Possibly a genius; almost certainly male. Maths is in the genes, we are told, and it is only a matter of time before scientists isolate the cause in the Y-chromosome. Four successful films - A Beautiful Mind, Enigma, Good Will Hunting and Pi - all depict maths geniuses as socially inept, lovable but disturbed men.
In maths, as in designer clothes, it seems, image is everything. Popular misconceptions and gender stereotypes are so ingrained in our psyche, that we often accept what we see and are told without question. In recent studies of adult students, men who were lousy at maths reckoned they were numerate (see 16-page Adult Learning special report in this week's TES).
Meanwhile, a study by Heather Mendick of Lancaster university, found that high-achieving schoolgirls doing two maths A-levels thought they were useless at the subject.
If bright girls underrate themselves, what of the lower-achievers? Research evidence shows that girls who leave school with poor maths grades find it much harder to become numerate than do low-achieving boys. And many girls who were ahead at GCSE and A-level fall behind again as adults.
There are numerous theories why so many girls do badly at maths. Professor Alan Smithers blames the "irrelevance" of the curriculum, which also discourages boys. Professor Adrian Smith, author of the recent maths inquiry report, agreed that the curriculum neither stretches the bright nor motivates the less able. Inspectors put the problem down to a "lack of imagination" in teaching methods. But adults who failed maths at school tend to blame attitudes. Unthinking teachers, they say, denigrate girls for not taking the risks that boys do. Worst of all, there is too little encouragement. Girls in particular want to hear: "You can do it."
Both the professors and parents are right. We are still a long way from having the ideal maths curriculum and teachers could do more to encourage girls. But without more being done to change social attitudes, no school reforms will work.