There's widespread confusion about the nature of mathematical ability, for a variety of reasons:

Most people don't know what math is.
Most people don't know enough statistics to analyze the question properly.
Most mathematicians are not very metacognitive.
Very few people have more than a casual interest in the subject.

If the nature of mathematical ability were exclusively an object of intellectual interest, this would be relatively inconsequential. For example, many people are confused about Einstein’s theory of relativity, but this doesn’t have much of an impact on their lives. But in practice, people’s misconceptions about the nature of mathematical ability seriously interfere with their own ability to learn and do math, something that hurts them both professionally and emotionally.

I have a long standing interest in the subject, and I’ve found myself in the unusual position of being an expert. My experiences include:

Completing a PhD in pure math at University of Illinois.
Four years of teaching math at the high school and college levels (precalculus, calculus, multivariable calculus and linear algebra)
Personal encounters with some of the best mathematicians in the world, and a study of great mathematicians’ biographies.
A long history of working with mathematically gifted children: as a counselor at MathPath for three summers, through one-on-one tutoring, and as an instructor at Art of Problem Solving.
Studying the literature on IQ and papers from the Study of Exceptional Talent as a part of my work for Cognito Mentoring.
Training as a full-stack web developer at App Academy.
Doing a large scale data science project where I applied statistics and machine learning to make new discoveries in social psychology.

I’ve thought about writing about the nature of mathematical ability for a long time, but there was a missing element: I myself had never done genuinely original and high quality mathematical research. After completing much of my data science project, I realized that this had changed. The experience sharpened my understanding of the issues.

This is a the first of a sequence of posts where I try to clarify the situation. My main point in this post is:

There are several different dimensions to mathematical ability. Common measures rarely assess all of these dimensions, and can paint a very incomplete picture of w

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