In a remarkable new paper, Maryna Viazovska has put forth a proof of a most efficient way to pack unit spheres in dimension 8. In a follow-up paper, Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Viazovska have a similar result in dimension 24.
Dimensions 8 and 24 are especially interesting and easy cases, because there are very symmetric, very efficient ways of packing the spheres together, so good that it makes it much easier to prove that you cannot do any better.
Read my column on dimension 8 at The Huffington Post.
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