On 1/8/06, Daniel Asimov <dasimov@earthlink.net> wrote:
The NY Times just printed an obituary for Raoul Bott, Emeritus of the Harvard math dept. who passed away Dec. 20: <http://www.nytimes.com/2006/01/08/national/08bott.html>. It mentions one of his best-known results, "Bott periodicity", which blew me away when I first learned of it as a grad student. [etc etc]
I have to admit I'd kinda assumed that "Bott periodicity" referred to the fact that the real Clifford algebra Cl(n+8,0) generated by n+8 square roots of +1 is isomorphic to 16x16 matrices over Cl(n,0), on no better grounds than that the relevant ur-text is M.F.Atiyah, R.Bott, A.Shapiro "Clifford Modules" Topology vol.3 (1964). Was this conclusion entirely unjustified, or is there some connection? Which reminds me that I recently acquired a copy of the august tome J.H.Conway, D.A Smith "On Quaternions and Octonions" and promptly became mired at Lemma 3 on page 6. I can prove this result easily, but I'm hanged if I can follow their (3 line) proof --- can another reader clarify? Fred Lunnon