For example in Atiyah's $KR$-theory there is the notion of a *Real vector bundle* in contrast to complex or real vector bundles. I am also familiar with the notion of a Real $C^*$-algebra and there are probably a lot more objects with sensible definitions of *Real*.

However Atiyah did not use a capitalized *Real* in his paper "K-theory and reality", so my question is:

Whose ideas was it to write

Realinstead ofreal?

I would also be interested in the general history of this notion, but that's probably too much to ask for (judging from remarks in the above mentioned paper I suspect it starts somewhere in algebraic geometry – of which I hardly know anything.)

notAtiyah in the article mentioned? $\endgroup$ – Mikhail Katz Apr 16 '18 at 9:59