Autism and Mathematical Talent
IOAN JAMES
Autism is a developmental or personality disorder, not an illness, but autism can coexist with mental illnesses such as schizophrenia and manic- depression. It shows itself in early childhood and is present throughout life; sometimes it becomes milder in old age. Nowadays it is recognized as a wide spectrum of disorders, with classical autism, where the individual is wrapped up in his or her own private world, at one extreme. It is estimated that in the United Kingdom slightly under one percent of the population, about half a million people, have a disorder on the autism spectrum. The corresponding figure for other countries is not available, although it is unlikely to be very different. Autism is present in all cultures and, as far as we know, has existed for untold generations.
Hans Asperger, a Viennese psychiatrist, found that some of his patients had a mild form of autism, with distinctive symptoms that later became known as Asperger's syndrome. He was not the first to describe the syndrome but he may have been the first to recognize a connection with mathematical talent. As he observed (see Frith [13]):
to our own amazement, we have seen that autistic individuals, as long as they are intellectually intact, can almost always achieve professional success, usually in highly specialized academic professions, often in very high positions, with a preference for abstract content. We found a large number of people whose mathematical ability determines their professions.
Later he wrote,
It seems that for success in science or art a dash of autism is essential. For success the necessary ingredient may be an ability to turn away from the everyday world, from the simple practical, an ability to rethink a subject with originality so as to create in new untrodden ways, with all abilities canalised into the one speciality.
He went on to describe autistic intelligence—a kind of intelligence untouched by tradition and culture—unconventional, unorthodox, strangely pure, and original. The ability to immerse oneself wholeheartedly in work or thought is something that is seen time and time again in the Asperger genius.
Asperger's syndrome is not the only form of autism with this connection. The Irish psychiatrist Michael Fitzgerald, for example, tells me that virtually all the people he diagnoses as autistic have an interest in mathematics. Their greatest wish, he says, is to bring the world under the control of pure reason, to create order and meaning out of the chaos that they experience around them, particularly in the puzzling social domain. Such people are naturally attracted to science, especially to the mathematical sciences, since mathematicians tend to create order where previously chaos seemed to reign. He attributes this attraction to a feeling of security that they find in the rational world of mathematics, which compensates for their inability to make sense of the mysterious social world.
Much has been written about this, and the general public are now more aware of the presence of mildly autistic people in everyday life. Since I first wrote about autism in mathematicians in the Intelligencer [20] some years ago, more has been learned about the disorder and more has been published. In this follow-up article I begin by describing research that places the link between autism and mathematical talent on a firmer footing. Then I describe some of the more recent case studies of Asperger geniuses in mathematics and associated subjects.
Simon Baron-Cohen, director of the Autism Research Centre in Cambridge, has tried to put the connection on a more quantitative basis. For this purpose he devised a self-administered questionnaire for measuring the degree to which an adult with normal intelligence has the traits associated with the autistic spectrum. From the answers to the questions a number is obtained, which he calls the autistic-spectrum quotient, providing an estimate of where a given individual is situated on the continuum from normality to autism. (Anyone who wishes to take the AQ test will easily find it by Googling Simon Baron-Cohen.)When the questionnaire was administered to students at Cambridge University, interesting results were obtained. Briefly, scientists scored higher than non- scientists; and within the sciences, mathematicians, physical scientists, computer scientists, and engineers scored higher than the more human or life-centered sciences of medicine and biology. Full statistical details are provided in [4] and [5]. This research was taken a step further in [6], where among 378 undergraduates reading mathematics at Cambridge there were seven who reported a formally diagnosed autism spectrum condition, whereas there was only one among 414 students in a control group of Cambridge undergraduates reading medicine, law, or social science.
In the mathematical world, the establishment of a link between autism and mathematical talent will come as no surprise, but its recognition may have significant practical consequences for education and for choice of occupation. At school autism is regarded as a learning disability; its positive side should be recognized. Children with mild autism, who get on well in mathematics, may struggle with other subjects. They are likely to perform poorly at interviews, when they apply for a job, but they may be good at the right kind of work, for example in information technology, where their special abilities are appreciated. Although the disorder is a handicap in many ways, in others it is a great advantage. For the majority, life is a struggle, and only a minority make a success of it. There can be no doubt that gifted individuals with some degree of autism have contributed a great deal to research in mathematics. Not always, however; the tragic lives of Robert Amman [25] and William Sidis [28] show what can go wrong.
When combined with high intelligence, as it often is, autism is associated with outstanding creativity, particularly in the arts and sciences. An enormous capacity for curiosity and a compulsion to understand are evident in those who have the syndrome, as is a tendency to reject received wisdom and the opinions of experts. They often suffer from depression, and mathematical work can have an antidepressant effect. Work is a form of self-expression for the autistic who finds other forms of expression difficult; it boosts their often low self esteem.
The link with autism may throw fresh light on some aspects of mathematical creativity. More than a hundred years ago Henri Poincare addressed a conference of psychologists in Paris on Mathematical Creation (translated by Halsted [17]). Poincare's disciple Jacques Hadamard wrote a well-known monograph [16] on The Psychology of Invention in the Mathematical Field, which is mainly about mathematical creativity; a more recent discussion of this may be found in Changeux and Connes [7]. Much has been written about creativity in general, much of which applies to mathematical creativity, but Nettle [24] emphasizes that this differs from creativity in the arts. In a recent survey, comparing the psychology of a small sample of research mathematicians with poets and visual artists, Nettle finds that the cognitive style of the mathematicians was associated with convergent thinking and autism, whereas poetry and art are more associated with divergent thinking, schizophrenia, and affective disorders, such as manic-depression. (Divergent thinking means the ability to create new ideas based on a given topic; convergent thinking means the ability to find a simple principle behind a collection of information.)
In the history of mathematics it is not difficult to find people who may have had Asperger's syndrome, although without the right kind of biographical information we cannot say for sure whether each person had the syndrome or not. It is much less common among females than among males; it is difficult to find an example of an outstanding woman mathematician who was a clear case. It is not uncommon for individuals to have only a few features of the syndrome, not the full profile. Examples of well-known mathematicians who showed more than a trace of Asperger behavior, without necessarily meeting all the diagnostic criteria, are Paul Erdos, Ronald Fisher, G. H. Hardy, Alan Turing, Andre Weil, and Norbert Wiener. A detailed analysis for Srinavasa Ramanujan has been provided by Fitzgerald [10], for William Rowan Hamilton by Walker and Fitzgerald [27]. Some other cases are discussed by Fitzgerald and James [12]), whereas Baron-Cohen [1] describes one (who was, in fact, a Fields Medalist).
Sheehan and Thurber [26] have suggested that John Couch Adams had the disorder and that this lay behind both his success in identifying the unknown planet Neptune as the cause of anomalies in the orbit of Uranus and also his failure to persuade the Astronomer Royal to search for it in the orbit he had calculated. Most of those who encountered the mathematical physicist Paul Dirac have a story to tell about his eccentricity. His recent biography by Farmelo [8] describes his aloofness, de- fensiveness, determination, lack of social sensitivity, literal-mindedness, obsessions, physical ineptitude, rigid pattern of activities, shyness, verbal economy, and much else. Some features of his complex personality can be attributed to his strange upbringing but most of it goes with some form of autism.
Some people are critical of linking the syndrome with persons of genius. There is often strong resistance from the general public to any suggestion that a famous person might have had Asperger's, but this is generally because of the popular misunderstanding of the nature of the disorder. People who are otherwise well informed find it difficult to believe what some of those with this disorder may be capable of achieving. Attempts at diagnoses of individuals no longer alive often result in controversy when experts differ and amateurs also become involved. Unless one is absolutely sure, it is advisable to be careful, for example, to say that someone displayed autistic traits rather than that person was autistic, even when the case is a strong one, since otherwise the diagnosis is liable to be questioned. Some of the standard books on the subject, notably Frith [14], discuss the problems of historical diagnosis. On the one hand, to know that there have been outstanding Asperger mathematicians impresses the rest of us and enhances the self-esteem of gifted people with the syndrome. On the other hand, those who are not so gifted may feel depressed that they cannot aspire to mathematical fame.
References
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