The story of John Nash offers interest and encouragement to patients, relatives and psychiatrists. He is a highly respected mathematician who as a young man published from Princeton an analysis that is relevant to economic bargaining, to governments, nuclear strategy, interpersonal relations and animal behaviour. Subsequently he developed schizophrenia and was disabled by his illness. His slow and impressive improvement enabled him to travel to Stockholm in 1994 to receive, in honour of his youthful work, the Nobel Prize for Economics. Some readers may recall that later he addressed a plenary session at the World Congress of Psychiatry in Madrid.

Nash derives from a stable American home with no history of schizophrenia. Yet at the age of 30 years he told colleagues that he was receiving encoded messages through newspapers. He noticed that men wearing red ties were signalling to him. Nash complained that his career was threatened by aliens from outer space. His recollection of this period is of mental exhaustion with an increasingly powerful understanding of a secret world unknown to others.

Twelve years ensued with involuntary admissions to psychiatric hospitals. Guilt, the need for penitence and dread became more prominent; voices argued within his head. Insulin coma and tranquillisers were given. Drug treatment conferred major benefits, renewing creativity, but he discontinued medication for a reason not usually proffered to psychiatrists: “If I take the drugs I stop hearing voices.” Eventually he was accepted home by his wife and allowed to attend Princeton informally.

During his 40s and 50s Nash and others noticed a gradual weakening of his psychosis. He still experiences abnormal thoughts and voices, though with minimal intensity. He now recognises their unnaturalness and rejects them, or wards them off by avoiding reflection on subjects, such as politics, that have provided a focus for psychotic beliefs.

What trick of genes or environment cruelly ensured that a son of Nash developed schizophrenia when 13 years younger than his father had been? Or determined that an illegitimate son, who spent his early years in a succession of foster homes, escaped the illness? More hopeful is the reminder that schizophrenia can substantially and spontaneously improve, even while untreated. Also reassuring is the success of medication, while it was taken, in dispelling both positive and negative symptoms and restoring talent. Credit should be given to his wife and to Princeton. Their tolerance and understanding are patently the opposite of strong expressions of emotion.

The biographer portrays mathematicians as usually remote or odd, citing examples that include the mental illnesses of Newton and Gödel. Yet her case is not proven; indeed she describes several practical and well balanced colleagues of Nash. With this minor reservation I recommend her sensitive account for professional and lay readers alike.