"Wow, where does the 10 come from?" The number 10 is so unspecial that mathematicians are pretty surprised when it appears and demand an explanationhttps://mathoverflow.net/a/218902/1233
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Yes, I wrote a series of 4 posts on that. I see the last one is riddled with typos that I need to fix.
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Okay, I fixed Part 4, which is Todd Trimble classifying the 10 real superdivision algebras, and connecting that to 8-fold Bott periodicity for R and 2-fold Bott periodicity for C: https://golem.ph.utexas.edu/category/2014/08/the_tenfold_way_part_4.html …
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