Vincent and the Doctor is the tenth episode of the fifth series of Doctor Who. It stars Matt Smith as The Eleventh Doctor, Karen Gillam as Amy Pond, and features Tony Curran as Vincent Van Gogh.
The story is set a short while after the last story, when Rory Williams, Amy's fiance, was erased from existence. Although his erasure from existence means that he has never existed, and Amy can no longer consciously remember him, but she is still upset. The Doctor, being a more experienced time traveler, can remember him, but can do nothing about his disappearance. Instead, he focuses on cheering up Amy. He brings her to an exhibit of the works of Vincent Van Gogh, only to discover that there is an odd figure in one of his paintings...which means there is a mystery to solve, and that means having to ask Van Gogh personally.
The Doctor and Amy find a Van Gogh who is depressed and defeated, drinking heavily and unappreciated for his art. Van Gogh is still hospitable to the two, especially to the beautiful (and now single) Amy. Such flirtations are cast out of the way as they find themselves facing a monster known as a Krafayis, which is a animal-like hunter that has the additional ability to turn invisible. Van Gogh's synesthetic vision allows him to see the monster. Working as a team, the three of them defeat the monster.
The alien monster plot being just a de rigeur part of Doctor Who, the actual point of the episode is Amy convincing The Doctor to take Van Gogh to an art museum in the future to see how high of regard he will be held in. After doing this, Amy and the Doctor then go back to the museum to see if Van Gogh has produced a greater body of work. But it turns out that he still committed suicide at the same time, because interference with time can't prevent that. The episode ends with a meditation on the meaning of time, loss and memory].
The episode, like many past episodes of Doctor Who, is based around The Doctor meeting with an important historical figure-- as he did with Charles Dickens, William Shakespeare or Agatha Christie. Although purists might squabble about fictionalizing a person, I think this episode, at least, was sensitive and insightful.
It also fits into several running themes of Series 5 and The Eleventh Doctor's run: perception, memory and the connection between them. Although the weekly monster might seem slightly hokey at first, it fits in symbolically because it is both blind and invisible. Van Gogh himself is someone who is invisible to his society. Amy struggles to remember Rory, and the Doctor tries to identify an alien by looking at it in a mirror. All of this is, in the grand tradition of symbolism, rather diffuse, but comes into focus when the series is watched as a whole.