He will be chaperoned to and from lectures by his father, and cannot enter bars to drink with his fellow students. It might not resemble normal student life, but Arran Fernandez is not a typical undergraduate. He is, in fact, the youngest student to grace the quadrangles of Cambridge University for 237 years, since the future prime minister, William Pitt the Younger, matriculated in 1773 at the age of 14.

Like Pitt, Arran has never been to school and was educated at home. The 15-year-old started at Fitzwilliam College yesterday and will attend his first maths lecture tomorrow. While he intends to join the bird-watching society and go punting on the River Cam as a pleasurable distraction from his studies, his youthful predecessor survived his time at university by downing a bottle of port a day – prescribed by his doctor to help him cope with crippling gout.

Modern medical thinking suggests that Dr Anthony Addington, who prescribed the somewhat peculiar cure, got it wrong and ended up exacerbating his patient's problem. But whatever the rights and wrongs of the case, Pitt's fondness for alcohol stayed with him for the rest of his days. Arran, however, is not keen to follow Pitt's example. He said: "I don't feel like I'm missing out on much. Even if I was 18 I wouldn't want to go out drinking."

Rather than drink, he would like to solve the Riemann hypothesis – a theory about the patterns of prime numbers that has baffled mathematicians for 150 years.

For his recreation at Cambridge, Pitt sought the company of peers of the realm, notably Lord Camden. By contrast, Arran's father, Neil, is renting accommodation in Cambridge to support his son during his time at the university. The teenager's mother, Hilde, intends to stay at the family home in Surrey and see her son at weekends and during the holidays.

From the start of his third year at Cambridge, Pitt, then 16, would make regular trips to London to listen to debates in Parliament. Historians have claimed he was consciously preparing himself for a life in government with studies that included political philosophy, classics, mathematics, chemistry, trigonometry and history.

Arran, however, will study only maths. His "Mathematical tripos", the official name of his degree, dates back to 1750 and includes Sir Isaac Newton and Stephen Hawking among its former alumni. The course is widely considered by mathematicians to be one of the most difficult in the world. "We generally admit between six and eight mathematics undergraduates each year," the college said. "There are about 10 to 12 hours of university lectures a week. In addition, there are supervisions [with tutors] in college about twice a week, normally in groups of two. We place greater stress than most colleges on the opportunity this system of teaching gives for building up personal links with the students and answering their mathematical questions individually."

Arran made history when he gained the highest grade in a GCSE foundation maths paper at the age of five. Two years later, he got an A* grade in the full maths GCSE. In order to make it to Cambridge this year, Arran was required to pass A-level physics. He duly attained an A* grade, adding this to the two As in maths and further maths he had already received.

The college also told him to sit three GCSEs in subjects unrelated to maths or physics, in order to broaden his knowledge. Naturally, he gained A* grades in English literature and French, as well as an A in English language. The university says it is trying to treat Arran like any other undergraduate – and few would argue that he doesn't deserve his place.

Pitt the Younger, who studied at Pembroke Hall (now College), was also home-schooled like Arran, largely because he was such a sickly child. Under the guidance of his tutor, Rev Edward Wilson, he became competent in Latin by the age of seven and was said to be more interested in books than "gentlemanly" sporting activities.

His father had decided his son would go to Cambridge because he did not want him to repeat the miserable educational experience he had at Oxford. At the end of his degree, Pitt took advantage of a little-known privilege available only to the sons of noblemen by graduating without having to pass examinations, using his ill-health as an excuse. He went on to become Britain's youngest prime minister at the age of 24.

Pitt's school days