  The possible existence of a complex structure on the 6-sphere has been a
famous unsolved problem for over 60 years. In that time many "solutions" have
been put forward, in both directions. Mistakes have always been found. In this
paper I present a short proof of the non-existence, based on ideas developed,
but not fully exploited, over 50 years ago. The only change in v2. is in
section 3, where the notation has been clarified.
