Probability and its problems

I am not good at probability. I am reminded of this daily when I open my sock drawer because for some reason, probability problems always involve socks. Perhaps it goes back to Danny Hillis. Danny Hillis founded the Thinking Machines Corporation in 1983, but before that he had a roommate at MIT that would match socks by pulling one sock from a hamper and then pulling sock after sock until he found a matching pair. This troubled Hillis a great deal. He probably wondered how someone could get into MIT, i.e. do many math problems about socks and probability correctly, and yet be so bad at actual socks. Is there a better way to do this? Sorting algorithms are very important in computer science and yet my computer science homework never involved socks. Which is just as well, because I am bad at computer science too.

The reason for this post is that I read a Science magazine article by Emily Riehl called Mathematics is hard for mathematicians to understand too. It’s a great article and there is also a companion Science podcast. While researching Emily Riehl, I discovered she co-taught a freely available Harvard EdX course called Fat Chance: Probability from the Ground Up.

As someone whose probability intuition is below ground level, if possible, I decided to see where the floor for three Harvard mathematicians could be. “Ground up” definitely meant we were starting at the third floor, and possibly outer space.

It turns out the ground floor is really the ground! In the introduction video, the three of them — Emily Riehl, Benedict Gross and John Harris — are at a pub drinking beers and discussing coin flips. It’s remarkably endearing and down to earth. And it doesn’t involve socks.

Benedict Gross passed away in December 2025, so it’s especially nice to see him on the screen making this formidable topic so accessible. His legendary YouTube series on abstract algebra from 12 years ago is still up if anyone is interested!