Well done, Mr Norris. Now tell us, what IS a national theatre?

Should it have been a woman for the first time in the National’s history?

The National Theatre will be in safe hands. Rufus Norris has not run an institution, but he is a superb director of plays – Festen, Cabaret et al. Besides, the current director, Sir Nicholas Hytner, had not run an institution either when he was appointed, and everyone is agreed that he has been a resounding success.

I regret that the National’s board overlooked Sir Kenneth Branagh. Not since Laurence Olivier, the NT’s founding director, has an established, world-famous actor run the show. And Branagh would have approached the job from a refreshingly different perspective from that of the past few decades. Theatre does not have to be director-led, bizarre as that assertion might seem to directors.

Should it have been a woman for the first time in the National’s history? Well, there was interest in a few key female directors, but they ruled themselves out pretty quickly. A number of smaller but important theatres are now being run by women, so next time the National post comes up, it will be near impossible to argue against a gender change at the top.

Norris, though, is likely to cement the National’s global reputation, and in certain areas extend it. His early remarks about increasing the venue’s reach “in terms of gender balance, cultural diversity and general diversity” are encouraging.

What I would like to see him do now is tell us what exactly he considers a national theatre to be. It’s a seemingly obvious point, but it is seldom addressed. Should it be the venue that is “national” in the sense of staging and championing home-grown writing, past and present? Should it be the venue that instead presents the best plays from around the world, performed to the highest standards? Should it be national in the sense of touring more widely? How should it relate to the National Theatres of Scotland and Wales, neither of which existed the last time the National Theatre appointed an artistic director?

Congratulations, Mr Norris, on being appointed head of the National Theatre. So what, in your view, is it?