Those of us who teach math are used to hearing two things when we inform anyone of our profession: “I hated math when I was in school” and “I was no good at math when I was in school.” Sometimes both. I sympathize. Math as it’s currently taught deserves to be hated and doesn’t deserve to be learned.

By the time a typical student graduates from high school, he or she has solved hundreds of quadratic equations, graphed scores of hyperbolas, used the phrases “alternate exterior angles” and “alternate interior angles” countless times, and drawn 30-60-90 triangles until his or her fingers were ready to fall off. Why do we make students do so much of these particular topics?

Some people probably think that it’s a natural decision: that’s just what math is, isn’t it? But there are vast landscapes of math that our current curriculum avoids entirely: topology, logic, combinatorics, graph theory, group theory, and many more. Most folks who don’t major in math in college will probably never know that most of these fields exist. They are not too hard to teach to children. Indeed there are children’s books out there which give introductions to all of these topics at levels that children can understand. There are even a few private schools that teach kids this stuff, starting in elementary school.

So why does the mainstream education system remain stuck with parabolas and polynomial long division? Bluntly, that’s what was chosen generations ago, and it hasn’t changed since then. (It’s changed *a little*, I suppose, but not much.) In the industrial revolution, people who worked with their brains needed to solve polynomials by hand and do other suck tasks, so we taught kids how to do that. Today technology has changed everything and the demands and scientists and engineers are totally different. Entire new fields, such as computer programming, have come into existence. We still prepare kids to meet the needs of the 19th century.

Some will say that it’s still important to teach kids how to do everything by hand, even if we have technology that can do it for them. Supposedly the skills are still important. But as a broad statement, this simply isn’t true. Take polynomial long division, the biggest waste of time in any pre-calculus class. Even if a child truly understands what it is, what it’s supposedly to accomplish, and how to do it, it’s still a dead end that does not lead the way to any other useful skills in math.

Math could be and should be an immense amount of fun. It would be if we expanded the curriculum to include other areas of math. Even among students not inclined towards enjoying math, the mere presence of variety and absence of endless repetition would spark their interest.