Mathematics at the elementary school level consists of some fundamental concepts like place value for writing numerals, and the four operations (addition, subtraction, multiplication and division) with whole numbers fractions, and decimals. These skills can be mastered by anyone of average IQ though some people of limited IQ will have to work harder than someone of higher IQ to achieve mastery.
High School Math
In junior high, ratio, proportion and operations with integers are the focus as a basis for the development of algebra. Even these concepts can be mastered by those of average IQ, but at this stage, those of higher than average IQ begin to distinguish themselves in their ability to transition more easily into algebraic concepts and particularly problem solving.
Proving theorems in Euclidean geometry becomes a significant obstacle to many lower IQ people as they attempt to master the theorems and create sequences of logical arguments. However, with an investment of time and work, even this and intermediate algebra are accessible to those of average IQ. However, by the time students reach the senior year in high school, being good at math becomes more strongly correlated with IQ.
College Math
The study of college math, including calculus, analysis, advanced geometry, statistics and applied mathematics carries a heavy cognitive load. Those of average IQ can master most of it with a heavy investment of time and effort, but excelling in math at this level is mainly the domain of those of high IQ.
Though it is not impossible for someone of average IQ to complete a graduate course in mathematics, excelling at this level is very unlikely. Those whom I’ve observed excelling in these courses are generally of high or very high IQ. Excelling in graduate courses in mathematics just takes too much psychic energy for a person of average IQ. However, IQ tests do not always reflect true intelligence and someone who has registered an IQ near 100 and is gifted with a huge dose of passion might be able to defy all the odds!
