What do mathematicians do

Lots of interesting math floating around the internet this week:

(1) Numberphile had an incredibly cool set of videos featuring Ron Graham talking about Graham’s Number,

(2) The NY Times had two articles on math education:  Why do Americans Stink at Math by Elizabeth Green and Don’t Teach Math, Coach It by Jordan Ellenberg,

(3) Two really interesting blog articles:  Jordan Ellenberg describes progress on understanding the rank of elliptic curves:  Are Ranks Unbounded? and Cathy O’Neil produced a neat little python notebook to walk people through RSA’s encription algorithm:  Nerding out: RSA on an iPython Notebook, and

(4) The “Twitter Math Camp 2014” teacher conference was happening in Oklahoma, which make for 100’s (of not 1000’s) of interesting discussions on twitter about teaching math.

All of of the fun math plus all of the ideas about teaching math made me want to step back and talk to the boys about what mathematicians do.    The math theme of the week seemed to be the difference between bounded and unbounded sets, so I tried to let that idea shape the discussion today.

We began by talking about Platonic solids.    Before turning on the camera we built a few of the Platonic solids out of our Zometool set for props.  Then we talked about what these shapes are and if there are infinitely many of them:

Next we talked about the prime numbers.  Ellenberg’s book How not to be Wrong has a wonderful discussion for a general audience about the prime numbers and I’ve been meaning to use some of his ideas to talk about the primes with the boys.  Luckily for me, right off the bat the boys were asking some questions about primes that Ellenberg answers. The main topic in this part of the talk is about the of primes, though my younger son wonders about the gaps between primes that will discuss in the next video:

Next, gaps between the primes. The boys seemed pretty interested in how the primes spread out. Ellengerg’s idea of using the even numbers and powers of 2 as an example turns out to be a really nice hook, and provides a great framework for talking about the new bounded gaps result:

After spending 10 minutes talking about some fun results about prime numbers, I wanted to spend the last few minutes talking about one way that prime numbers come into play in our daily lives. This part was inspired by Cathy O’Neil’s piece this week. I sort of daydreamed for a bit about an “rank of elliptic curves for kids” talk, but, um . . . , no.

What I focused on instead was the idea from O’Neil’s python notebook that it is easy to multiply two numbers and not so easy to factor. This idea forms the basis of encryption algorithms. Elliptic curves come into play, too, and Ed Frenkel discusses that a little bit in this fascinating video: Elliptic Curves and Cryptography.  But again, that’s for another day.

Definitely a fun week. Neat to see some new and exciting ideas from math in some blogs, and fun to see so much spirited discussion about math education. I think that many of the ideas in theoretical math will appeal to kids – Graham’s number and cryptography are just the two that emerged this week – and it is fun to be able to talk about these ideas and why mathematicians find these ideas interesting with my own kids.

Now, in the spirit of teaching and coaching from Ellenberg’s NYT article, I’m off to Boston to coach Brute Squad.