Some Math Problems Seem Impossible. That Can Be a Good Thing — Quanta Magazine

In my latest column for Quanta Magazine I write about the secret power of impossible math problems.

Construct a convex octagon with four right angles.

It probably says a lot about me as a teacher that I assign problems like this. I watch as students try to arrange the right angles consecutively. When that doesn’t work, some try alternating the right angles. Failing again, they insert them randomly into the polygon. They scribble, erase and argue. The sound of productive struggle is music to a teacher’s ears.

Working on impossible problems has a way of helping us better understand what is possible in math, and the impossible plays an important role in the history of mathematics. In my column I explain using several examples, and include a few extra exercises to play around with. The impossible can be frustrating, but also fun!

The entire article is freely available here.