Not many first-year university students have to juggle late-night essay crises with the pressures of addressing delegates at Davos. For Malala Yousafzai, the hardest thing about starting at Oxford has been working out how much time to spend campaigning for girls’ education globally and how much to devote to her own education.

As everyone around her seems to be in a permanent state of alarm about the amount of work they must do, her own battle to squeeze everything in feels bearable. “Sometimes, it is challenging. You have to stay awake until late and finish your work; you have to ask to extend your deadline; you have to work a bit harder,” she says in a phone call between classes. “Everyone struggles. Everyone is panicking with their reading. It is hard to do all the reading and finish a 2,000-word essay – it is normal for everyone to struggle.”

Before she arrived, she worried that her unique position as a Nobel prize-winning fresher might make it difficult to fit in. “I was nervous, I was actually scared wondering how people would react. How would I make friends? How would people perceive me? But I was welcomed as a student. It’s my second term now, I’ve made so many friends,” she says. She has an endearingly breezy way of brushing away the extraordinariness of her situation and modestly suggests that her challenges are pretty much those faced by most students (although this term, as well as the trip to Davos, she has been finalising a partnership with Apple to allow her Malala Fund to extend grants for secondary education to more than 100,000 girls – and she has been promoting a new book). “I just feel like an Oxford student; I feel so grateful.”

Facebook Twitter Pinterest David Letterman with Malala Yousafzai. Photograph: Michele K Short/Netflix

Yousafzai, 20, is studying politics, philosophy and economics (PPE) at Lady Margaret Hall, and recently allowed the US chatshow host David Letterman to follow her around for a day, giving a snapshot of her life (taking him on a rapid tour of the college canteen and gardens, politely smiling at his jokes and halfheartedly playing table football with him); the footage is now available on Netflix, as part of the My Next Guest Needs No Introduction series.

She has joined the Oxford Union, the Pakistan society and a cricket team, but is steering clear of student politics and has revised her ambition to follow in the footsteps of Benazir Bhutto (who also studied PPE at the same college) to become prime minister of Pakistan. “I wanted to be prime minister when I was younger, when I was 11, because I thought that by becoming prime minister I could fix everything. But now that I have met so many presidents and prime ministers around the world, it just seems that things are not simple and there are other ways that I can bring the change that I want to see,” she says. “I think we have a lot of time to join politics in Pakistan – so, right now, I am not thinking about that, I have no plans.”

It is five-and-a-half years since Malala was shot in the head by a gunman who disliked her campaign against the Taliban’s ban on female education in Pakistan’s Swat valley, where she lived. She was flown to Birmingham for treatment and has lived in the UK since, gradually revising her perceptions about a country she now sees with all its flaws.

She was “surprised and shocked”, she says, to discover how far Britain is from having gender equality; as a child, she had assumed that equal access to education here would mean there was a wider equality. “The western world is viewed as an ideal for other countries, especially developing countries, in terms of development, progress and gender equality. There are things I have seen here which I value and appreciate: no girl is told not to go to school because she is a girl, you don’t see women told to stay in houses and to cover their whole face and their whole body, and not go to market. But there is still a lot of work to be done on the representation of women in parliament, or if you look at the equal pay issue, or the sexual harassment issue, there are so many issues that the UK still needs to fight against to achieve equality.”

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She hasn’t personally encountered racism or sexism, but is annoyed at how the media depicts women here. “If you look at how women are portrayed in movies, films or ads, they are viewed as these delicate bodies who should dress in a certain way, behave in a certain way, talk in a certain way. This is something we have to challenge … it is women who should be deciding what they want to wear, what they want to say, what they want to do. It should not be someone else’s job to tell us how to dress, how to talk, how to walk.”

A more relaxed vision of Malala the student comes in a YouTube interview with a fellow student, known as Miss Varz, when they talk about books and takeaway food. This side of her comes across too on her Twitter account – she signed up on the day her A-levels finished last June, posting a screenshot of her Oxford acceptance news a few weeks later, along with pictures of her younger brother getting his hair dyed blond, and of herself eating pakoras with her best friend from school. But, mostly, the posts offer a portrait of the extraordinary pace of her life. On New Year’s Eve, she posted a list of her 2017 highlights – A-levels, Oxford, writing a book for children, visiting the UN general assembly, becoming a UN messenger of peace and a Canadian honorary citizen, and visiting Iraq and Kurdistan, Nigeria, Mexico and Canada. The list goes on.

She is used to the juggling act. “I’ve been struggling with studies and the work that I do outside school for girls’ education [for] the last five to six years. I had to take my GCSEs and now do my A-levels – and now university,” she says. “So far, it has gone well.”