Daniel's world is a rich and strange one, where every number up to 10,000 has colour, texture and emotional resonance. "The number one is a brilliant and bright white, like somebody shining a torch beam into my eyes ... Four is shy and quiet, like me. Eighty-nine is like falling snow ..." More remarkable still, he has described it all inBorn on a Blue Day, his memoir of his life with synaesthesia and savant syndrome, a rare form of Asperger's. Dr Darold Treffert, a leading researcher in autism, says: "Such first-person explanations of savant abilities are extremely rare, in fact nearly non-existent."
Daniel's condition brings him great riches: his visualisation of numbers means he can perform extraordinary mathematical feats, and he holds the British and European record for reciting pi from memory to 22,514 decimal places. It also has its limitations. Forming relationships was difficult ("until I was eight or nine, I didn't realise that other children were people with thoughts and feelings"); supermarkets still are (too brightly coloured, too confusing).
When I meet him in the quiet London offices of his publisher, there are only a few signs of how different he is, a slight creakiness in his gait, a subtle over-intensity in his gaze. "I had to teach myself to look in somebody's eyes, to make eye contact," he explains. "Before that, I used to look at their mouth, because it was the part of their face that was moving," he says, as if it were the easiest mistake to make in the world. Which, in a way, it is, or certainly the most logical.
There's also a stiffness, a vulnerability in his bearing. I watch as he stands before The Independent on Sunday's photographer, as rigid as if he were in front of a firing squad. Sunlight flashes on his face and he begins to squint; immediately, his boyfriend, a mild-mannered computer programmer called Neil, bounds towards him solicitously. "Are you OK?"
Later, I ask Daniel if the photoshoot was such an ordeal that he used numbers to help him through. "Yes. While we were outside I noticed a spiral staircase in one of the buildings which was nice as it reminded me of doing a fraction in my head."
Mental arithmetic is a gorgeous kaleidoscopic process for Daniel. "Squaring numbers is a symmetrical process that I like very much," he says. "And when I divide one number by another, say, 13 divided by 97, I see a spiral rotating downwards in larger and larger loops that seem to warp and curve. The shapes coalesce into the right number. I never write anything down."
His mathematical abilities are so extraordinary that it took a long time for them to be recognised. Daniel struggled at school (why, he wondered, were the numbers in the textbook not printed in their true colours, nine in blue, and so on?). He got a B at Maths GCSE. He wasn't diagnosed with Asperger's syndrome until three years ago, at 25. Sooner would have been better "both for me and my parents"; consciousness-raising is part of his motivation for writing his book. "My condition is invisible otherwise."
Scientists at California's Center for Brain Studies were astounded when, two years ago, they discovered his facility for discerning prime numbers. They had assumed he must have been trained to do it. But to him, it is more like an instinctive process: "Prime numbers feel smooth, like pebbles". The centre stays in close contact with Daniel.
"The scientists and researchers come to me so I can help them design the parameters of their experiments," he says in his habitual monotone, neither proud nor modest. It is important to Daniel that he uses his gifts responsibly, perhaps for science, perhaps for teaching: he is already devising a new system of visualisation to help with language learning and dyslexia.
"When I was growing up, my parents were very concerned that people shouldn't just get me to do tricks for them," he says. (He is a whizz at crowd-pleasers such as working out, from your date of birth, which day of the week you were born on.) "My parents had this phrase 'performing seal'. They didn't want me to be one."
Growing up as an undiagnosed savant was never easy. Daniel was lonely. "I was desperate for a friend and I used to lie in bed at night thinking about what it would be like. My younger brothers and sisters had friends and I used to watch them playing to try to work out what they did and how friendship worked. Then, I would have traded everything for normality. But I've since learned that being different isn't necessarily a bad thing."
Falling in love with Neil has been a large part of this. Emotions used to be difficult for him to understand without recourse to numbers. "If I heard somebody was sad I would picture myself sitting in the dark hollowness of number six to help me understand the feeling." Now his emotional life is more like everyone else's. "Love by its very nature puts things in perspective, joins the dots and helps me see life in a bigger way."
Neil and Daniel, who have been together for six years, share an odd kind of domestic bliss. They have their tea together at exactly the same time every day; they have exactly 45g of porridge for breakfast, weighed on an electronic scale. "Neil is very patient with me, and the routines I need to have to help with my anxieties," says Daniel. "I don't know what I'd do without him."
Generally, Daniel feels he is progressing all the time towards "outgrowing" his autism. He cried for the first time in his adult life a few years ago, when his cat died. "My face was wet, and I knew that I was crying." Latterly, he has acquired a strong religious faith, which grew from an intellectual appreciation of the writings of G K Chesterton. And he is getting steadily better at social interaction. "Every experience I have I add to my mental library and hopefully life should then get easier." In this, he seems to sum up the progress we all hope for.
But some experiences remain unique to him. "I don't normally like films about emotions because I can't understand them. I enjoyed March of the Penguins, though. But when I watched the trailers first, I found that because they show the most dramatic moments one after another in quick succession, it made me feel so overwhelmed I burst into tears. No one else was affected, of course, and I felt silly. Next time I'll know to maybe not watch the trailers."
A LIFE IN NUMBERS" 'Pi is for me a beautiful thing'
Daniel Tammet can speak 10 languages, including Lithuanian and Welsh, as well as his own invented language, "Mänti", which has about 1,000 words.
As part of a documentary that was made about him, called 'Brainman', Tammet learned Icelandic in a week, in front of the cameras. The culmination of the challenge was a live interview on Icelandic TV, which he coped with brilliantly.
He can recognise every prime number up to 9,973.
In 2003, he gave a public recital of pi in Oxford, in aid of the National Society for Epilepsy. Tammet recited it for five hours nine minutes, reaching 22,514 decimal places. "Pi is for me an extremely beautiful thing," he says, "like the Mona Lisa or a Mozart symphony."
On The Late Show with David Letterman, he calculated instantly that since Letterman's birth date was 12 April 1947, he must have been born on a Saturday and would reach 65 on a Thursday.
'Born on a Blue Day' by Daniel Tammet is published by Hodder & Stoughton (£16.99)
*By the way, the correct answer to the headline sum is 45,212,176
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