As Stephen Hawking seeks a new graduate assistant, previous incumbents tell Anna Fazackerley that the job is exhilarating, exasperating and the stuff of killer dinner party stories.

Julian Luttrell knew that having Stephen Hawking, one of the most eminent scientists in the world, as his PhD supervisor was never going to be an average experience. He was not disappointed. Hawking was brilliant, inspiring and exciting. He was also terrifyingly hot-tempered.

"Stephen is very stubborn. I learnt quickly that if he wants something, you do it. Don't argue," Luttrell recalls. "He can get very, very angry very quickly, and that is not a pretty sight."

It is hard to imagine Hawking, who has amyotrophic lateral sclerosis, a form of motor neurone disease that leads to paralysis, being capable of physical intimidation. But Luttrell says: "He has been known to run over your feet in his wheelchair in fury."

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When Luttrell was a research student in the early 1980s, Hawking could still talk through an interpreter, but he could not write and was totally wheelchair-bound. "I think he got very frustrated that he couldn't express himself properly," Luttrell says. "When it came to the pastoral, he wasn't very good. He hadn't had any intellectual problems as a PhD student so he couldn't put himself in your place. He couldn't understand why you might have difficulty."

Yet Luttrell, like most of Hawking's students, is clearly very fond of his mentor - even if he did not do much mentoring. He recalls being obsessed with the ideas they were exploring and marvelling at the way in which Hawking scythed through problems in his head. "He had a wonderful way of cutting to the core. That rubbed off on me," he says.

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After completing his physics PhD, Luttrell turned his back on academia, which he felt "had nothing to do with the price of eggs", and set up a technology consultancy. But he still works with universities and is often reminded of how unusual his experience was.

While other research students were channelling all their energy into producing their theses, he was travelling around the world assisting Hawking with big scientific presentations. His daily life brought him into contact with Nobel laureates and prime ministers. And he had to take his boss to the lavatory.

On one occasion he accompanied Hawking to Dublin for a conference celebrating the birthday of Erwin Schrodinger, the great Austrian physicist. "We were invited to the Austrian Embassy for dinner. But when we arrived in a taxi there were ten huge steps up to the front door," he remembers, laughing. "There was a flunky on the door, so I went and explained and he helped me heave Stephen up the steps in his wheelchair. We got him to the top and he sailed past and introduced himself as the ambassador. He is very mischievous."

Hawking, who is now 63 and the Lucasian professor of mathematics at Cambridge University, is looking for a new graduate assistant. His PA is currently wading through a mountain of applications - a task that includes weeding out the spoof responses.

Newspapers seized on the recent job advertisement, with headlines trumpeting: "Assistant wanted for one of the world's greatest scientists."

It certainly sounds glamorous, but past assistants agree that it is a rather peculiar role.

Neel Shearer was Hawking's assistant between 2000 and 2002 after graduating in physics from Durham University.He is now a technology officer at Edinburgh University. He says: "I couldn't imagine any other job where I would have had so many different experiences. I helped him write a couple of books, and that was amazing. I also had to be a PA, driver, bodyguard, press relations person, personal shopper, carer. You name it, I did it."

Shearer says that he knew a bit about Hawking already, and he had read his runaway bestseller A Brief History of Time before doing his degree - and managed to absorb at least some of it. "Like every other graduate, I was looking for work after I finished, and the accountancy firms weren't my idea of a job," he explains. "This came up in November. The ad was quite understated. I was intrigued."

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Hawking spends about a third of the year travelling, and his graduate assistant organises everything, accompanies him and is responsible for the whole Hawking entourage of carers, family members and research students wherever they go. "To start with it was terrifying, because I had to deal with everyone from photographers to presidents," Shearer explains. "The things that stick in my head are the really crazy stuff, like trying to get him up to the Great Wall of China in a cable car. We had to take him out of the chair, and the chair came behind on a little platform with two Chinese guys hanging precariously off the sides."

He says, without hesitation, that Hawking was a "brilliant" boss, but he adds: "The new graduate assistant will need to be easygoing and prepared to do whatever is asked. It is 24/7. You are on call from the moment you take the job until the day you leave. If they can handle that, they'll have a great time."

In short, this is not a research job. It is about assisting Hawking in the most practical sense of the word. As Shearer points out, there is no career progression (although Hawking is a word that always looks good on a CV).

"It doesn't go anywhere - you can't become Professor Hawking," he says wryly. "That took me a little bit longer than some of the others to work out."

Simon Gill, who held the post in 1993, spent a lot of his time helping Hawking prepare lectures. "We would sit together for ages and ages, and he would try to explain what slides he wanted and I'd put them together."

After booking the hotel and flights, and driving him to the conference, Gill would stand on stage with Hawking while he gave his talks, sometimes to huge numbers of people. "It wasn't too intimidating for either of us, but it was worse for me than for him," he says. "He would have his file with the talk on and he'd start the computer up and it would say it all."

But if the computer crashed, disaster struck. And it would be Gill who was left to explain what was happening to the bewildered audience.

His advice to the new assistant is to stay calm. He says he got on with Hawking extremely well, although he agrees that "he didn't always get on with people - I was lucky". He puts their good relationship down to being laid-back. "The first thing that caught me out was that quite a few weird people ring Stephen up and you have to deal with them," he adds. "I got people from California saying they had discovered black holes in their bathroom, or they had added up all the syllables in the book of Genesis and it added up to some cosmological constant."

Working for Hawking might be unpredictable, exhausting and stressful, but it seems that none of his past assistants or students is left short of a killer dinner party story. Yet the experience is a little more profound than that. Harvey Reall, who did his PhD under Hawking and now works as a Royal Society research fellow in the School of Physics and Astronomy at Nottingham University, sums it up. "Why was he so special to work with? You are asking me to define genius," he says simply. "Stephen Hawking is a genius."

Stephen Hawking was invited to contribute to this article but declined.

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Hawking will be awarded the world's oldest prize for scientific achievement, the Royal Society's Copley Medal, for his outstanding contribution to theoretical physics and theoretical cosmology, on November 30.