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He is playing the part of a curator of an exhibition of Vincent van Gogh. It is episode 10 in Series 31, written by Richard Curtis (The Black Adder, Mr. Bean).
Digital Spy reports that a 'set insider' told them, "It was a real coup to get Bill Nighy in Doctor Who, especially in Richard Curtis's amazing episode. Bill plays a van Gogh expert with some similar fashion choices to The Doctor himself."
It is said that this story is to take place in 19th century France as well as present day.
Richard Curtis, known to most for creating the popular Blackadder series starring Rowan Atkinson and for romantic comedies like Four Weddings and a Funeral has told The Sun that he will be writing a story for the 11th Doctor (Matt Smith).
Curtis, aged 52, revealed, "There will be a monster. And a famous historical figure will battle the monster." He can not reveal much more.
Some of speculated that the historical figure could be none other than Sir Edmund Blackadder himself. Though this is just speculation.