About two years ago I saw this Numberphile interview with Ed Frenkel:
One of the ideas that Frenkel mentions in the interview is that professional mathematicians haven’t done a good job sharing math with the general public. Although I’m not really the kind of professional mathematician Frenkel was talking about, I took his words to heart and have been on the lookout for math to share – especially with kids.
It turns out that there are some fantastic ideas that are out there for kids to see. Some surprising fun I had sharing Larry Guth’s “no rectangles” problem with kids earlier this week (see below) made me want to share some of the ideas I’ve found in the last couple of years, so here are a few examples:
(1) One of the most incredible lectures that you’ll ever see is Terry Tao’s “Cosmic Distance Ladder” lecture at the Museum of Mathematics in New York City:
I used Tao’s video for three projects with my kids – but there are probably 20 math projects for kids you could get out of it.
Part 1 of using Terry Tao’s MoMath lecture to talk about math with kids – the Moon and the Earth
Part 2 of using Terry Tao’s MoMath lecture to talk about math with kids – Clocks and Mars
Terry Tao’s MoMath lecture part 3 – the speed of light and paralax
(2) The Museum of Math’s public lectures are a great source beyond Tao’s lecture.
Here’s a project based on Bryna Kra’s lecture:
Angry Birds and Snap Cubes – Using Bryna Kra’s MoMath public lecture to talk math with kids
Eric Demaine’s lecture was part of our Fold and Cut theorem project:
Fold and Cut part 3
and I can’t say enough good thinks about Laura Taalman’s work – she’s inspired dozens of our projects. Just search for her name on the blog:
(3) and Speaking of Fold and Cut . . .
Katie Steckles and Numberphile put together an incredible video about the Fold and Cut theorem. I used the video this week for project with 2nd and 3rd graders at my younger son’s school earlier this week. Steckles’s presentation is so incredible – this is the kind of math that really inspires kids:
We used it for three projects (including the Eric Demaine one above):
Our One Cut Project
The Fold and Cut Theorem is Awesome!
In prepping for the grades 2 and 3 projects I also totally coincidentally ran across a “fold and punch” exercise that is a great activity to try with kids before trying out fold and cut:
(4) Another great success with the 2nd and 3rd graders was Larry Guth’s “no rectangles” problem. I had a great time playing around with this problem with my kids, but nothing prepared me for how enthusiastic the kids in the two programs were about this problem.
Larry Guth’s “No Rectangles” problem
After the 3rd grade night, Patrick Honner sent me this picture that I used to wrap things up with the 2nd graders.
(5) The Surreal Numbers
I’d seen John Conway’s surreal numbers previously via an amazing Jim Propp blog post:
The Life of Games.
and I wanted to revisit them after finally reading Donald Knuth’s book:
Revisiting the Surreal Numbers
Infinity + 1 and other Surreal Numbers
Playing with the surreal numbers via checker stacks is an incredibly engaging way for kids to learn about mathematical thinking.
(6) Speaking of John Conway –
In the 2014 edition of the Best Writing in Mathematics Conway had an article about variations on the Collatz conjecture. It was a fascinating article that even gave us the idea to translate some of the math into music.
The Collatz Conjecture and John Conway’s “Amusical” variation
I’ve also talked with the boys about the standard version of the Collatz conjecture:
It is a great way to introduce kids to an unsolved problem in math while also sneaking in a little bit of arithmetic practice!
(7) Occasional contest math problems
I happened to run across another MoMath lecture yesterday – this one by Po-Shen Loh. He was talking about “Massive Numbers.” I thought maybe he’d be talking about the book “Really Big Numbers” by Richard Evan Schwartz:
A few projects for kids from Richard Evan Schwartz’s “Really Big Numbers”
or maybe Graham’s Number:
An attempt to explain Graham’s number to kids
The last 4 digits of Graham’s number
but instead he talked about a neat problem from the 2010 International Mathematics Olympiad:
His presentation is fascinating and I even talked through the first version of the problem with my younger son:
Another math contest-like problem I really enjoyed talking about with the kids was this one:
Show that any positive integer n has a (positive) multiple which has only the digits 1 and 0 when represented in base 10.
A challenging arithmetic / number theory problem
(8) Building off of popular books by mathematicians as well as public lectures
I was surprised at how much great math writing and speaking there has been for the general public in the last couple of years.
Jordan Ellenberg’s “How not to be Wrong” inspired several projects – probably my favorite was using his idea of “algebraic intimidation” to talk about the famous 1 + 2 + 3 + . . . = -1/12 video by Numberphile. :
Jordan Ellenberg’s Algebraic Intimidation
Jacob Lurie’s Breakthrough Prize public lecture inspired two projects about a year apart from each other:
Using Jacob Lurie’s Breakthrough Prize Lecture to Inspire Kids
Using Jacob Lurie’s Breakthrough Prize talk with kids
And, Ed Frenkel, who got me thinking about sharing advanced math with kids in the first place has inspired a few projects, too:
Fine Ed Frenkel – you convinced me
Ed Frenkel, the square root of 2, and i
and one of my all time favorites:
A list Ed Frenkel will love
(9) Finally, it would be impossible to write a post like this one without mentioning the work that Evelyn Lamb is doing writing math articles for the general public. I’ve lost count of how many projects she’s inspired, but it is probably well over 20. I’m especially grateful for her talk about topology which have generated really fun conversations with the boys. For example:
Using Evelyn Lamb’s Infinite Earring with kids
Evelyn Lamb’s fun torus tweet
Henry Segerman’s Flat Torus
which arose after Lamb pointed out this video:
So, I’m really happy that mathematicians are sharing so many amazing ideas. I think this is the sort of math promotion that Frenkel had in mind. Hopefully it continues for many years to come 🙂