As a teacher I encounter all of the typical kinds of students. There’s one kind of student I routinely encounter, usually in a freshman calculus course, that really boils my blood: the failing student who “has always been good at math.”

Oh it’s so annoying! And it’s even worse to hear because the stuff we teach in calculus isn’t really math either. The irony is so thick in the air when a student says it I’m surprised I don’t cough. Invariably, they never actually understood the “math” they were always so good at. I don’t get angry because they don’t understand the material (indeed, that’s the point of the class!). I get mad because they have absorbed a message about what constitutes mathematics that is, at best, misguided.

Of course, the problem is deeper than a handful of students who accidentally say ironically stupid things. The problem is that American high school students are...

The depiction of mathematics in popular science often falls woefully short of reality. Authors tend to prance around the “beauty” of numbers like e, π, and the golden ratio φ, but in all honesty numbers are only one part of mathematics, and they’re not even the best part.

In a series of short vignettes, I want to take a quick dip into some mind-bending ideas that mathematicians enjoy (and use as tools) on a daily basis. Hopefully you can experience the same kind of joy I did when I first learned about these topics, and with luck you just might be enticed enough to dive deeper.

The beauty of mathematics lies in proofs

While there are many different styles of doing mathematics (I plan to write a separate article about this soon), one thing that all mathematicians agree on is the value of a good proof. It’s weird to think of proofs as having an aesthetic quality, but they do. Good proofs...

The depiction of mathematics in popular science often falls woefully short of reality. Authors tend to prance around the “beauty” of numbers like e, π, and the golden ratio φ, but in all honesty numbers are only one part of mathematics, and they’re not even the best part.

In a series of short vignettes, I want to take a quick dip into some mind-bending ideas that mathematicians enjoy (and use as tools) on a daily basis. Hopefully you can experience the same kind of joy I did when I first learned about these topics, and with luck you just might be enticed enough to dive deeper.

There is more than one kind of infinity

This may come as a surprise to many of you. In primary and secondary school very few teachers have a serious discussion about infinity, and how infinity works. Is it a number? Does it obey usual laws of arithmetic? In most American elementary and secondary schools...