The young Mozart – dragged around the courts of Europe like a performing flea by his father, cooed over when he played the violin sonatas he composed at the age of seven – was viewed as an intriguing freak, and those who droolingly patronised him lost interest when he grew up.

Perhaps maimed by those early years of exploitation, Mozart, like a rococo Jacko, defended himself by trying to remain an infant, with a fondness for scatological baby talk and a cunning expectation that he would always be loved, indulged and subsidised.

It was the 19th century that sanctified childhood. For Wordsworth, it was a time spent in a shining, earthly Eden; those who unluckily lived beyond it were bound to lose their lustre. Hence Wordsworth’s homage to ‘the marvellous boy’ – Thomas Chatterton, who forged some poems by a medieval cleric and then, when the fraud was exposed, killed himself at the age of 18. Keats added to art’s martyrology by dying at 25. Shelley lasted until he was 29 when, recklessly eager for extinction, he drowned in a storm off the Italian coast. Byron, having reached decrepitude at 36, pointlessly perished during a chivalric escapade in the Greek war of independence.

Romantic writers worked with an almost crazed acceleration, aware that maturity was a death sentence. Georg Buchner, battling meningitis and depression while fending off political persecution, revolutionised dramatic form in plays like Danton’s Death (written in five weeks) and Wozzeck (part of the Barbican’s Young Genius season), which he hadn’t quite finished when he died of typhus in 1837, aged 23.

Pushkin single-handedly invented Russian literature, then died in the same year as Buchner in an inane duel; he was 38, and had disgraced himself by outliving his self-destructive idol, Byron. Baudelaire paid tribute to the artist’s stubborn refusal to accept inexorable time: genius, he said, was childhood recovered at will (and with the aid, although he didn’t say so, of hashish).

The cult of the wise child – somehow infused with a secret knowledge of the paradise we lived in, according to Wordsworth, before we were born – launched some odd, anachronistic careers. In the theatre, child actors impersonated their elders. Edmund Kean made his debut in 1798 at the age of nine. Master Betty, known as ‘The Wonderful Boy’, was all of 11 when he first strutted and fretted on stage in 1804; with his voice still unbroken, he went on to give pubescent performances of the great Shakespearean tragic roles. Audiences accepted the incongruity or absurdity because Master Betty’s possession of such skills seemed mysterious, even mystical.

How could he simulate passions he was physically incapable of feeling? Was he a fallen angel, or had he entered into a Faustian pact with the devil? Victor Hugo, writing about Shakespeare, summed up the almost religious awe with which such prodigies were regarded: ‘Each new genius is an abyss.’ Life’s conventional routine suddenly disrupted; we are confronted by a superhuman or inhuman exception to the norm.

Scientific innovators, like musical virtuosi, have often been shockingly youthful; two at least were abruptly cut off as they were in the process of reconstructing the universe. A Lancashire lad called Jeremiah Horrocks noticed errors in the calculations of planetary orbits while he was still a teenager, and correctly calculated the transit of Venus. Horrocks published his findings in 1639, and died suddenly two years later; he was 22.

In 1832 Evariste Galois challenged an acquaintance to a duel in order to avenge a woman’s honour. The night before the meeting, he sat up to record his mathematical testament, a prophetic exposition of abstract algebra. In those few hours, he invented what we call group theory. Galois was killed the next morning. As peritonitis from his wound wracked him, he said to his brother: ‘Don’t cry. It takes all my courage to die at 20.’

A character like Thomasina in Stoppard’s Arcadia – a teenager who formulates the second law of thermodynamics in 1809 – is not so very improbable. Her mathematical-doodling computes the heat loss that will bring the world to an end; she confirms the truth of her prediction by dying soon afterwards in a house fire.

By the early 20th century, the cult had worn thin. In 1908, when he was 11, Erich Wolfgang Korngold composed the score for a ballet, Der Schneeman. ‘A genius! A genius!’ cried Mahler, as if announcing the second coming of Mozart. Sceptics thought Korngold’s music was written for him by his father, a critic; once, when the boy queried tempi at a rehearsal of his piano trio, his father told him to shut up.

Korngold’s later music came to sound more and more like pastiche, and in the 1930s, having emigrated to California, he began supplying slush for the soundtracks of Warner Brothers films. It’s interesting and a little sad that one of Korngold’s current supporters is Andre Previn, who at the age of 16 caught the bus from school to MGM, where he orchestrated scores for what he calls ‘cornball musicals’. Previn is now in his late seventies, hobbled by arthritis. Honouring Korngold, he is remembering his own ‘after-school pilgrimage’ to the studio, and perhaps also regretting lost youth and wasted promise.

Orson Welles – the most notorious young over-achiever of the last century – came to consider his own precocity a curse. It was as if he had mortgaged his future by impatiently speeding in advance through the ages of man. He began playing King Lear, who is meant to be over 80, when he was 10. For his first appearance on screen, in Citizen Kane aged 25, he mummified and mortified himself inside pads of sponge rubber and latex pouches; membranes like cobwebs were applied to his sagging face, and lenses with rheumy fluid covered his eyes. But the improvident, unreliable boy wonder soon exasperated his bosses, who saw to it that Welles had no chance to sustain his early successes. He kept his baby face, which looked on, sadly uncomprehending, as the rest of him turned to cumbrous, wheezing flab.

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