Scientists have for the first time found powerful evidence that genius may be linked with madness.

Speculation that the two may be related dates back millennia, and can be found in the writings of Aristotle, Plato and Socrates. Aristotle once claimed that "there is no great genius without a mixture of madness", but the scientific evidence for an association has been weak – until now.

A study of more than 700,000 adults showed that those who scored top grades at school were four times more likely to develop bipolar disorder than those with average grades.

The link was strongest among those who studied music or literature, the two disciplines in which genius and madness are most often linked in historical records. The study was conducted by researchers from the Institute of Psychiatry, King's College London, with colleagues from the Karolinska Institute in Stockholm, Sweden.

Bipolar disorder, also known as manic depression, affects about 1 per cent of the population and is characterised by swings in mood from elation (mania) to depression. During the manic phase there can be feelings of inflated self-esteem, verging on grandiosity, racing thoughts, restlessness and insomnia.

The 19th-century author Edgar Allen Poe, who is thought to have suffered from manic depression, once wrote: "Men have called me mad, but the question is not yet settled whether madness is or is not the loftiest intelligence..."

In recent years psychoanalysts, psychiatrists and psychologists have argued that genius and madness are linked to underlying degenerative neurological disorders. The problem has been that both genius and severe mental illness are rare, and high intelligence or achievement is subjectively defined. Claims about the link have been based on historical studies of creative individuals which are highly selective, subject to bias and rely on retrospective assessments of their mental state.

The study, led by James MacCabe, a senior lecturer in psychiatric epidemiology at the Institute of Psychiatry, compared the final school exam grades of all Swedish pupils aged 15-16 from 1988 to 1997, with hospital records showing admissions for bipolar disorder up to age 31. The fourfold increased risk of the condition for pupils with excellent exam results remained after researchers controlled for parental education or income. The findings are published in the British Journal of Psychiatry. They suggest that mania may improve intellectual and academic performance, accounting for the link with "genius". People with mild mania are often witty and inventive, appearing to have "enhanced access to vocabulary, memory and other cognitive resources". They tend to have exaggerated emotional responses which may "facilitate their talent in art, literature or music". In a manic state individuals have "extraordinary levels of stamina and a tireless capacity for sustained concentration".

Dr MacCabe said: "We found that achieving an A-grade is associated with increased risk for bipolar disorder, particularly in humanities and, to a lesser extent, in science subjects. A-grades in Swedish and music had particularly strong associations, supporting the literature which consistently finds associations between linguistic and musical creativity and bipolar disorder."

School pupils with low exam grades also had an increased risk of developing bipolar disorder later in life. The researchers suggest there may be two distinct groups of people with the condition – high achievers, in whom mania raises their game – and low achievers, especially those with low scores in sport and handicrafts indicating poor motor skills, who may have "subtle neurodevelopmental abnormalities".

The link was stronger in men than in women, but the difference was not statistically significant, Dr MacCabe said: "Although having A-grades increases your chance of bipolar disorder in later life, we should remember that the majority of people with A-grades enjoy good mental health."

Tortured talents: Suspected sufferers

Vincent Van Gogh

Throughout his life, the artist showed signs of mental instability. Various biographies describe him as suffering from epilepsy, depression, psychotic attacks, delusions, and bipolar disorder. In December 1888, he experienced a psychotic episode in which he threatened the life of Gauguin, his fellow artist and a personal friend, and cut off a piece of his own left ear before offering it as a gift to a prostitute.

Sylvia Plath

The poet handled very painful and intense subjects such as suicide, self-loathing, shock treatment and dysfunctional relationships. Since the day she died – by thrusting her head into a gas oven – readers and scholars have tried to unlock the enigma of her suicide. Her unabridged journals lend credence to the theory that she suffered from mental illness (probably bipolar disorder).

Stephen Fry

Fry spoke about his disorder in the BBC 2 documentary The Secret Life of the Manic Depressive. "It's infuriating I know, but I do get a huge buzz out of the manic side. I rely on it to give my life a sense of adventure, and I think most of the good about me has developed as a result of my mood swings. It's tormented me all my life with the deepest of depressions, while giving me the energy and creativity that perhaps has made my career."

Sting

In a May 1996 interview with Live! magazine, Sting was quoted as saying: "During that period with The Police, I was suicidal. My first marriage and my relationship with the other members of the band was collapsing. I was manic-depressive... I was out to lunch." However, it is unclear whether he was genuinely bipolar or using the term manic depressive as a figure of speech.

Virginia Woolf