Six-year-old Pierre Bruyère begins to see nothing but white while sleeping. His father takes him to a doctor, who tells him that dreams are unimportant and who is unsure as to whether the dreams will remain. Pierre says that he doesn't want the dreams to go as he likes them.
While visiting an exhibition of Arctic exploration in Paris, Pierre soon realises that this is what his dreams are about and resolves to be an Arctic explorer.
Growing older, he becomes more worried that others will reach the North Pole, and feels guilty that, whenever another expedition failed, he feels delight, despite the deaths involved. At a meeting attended by the Tenth Doctor and Martha Jones, he announces he will reach the North Pole by balloon. He explains the positive aspects of using balloons.
Meanwhile the Doctor is listing negative aspects. Pierre says that his life and that of his two crew members will be the only lives in danger. The Doctor tells Martha that the "big problem" in the situation is that Pierre disappeared in April 1890, and it is currently June 1890.
The Doctor and Martha accompany Pierre on his expedition. The Doctor observes a stall selling clockwork penguins, commenting that "They don't even have penguins in the Arctic." The balloon lifts into the sky, and the Doctor is still talking about penguins.
Pierre spends the next three hours writing in his journal, explaining that the journal is the most important part of the expedition, being a record which will survive even if they die.
A sleep rota is set up. Martha will sleep first. Martha is having her childhood dream that she will one day be a doctor. She realises that she is a doctor, but in her dream, becoming one is a seemingly impossible goal. Suddenly, she is at her medical exams, with the teacher asking her to tell her about the bones of the human body, and about Martha's hopes and dreams. As she begins, the teacher starts to purr. The teacher states that it is cold, and she must feast to keep warm. Martha can now see that the teachers eyes are shards of ice, which makes her think of the ice beneath the balloon. Remembering the balloon, she wakes.
The Doctor says that there is a problem, and dashes around the balloon, tossing things over the side. Pierre shouts that they are still losing height. The balloon is plummeting, and the Doctor begins to throw over the food. The balloon has slowed down, and the Doctor states that "it" wants them to get rid of the food. Pierre replies that the only force there is gravity, and the Doctor argues that they should have crashed on the ice already-something is keeping them aloft.
When they throw over the remaining three food hampers, the balloon begins to rise, and the Doctor states that the mysterious force wants them at its mercy.
One day, Pierre announces that they have reached the North Pole. The Doctor begins to gather everything which they can throw overboard, in case this is necessary.
Martha is feeling less and less hungry, and after more than a week she suddenly realises that she should be starving, but isn't. She falls asleep.
More often than not, her dreams are interrupted by the examiner, who says, "Tell me about the bones, Martha. It's so very cold, I must feast. Tell me about the bones, and why you love them so much."
One day, Pierre announces that they have reached the North Pole. Martha asks how he knows, and he explains that for the past months, they have been travelling at a steady speed. Martha asks him how long they have been travelling for. He says that they have been travelling for four or five months. Martha states that it was a fortnight. Pierre asks the Doctor, who says that they have spent so many years in the balloon that he lost count, and that he tried to shield them from the worst of it. Taking out his sonic screwdriver, he creates a light reaching the ground, which reveals the jettisoned food.
The Doctor explains that the mysterious force has run the same seconds over and over. Pierre passes his journal to the Doctor, who discovers that Pierre has written the same entry in it endlessly.
The Doctor uses his sonic screwdriver to burst the balloon, which remains floating. Hundreds of balloons are revealed, all of which are identical. The only difference is that the copy of Pierre in each is standing between different people.
The Doctor explains that "it" has caught Pierre in a loop, making him repeat the expedition over and over again with different companions, and that the expedition is always doomed to failure. Martha asks why a creature would do that. The Doctor answers that the only thing it can do is eat, and that it feeds on human ambition. Pierre is horrified by this revelation, wondering if his desire to add to human knowledge was actually his.
The nearest copy of Pierre appears to consider this, and begins to climb over the edge of his balloon. The time distortion is corrected and in a rewritten timeline, he becomes a baker at his parents' bakery. On some occasions, he had flashbacks of the 'pure whiteness'.
- At some point Martha went on a date with Leonardo DiCaprio.
- The Doctor has visited the North West Passage.
- Martha once went on holiday to Bermuda.
- An audio version of this story was released separately from The Story of Martha purchasable by download only, on 11 June 2009.
to be added