He came to fame with A Resounding Tinkle in 1958, which concerned a suburban couple who had been delivered the wrong-sized elephant. ("If it goes berserk in the night I'm not getting up for it.")
Among other plays, he produced his masterpiece, One Way Pendulum, which again featured a suburban family - this time training 500 Speak Your Weight machines to sing the Hallelujah Chorus.
Simpson is a philosopher with an inventive comic brain who commits his aphorisms to theatre, but he is not a natural playwright: he has little interest in character and none at all in plot.
"I live in the present, always have done. I don't know what happens next, and I don't want to. That may be why I cannot handle narrative. I hear the dialogue."
A new play entitled If So, Then Yes ........ is set in an old people's home where a resident dictates his memoirs despite constant interruptions from visitors and an invasion of downmarket pensioners from the Cairngorms.
The script contains shafts of pure Simpsonian comedy: it argues that Sartre won the Nobel Prize largely because of his teeth, for example, and that it was not actually a serpent in the Garden of Eden but an unusually long sausage dog.
Already the National Theatre has baulked at its lack of structure and large cast, which includes "5,000 Red Indians - optional".
Count me in at the Donmar and the National, though I'm a little concerned I can't find any relevant details on the NT's website.