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more spheresQuanta Magazine
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86% Informative
Isaac Newton and David Gregory came up with the "kissing" problem in 1694 .
In three dimensions, it’s trivial to position 12 spheres around a central one so that each touches it at a single point.
It took mathematicians until 1952 to prove Newton right: In our familiar 3 dimensions, the maximum “kissing number” is 12 .
But in all other dimensions, where more space appears between the spheres, the problem remains open.
The Leech lattice gave mathematicians their best estimates of kissing numbers in dimensions 17 through 23 .
The lattice also gives the best kissing arrangement: Each sphere touches 196,560 neighbors.
In 2022 , graduate student Li decided to try a new way to pack spheres as densely as possible into 24 -dimensional space.
The new structures look very different from the highly symmetric ones inspired by the Leech lattice.
The code-based methods they used to add spheres gave them more irregular configurations.
It’s not clear why changing the signs creates enough space for more spheres.
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