Andrew Motion does it on the beach, Linda Colley in the pool and Freeman Dyson on the bus. Anthea Lipsett explores some inspirational places

On the wide sands of Holkham beach there is plenty of space to think. Andrew Motion often walks along that expansive stretch of the Norfolk coast, occasionally happening upon the ideas he seeks. The Poet Laureate and professor of creative writing at Royal Holloway, University of London, knows that however many others are attracted to the beach, there will always be enough room for his thoughts to remain undisturbed.

"I like the pine trees on the sand, and the sand and sea smells all mixing together," he says. Here, he finds solace and time for contemplation.

While many cite long, weighty discussions with gifted peers as the ideal incubator for intellectual inspiration, Motion eschews such stimulation. He prefers peace. He might find this during long hours spent at his desk without the phone ringing; he notes that any fool might, simply by getting up an hour or two earlier than usual.

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But Motion also engineers space for what Keats described as "delicious diligent indolence", a concept ingrained in his heart. This, of course, is harder to arrange. "What's needed is a mixture of apparent idleness coupled with a tremendous sense of 'yeasting-up'," he says. "That's where people's best thoughts come from and it can't be planned to happen at six or seven o'clock in the morning. That time just has to emerge."

It helps to escape. "That's an indolence that then works," Motion says. "I need to get away, preferably from England, not because I don't like it here, I love it, but the further away the better for unfamiliar sights - foreign, overseas versions of what you are used to."

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Failing that, though, the expanse of Holkham beach provides the poet with what he needs. Alternatively, fishing is also effective. Not the kind that involves sitting under a green umbrella avoiding the family, but fly fishing, often in Scotland. "I do my thinking in the wilderness up there," Motion says. "That produces the first scraps of poems, which I can then work on when I get back to my desk."

The River Torridge in Devon is another favoured site, incidentally an old haunt of Ted Hughes. "It's difficult to fish because it's a bit more overgrown, but I don't mind," Motion says. "I like a challenge." The key is repetition and distance from the madding crowd.

Motion finds genuine inspiration from these few places and activities, the concepts and words he needs, perhaps as much as half an entire poem, before he starts to write. "I don't want to waste my time," he says. "I have a good idea of where something's going by the time I get to my desk. It's almost as if I want save myself the embarrassment of not having a winner."

Invention and insight fuel the engines of our society and are the intellectual life blood of our universities. Philosophers Thomas Kuhn and Karl Popper held opposing views on the source of ideas, according to Peter Lipton, philosophy of science professor at Cambridge University. Kuhn said that new ideas came from old successful ones, Popper that they came from old failed ones. "Both of them are right," Lipton says.

Yet original ideas are rare. James Watson, Nobel prizewinning discoverer of the molecular structure of DNA, alleges that he seldom has more than one a year. "They generally arise when a seminar or journal article exposes me to an unexpected observation that cries out for a plausible explanation," he observes.

And while author Linda Colley, professor of history at Princeton University and author of Britons: Forging the Nation 1707-1837 , says she finds swimming lengths "helps sort out paragraphs wonderfully", she is most inspired by her peers. "Listening to friends and colleagues enthusing about their projects and methodologies, and going to different universities and encountering new minds, is the best intellectual tonic I know," she says.

Freeman Dyson, the theoretical physicist, notes: "Being among bright people, of course, is very important. There are always two stages - talking with people and borrowing ideas, and sitting quietly and actually thinking. They are very different - you need both."

But finding time to think is a challenge for everyone. The right environment can be essential. Albert Einstein claimed that creativity flowed from the three Bs - not Motion's beach, but bath, bed or bus. That maxim has much support, not least from Archimedes' celebrated eureka moment. Dyson's experience adds further weight.

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The great mathematician and polymath was indeed on a bus, travelling from San Francisco to Chicago, when he did much of the thinking - "mental scribbling" - that enabled him to unify the prevailing theories in particle physics.

"Scribbling equations is what I do and that's when the ideas come," Dyson says. "The bus is a good place to be if you want to be forced to use your brains because there's nothing else to do except think. You get into a kind of stupor where you are half asleep and half awake and that's probably a good state to be in.

"I took a bus ride all across the US for three days and three nights and that put me in the right frame of mind." By the time his bus had reached its destination, Dyson was well on the road to reorganising the calculations that his peers had been struggling with.

Having a specific problem in mind helped another of Dyson's ideas to reach fruition, this time while he was in the middle of a walk. His company had challenged him to design a nuclear reactor. "We made a lot of designs with complicated mechanical gadgets, which relied on the expansion of metal.

When the reactor got too hot it would move from one place to another and we tried to make an engineered device to control it. All these things were just not robust. I was aware of what I wanted - a scheme that would make the reactor safe without any moving parts." But a solution to the problem evaded him.

"I well remember when it happened," he says. "I was taking a walk in the early morning along the streets of San Diego. As with all good ideas, the solution was simple. Once it came and I understood how to do it, it was obvious. You think, 'why didn't I think of that before?' You never know when the lightning is going to strike."

Dyson's design, the only piece of real engineering he did, is still used in power production today, 50 years after its conception.

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Sir Martin Rees, Astronomer Royal and president of the Royal Society, also finds that travelling helps prompt original thought. "My good ideas are few and far between, and working them out is a struggle," he says. One such insight into the origin of gamma ray bursts, the most energetic phenomena in the universe, was eased out during just such a journey. "I'm a workaholic and I feel less guilty looking out of the window on planes or trains when I'm travelling because I'm getting somewhere," Rees admits.

Running, albeit slowly, on Primrose Hill and Hampstead Heath is a favourite of biologist Lewis Wolpert, emeritus professor of biology as applied to medicine at University College London. "A friend came with me the other day and apologised for walking too fast for me to keep up," he says.

Why does it work for him? "There's nothing else to do while I'm jogging. You can think about things quietly. I haven't had great ideas but have thought through good ones. I think ideas sometimes just come to you. You can't tell when, but jogging helps."

Such an approach is not for everyone. Martha Nussbaum, Chicago University philosopher of law and ethics, finds running "too exacting to be a good place to think". Instead, she considers walking 30km of lakeshore more fruitful. It is an experience she never tires of. "Chicago is like a Monet series painting," she says. "Just now the lakeshore outside my window is wrapped in fog. Yesterday it was bright blues and greens."

Along with the exchange of ideas with colleagues, Nussbaum also finds teaching inspirational, especially given that many of her students are not majoring in philosophy and so hold a wide variety of views.

"Teaching is a great source of ideas," she says, "it let's you show undergraduates the deeper human importance of your subject and let's you put yourself on the line to explain why your subject excites you."

Ideas, Nussbaum argues, are usually built on what has been posited before. "Often it's not a matter of getting something totally new but going more deeply into the things I have known already and understanding them better."

Niall Ferguson, professor of international history at Harvard University, says his best ideas come when he is completely relaxed. "For me, the most conducive situation of all would seem to be when my wife and I make our annual pilgrimage to Venice to celebrate our wedding anniversary," says the author of Colossus: The Rise and Fall of the American Empire. "Our lunches at Locanda Cipriani on the sublime island of Torcello have consistently produced good new ideas or clarified old ones."

Sleep helps John Pendry, professor of physics at Imperial College London who was knighted last year for his work on optical materials, to unlock his ideas. "To get 100 per cent concentration on a very difficult problem at work is hard," he says. "Sleeping on something straightens things out an awful lot."

Pendry, whose work on refraction went against orthodox opinion, also sets aside time to daydream. "Some people work terribly hard and produce mountains of stuff but there's that vital spark missing," he says. His advice? "Think the unthinkable and the ridiculous. Having done that, and checked your work very carefully, have the courage of your convictions.

When people are rude about your work, keep calm and answer politely. You can always say 'I told you so' later."

Sleeping on a problem is also a favoured strategy of John Carey, literary critic and professor of literature at Oxford University. "I have found again and again that I go to bed thinking of a problem and when I wake up it is clear in my mind," he says. "I don't know why this is, and have never talked to a psychologist about it - though it would be interesting to do so. Perhaps it is because sleep suppresses a lot of mental operations that normally block or interfere with thought. Or maybe the brain is too tired to cope until it has had some rest."

But Steven Pinker, professor of psychology at Harvard, finds the premise that good ones come to people when they are otherwise engaged dubious. Every time he hears academics credit a moorland ramble for their inspiration, he recognises a workaholic allowing themselves guilt-free time off.

"I suspect that if scientists kept close track of when good ideas hit them, as opposed to thinking back on isolated instances, they'd find that the best ideas come while thoroughly immersed in solving the problem, that is, when writing up papers or grant proposals or discussing it with students and colleagues," he says. "That is certainly true for me."

The harsh truth as Pinker sees it is that most problems are just too hard to tackle with anything short of 100 per cent concentration, notes, figures and "a half-completed verbiage on the computer screen begging for a tenable completion". He is scathing about ideas springing from the subconscious - "research on the psychology of creativity suggests that that Romantic notion is mostly wrong".

Time away from intense problem-solving is important, he concedes, to combat fatigue and to allow false trails the time to dissipate. "There's no doubt that some ideas occur to me while kayaking, jogging, biking, walking, daydreaming, while in the shower and so on," Pinker admits. "But I think that most of them are vague or wrong, like the 'insights' that one has while dreaming that turn out in the morning to be banal or gibberish.

"After all, why would the brain be equipped with deliberate, conscious, pain-staking cognition in the first place if, as many intellectuals claim, their best ideas come to them while on a beautiful walk?"

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