Competence in mathematics is a basic requirement for effective citizenship in a modern numerate society (Cockcroft, 1982). Poor numeracy skills are known to be a serious handicap for paid employment in the US (Rivera-Batiz, 1992) and the UK (Bynner & Parsons, 1997). Indeed, the UK Basic Skills Agency has published a report suggesting that numeracy is more important even than literacy in terms of career prospects in the UK (Bynner & Parsons, 1997). And the trend is toward an even greater emphasis on numeracy: recent research for the British Science, Technology and Mathematics Council shows that “mathematical skills in the workplace are changing, with increasing numbers of people engaged in mathematics-related work, and with such work involving increasingly sophisticated mathematical activities” (Hoyles, Wolf, Molyneux-Hodgson, & Kent, 2002).

The level of competence routinely demanded in numerate cultures today would have been considered quite exceptional 200 years ago. How then does one distinguish today's expert from the normally competent school-leaver who can handle numbers of arbitrary size, fractions and decimals, logarithms, equations with unknowns and negative roots, and some differentiation and integration? One could arbitrarily take the top n% of a standard test (like the SAT-M), but what should n be? Francis Galton, in Hereditary Genius, used obituaries from The Times of London and a biographical dictionary, Men of our Time, as the criteria of “eminence.” This gave him an estimated proportion of 0.025% of the population. Really exceptional individuals, his class G, were about one-twentieth of these.