The Polymath Project aimed to prove a mathematical result known as the density Hales-Jewett (DHJ) theorem. Although the proof of DHJ is complex, the basic statement can be understood by anyone. Take a look at the following three-by-three grid:

I’ve marked seven of the squares on the grid with a dot; as you can see, it’s possible to draw a line through three of those dots. By contrast, the configuration in the following picture is *line-free*—you can’t draw a line through any three of the dots:

If you play around a bit, you’ll discover that this configuration is the largest possible line-free ...

Start Free Trial

No credit card required