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Mathematicians discover new way for spheres to 'kiss'

(www.quantamagazine.org)
161 points isaacfrond | 1 comments | 16 Jan 25 09:57 UTC | HN request time: 0s | source
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danwills ◴[16 Jan 25 11:34 UTC] No.42724002[source]▶
I'd really love to know what the mathematicians are actually doing when they work this stuff out? Is it all on computers now? Can they somehow visualize 24-dimensional-sphere-packings in their minds? Are they maybe rigorously checking results of a 'test function' that tells them they found a correct/optimal packing? I would love to know more about what the day-to-day work involved in this type of research actually would be!
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davethedevguy ◴[16 Jan 25 11:54 UTC] No.42724129[source]▶
Likewise!

In higher dimensions, are the spheres just a visual metaphor based on the 3-dimensional problem, or are mathematicians really visualising spheres with physical space between them?

Is that even a valid question, or does it just betray my inability to perceive higher dimensions?

This is fascinating and I'm in awe of the people that do this work.

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1. tomrod ◴[16 Jan 25 13:24 UTC] No.42724768[source]▶
A circle from a flat 2d manifold can be from a 3d sphere, cylinder, or other cross section.

Our mental models don't extend well beyond 3, possibly 4, dimensions, hence _all_ of our intuition starts to be doubtful after 3 dimensions.