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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: 0.246s | 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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1. jebarker ◴[16 Jan 25 23:58 UTC] No.42732516[source]▶
They definitely don't visualize 24 dimensional spheres. When I did my PhD in pure math I found that gradually I just became comfortable working without any visual or spatial intuition and instead relying on the (algebraic and topological) machinery that had been put in place before me. Terence Tao had a nice essay [1] talking about how the final stage in becoming a professional mathematician is developing the intuition to know what is likely true or not in these very abstract spaces.

I also never used a computer for anything other than latex.

[1] https://terrytao.wordpress.com/career-advice/theres-more-to-...