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Now a small but growing number of researchers see hope in a tool called transcranial magnetic stimulation, which lets scientists spark activity in specific areas of the brain and watch what happens to patients' behavior. The technology may illuminate some of the biology behind the disease, and some specialists speculate it may one day offer a treatment.

John Gabrieli, a neuroscientist at Massachusetts Institute of Technology. Transcranial magnetic stimulation "is fantastic for identifying brain regions that are essential for specific mental functions. . . . I think if we can start to use it more systematically with autism, one could hope we'd understand a lot more about what's going on."

Researchers at the Boston hospital's Berenson-Allen Center for Noninvasive Brain Stimulation used rapid, repetitive stimulation to simulate what happens in the brain when people learn a new task. Then they gave a single pulse of stimulation and measured minute muscle twitches that told them how long people's brains maintained connections formed by the initial stimulation.In people with no evidence of autism, changes lasted about 30 minutes, on average. But in people on the autism spectrum, the initial stimulation caused brain changes that lasted much longer - on average an hour and a half.

A study published this week by Patricia Howlin of King’s College, London, reinforces this point. It suggests that as many as 30% of autistic people have some sort of savant-like capability in areas such as calculation or music.

Francesca Happé of King’s College, London, is one of them. As she observes, obsessional interests and repetitive behaviours would allow someone to practice, albeit inadvertently, whichever skill they were obsessed by. Malcolm Gladwell, in a book called “Outliers” which collated research done on outstanding people, suggested that anyone could become an expert in anything by practising for 10,000 hours. It would not be hard for an autistic individual to clock up that level of practice for the sort of skills, such as mathematical puzzles, that many neurotypicals would rapidly give up on.

Simon Baron-Cohen, a doyen of the field who works at Cambridge University, draws similar conclusions. He suggests the secret of becoming a savant is “hyper-systematising and hyper-attention to detail”. But he adds sensory hypersensitivity to the list. His team have shown one example of this using what is known as the Freiburg visual acuity and contrast test, which asks people to identify the gap in a letter “c” presented in four different orientations. Those on the autistic spectrum do significantly better at this than do neurotypicals. That might help explain Dr Happé’s observations about coins and raindrops.