Genevieve’s hair is cut in spikes. She’s 16, petite, sexy, stylish, likes to go to clubs and giggle with her friends. You’ve met hundreds like her, in the classroom, on the beach, taking your order in fast-food joints, pouring down the high street on a Saturday night.

Genevieve’s hobby is a little unusual. She spends her spare time playing with numbers. She’s hooked. She’s taught herself calculus with the help of a family friend; she likes to mess about with trigonometry. She thinks the maths behind her big brother’s favourite computer game could be improved and, on the Saturdays when she doesn’t go clubbing, she stays up all night trying out solutions to this self-imposed problem.

At school, Genevieve is still doing GCSEs. She’s not particularly keen on school maths, though she is in the top set. Her options include music and drama: she wants to be an actress. She is fiercely independent but still curls up in her mother’s lap. She hasn’t got an important boyfriend, preferring to go around in a gang of girls.

When teachers talk to her, her words flash out, challengingly. “Why do you think that?” she’ll ask. “Did you get that idea when you were at college?” Some teachers dislike this cheekiness. They’ve seen all too many challenging teenagers who have nothing to contribute except a sneer and a jibe.

Sarah, the drama teacher, positively enjoys Genevieve’s arms-akimbo stance on life - that’s probably why drama has become her favourite subject. Yet drama is called a “soft” or “girly” subject. In fact, in Genevieve’s school, most of the best drama students are girls.

It is otherwise in maths. Boys dominate. Genevieve is frustrated in her maths class. Somehow, there is no scope for her to follow her own creative spark. There would be no point in bringing in her own mathematically-based project. Rightly or wrongly, Genevieve feels that Mr Newton doesn’t welcome that kind of thing from girls, especially not girls with double piercings in their nose.

Mr Newton wants A* grades, and the more the better. Anything else can wait till sixth-form level. Still, Genevieve doesn’t want to wait, she feels her problem flickering away at the centre of her mind. It distracts her, it focuses her, it delights her and torments her. It is making her grow and it fills her with excitement and dizzying waves of self-confidence when she masters a new bit of theory. But none of this comes to school. “School makes me mental,” she says.

Genevieve would flinch if you called her a genius. A genius, that’s some kind of geek, isn’t it? Genevieve matches the formula - 90 per cent perspiration, 10 per cent inspiration - but she’s “normal”. How can she be...Blake struggling in a garret, Schumann going mad in an asylum? Must people with extraordinary abilities struggle with misery and rejection as well as with their self-imposed tasks?

Supposing a “genius”, a perfectly healthy individual, doesn’t want to suffer?

Self-interest dictates that Genevieve’s school concentrates on its place in the league tables. You can’t get more than an A*, so don’t bother. Self-interest tells Genevieve to stop doing school maths. Something doesn’t quite compute - and it isn’t Gene-vieve’s sums.