A challenge for professional mathematicians

[March 24th, 2016 update – I’m going to link some articles at the end of the blog as I see them. There are two from today. I’m really happy that people are writing about this!]

I saw this article on gravity waves via a Steven Strogatz tweet this morning:

Seeing the article reminded me of the interview that Numberphile did with Ed Frenkel a while back – in particular, the part from roughly 5:00 to 7:00 when Frenkel discuses the need for mathematicians to do better at sharing their ideas with the public:

Frenkel’s point is that even though the ideas in fields such as biology and physics are just as complicated as the ideas in math, these other areas of science are much better at communicating with the public than mathematics is.

I was reminded of Frenkel’s point again this morning when I learned that earlier this month Maryna S. Viazovska solved the 8-dimensional sphere packing problem. Viazovska’s paper on arxiv.org is here:

The sphere packing problem in dimension 8

Maybe I’m a little biased – especially right now because I’ve been spending this week playing around with 4-dimensional shapes with my kids . . .

img_0947

but I think that the sphere packing problem (i) is something that can be explained to the public (it certainly seems less complicated than gravity waves) and (ii) is something that the public would find to be interesting. There’s not been much of any coverage of Viazovska’s result, though. Here’s what I found doing a simple Google news search:

Screen Shot 2016-03-22 at 2.24.44 PM

So, it sure seems this new result is something that would be great to share with the general public. There are, of course, many different directions an article could go – just off the top of my head:

(A) Jordan Ellenberg does a great job explaining the sphere packing problem and the connection to things like the Leech lattice and Hamming codes in How not to be Wrong,

(B) John Cook and Keith Devlin both have recent blog post with connections to higher dimensional spheres / cubes:

The empty middle: why no one is average by John Cook

Theorem: You are Exceptional by Keith Devlin

(C) Two years ago, Steven Strogatz shared this wonderful paper on N-dimensional spheres:

(D) The 2-dimensional problem of circle packing is something anyone can understand and is pretty fun to play with – here’s an old project I did with the boys using disc golf discs, for example:

 

Screen Shot 2016-03-22 at 2.51.32 PM

Sphere packing (well . . . circle packing)

Also, a version of the circle packing problem was in Jim Propp’s most recent blog post about mathematical thinking:

Believe it, then don’t: Toward a Pedagogy of Discomfort

So – come on professional mathematicians!! – here’s a great opportunity to promote a neat result and bring some really cool math to the public’s attention. Don’t let the physics crowd have all the fun!

A few articles that I’ve seen:

On Gil Kalai’s blog:

A Breakthrough by Maryna Viazovska lead to the long awaited solutions for the densest packing problem in dimensions 8 and 24

Kalai’s blog post also led to a question on Quora:

Why is the solution in dimension 8 such a breakthrough?

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  1. Update: a Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska, building upon Viazovska’s work, have succeeded in proving that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions, and that it is the unique optimal periodic packing. See http://arxiv.org/abs/1603.06518 .

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