Apparently Atiyah was talking about the "Galois group of the octonions" and the unification of the forces of physics at the Heidelberg Forum. Unfortunately not on the stage -- it didn't make its way into his talk. Can anyone who has heard Atiyah talk about this (at the Heidelberg Forum or elsewhere) say what he has said? (If Atiyah is ok with that being posted here, of course).
"Listening in on some of his conversations, I don’t think I’m violating any confidentiality by reporting that he’s quite taken with the idea that if one could make sense of the “Galois group of the octonions” one would find that it lies at the heart of unification of the forces of physics. I can’t do justice to his arguments for this, but, if you can find him, I’m sure you’ll get an enthusiastic explanation." (Via http://scilogs.spektrum.de/hlf/sir-michael-atiyah-unity-mathematics-physics/ )