Brain accidents and injuries can occasionally unleash amazing new talents. In the following years, Padgett stopped going to work and spent all of his time studying maths and physics, focusing on fractals (repeated geometric patterns), which he found he could draw in extraordinary detail. But he realised he was not alone when he saw a BBC documentary about Daniel Tammet, a young Londoner with savant syndrome - the condition in which a person with a mental disability (in Tammet's case, autism, a condition shared by 50 per cent of savants) shows prodigious abilities in memory and art, maths and music, far in excess of what is considered normal. ''That's it! That's what's going on with me. Oh, my god! Someone else can see what I see!'' Padgett thought, as he recalls in his new book Struck by Genius: How a Brain Injury Made Me a Mathematical Marvel. He contacted Dr Darold Treffert, a Wisconsin-based psychiatrist and the leading expert on savantism, who diagnosed ''acquired savant syndrome''. According to Treffert, there are three levels of savant ability (which is more common in men than women, with male savants outnumbering females six to one). ''First, there's something called splinter skills - this would be a case with someone who has a talent for memorisation above the norm, for example,'' he says.

''Then there's something called a talented savant (someone who has a marked talent in one area) and finally, there's something called the prodigious savant - someone with truly extraordinary gifts. There are fewer than 100 known prodigious savants living, worldwide.'' Even Padgett would fall into the merely ''talented'' sub-group. Probably the most famous savant is fictional: Raymond, Dustin Hoffman's character in the 1988 film Rain Man. Raymond was, however, based on a real-life savant called Kim Peek who, despite having an IQ measuring just 72 (below normal), had a stunning memory and ability to read and recall information. Unlike Raymond, Peek was not autistic but had suffered brain and possible chromosomal damage before birth. He did, though, exhibit similarly astonishing abilities, described as being able to recall information from 12,000 books, speed-reading through them at about an hour per book. While Peek was known in the US, affectionately, as ''Kimputer'', all savants boast a very deep memory, Treffert has reported. For example, on March 14, 2004, Daniel Tammet publicly recited, from memory, pi to 22,514 decimal places. It took him five hours and nine minutes. He explained how he had committed the sequence to memory in his book Thinking in Numbers. ''Printed out on crisp, letter-sized sheets of paper, 1000 digits to a page, I gazed on them as a painter gazes on a favourite landscape.'' Sometimes called ''Brainman'', Tammet has also taught himself 11 languages (including Icelandic in just a week).

But savants' powers extend far beyond mere recall. Treffert has identified the most significant areas of savant skill - what he calls ''islands of ability'' - as taking in art, music, calendar calculation, maths and spatial skills. For instance, Leslie Lemke, from Wisconsin, born with such severe birth defects that doctors had to remove both his eyes, was put up for adoption and could not stand unaided until he was 12. Four years later, his adopted mother woke up one night to hear him playing Tchaikovsky's Piano Concerto No. 1. Lemke, who had no classical music training, was playing the piece flawlessly after hearing it just once earlier on television. His remarkable ability to play by ear saw him performing and recording until ill-health finally scuppered his talent. Padgett, however, is arguably still more special, in that he has acquired his savant syndrome - rather than being born with it. He is not alone. After a head injury as a toddler, Alonso Clemons of Boulder, Colorado, now in his 50s, discovered an ability to sculpt animals to a remarkably life-like degree just using his hands and fingernails. Orlando Serrell could tell the day of the week of any given date after being struck by a baseball at the age of 10 in 1979. Anthony Cicoria, a 62-year-old orthopaedic surgeon from Oneonta, New York, could play the piano to concert standard following a lightning strike in 1994. Meanwhile, Pip Taylor, a 49-year-old woman from Birkenhead, north-west England, recently discovered a talent as an artist after hitting her head falling down the stairs. She is now being commissioned to produce portraits. So what lies behind these astonishing brain boosts? Some neurologists believe that it is the brain's ability to bend and rewire itself, its neuroplasticity, which leads to the development of extraordinary new skills. Behavioural neurologist Dr Bruce Miller, of the UCSF Memory and Ageing Centre in San Francisco, however, has come up with a new theory to explain the phenomenon. He believes the talents of a savant emerge when the areas damaged - those associated with logic, verbal communication, and comprehension - have inhibited latent artistic abilities already present. According to this theory, these hyper skills, such as great proficiency in music, manifest themselves as the areas of the right brain associated with creativity operate unchecked for the first time.

Luke Griggs, a spokesman for Headway, the brain injury association, says that the process by which these new abilities are acquired remains uncharted. ''Jason Padgett's case is extremely rare,'' he says. ''We don't understand the exact mechanisms by which such dramatic new abilities can suddenly appear. ''Different parts of the brain are massively interconnected and it is possible that inhibition in one part of the brain following injury can lead to increased activity in other areas, which can sometimes result in surprising and unexpected effects. ''However, it is important to remember that brain injury almost always impairs rather than enhances people.'' Indeed, despite Padgett's new savant status, he too has spoken about the toll his injury has exacted. While he was once outgoing, the shock of discovering his new skills made him introverted, and he started to spend all of his time at home, covering up his windows with blankets and refusing visitors. He became obsessed with bacteria and would scrub his hands until they were red. He would not even hug his own daughter until she had washed her hands.

It is crucial to remember, after all, that behind a sudden savant's eye-catching new powers are real human stories - a point Treffert reminded the medical community in 2009, as he summarised his life's work for the Royal Society journal Philosophical Transactions B. While he was relieved to note that the derogatory term idiot savant had fallen from favour (as being blatantly untrue), he pointed out: ''No model of brain function, including memory, will be complete until it can account for, and fully incorporate, the rare but spectacular condition of savant syndrome. ''There is more to savant syndrome than genes, circuitry and the brain's marvellous intricacy. Human potential consists of more than neurons and synapses. It also comprises, and is propelled along by, the vital forces of encouragement and reinforcement that flow from the unconditional love, belief, support and determination of those families and friends who not only care for the savant, but care about him or her as well.'' In the process of understanding sudden savants, he said, ''we can also learn more about ourselves, explore the 'challenge to our capabilities' and uncover the hidden potential - the little Rain Man - that resides, perhaps, within us all''. Telegraph, London