodical problem solving over an extended time. Vadim Krutetskii who conducted a comprehensive 12-year study of mathematically gifted students in the former Soviet Union stated:
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 that occur in mathematical competitions have little time for the subconscious rumination that is often in play in subconscious problem solving. For a top olympiad competitor, the 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 cognitive processes as in mathematics research, we would expect that winners of competitions would also perform well in mathematical research and conversely.
While many winners of math olympiads go on to perform at the highest level in mathematics or physics research, 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– time that is not available in mathematical competitions, nor on an IQ test. So, we can regard IQ as a good approximation of intelligence, but it should not be seen as a limit to, nor a guarantee of, intellectual performance.
