We’ve come to the end of our Introduction to Number Theory book. The last thing that we looked at today proved to be pretty interesting, though, so I thought I’d write it up. It is a fun way for kids to learn a little math history, get a little arithmetic practice, and also see (and understand a little bit) of pretty deep math.

The topic begins with Lagrange’s four squares theorem – every positive integer can be written as the sum of four squares:

Next we move forward a little over 100 years to the work of Ramanujan. He found a total of 53 ways to write the positive integers using perfect squares. We explore one of Ramanujan’s formulas here:

Finally, I introduce the work of John Conway and Manjul Bhargava, though we don’t work through any examples. Instead after this short video I showed my son the video that Quanta Magazine made when Bhargava won the 2014 Fields Medal:

Here’s the Quanta magazine article and video is here. If you can choose only one video about mathematicians to show to kids, pick this one – so many points in it to draw in young kids:

My son has really loved learning about number theory. I’m really happy that we were able to go through this book together. He told me last night that he’s decided that he wants to learn more from our old Prealgebra book, so that’s going to be the next topic. My plan now is to make number theory the topic for a relaxed summer math course for both kids – can’t wait for summer to come!