## ABSTRACT

In chapter 1, we observed that not only was public counting associated with political accountability, it became a symbol of, or a way of talking about, political participation and the role of the citizen. Moreover, accounts were but one of several mathematical activities that took place in a public context: there were also commercial arithmetic, practised by traders and bankers, the geometry of land division, and in general the mathematics associated with the technai, for instance architecture. Land division and commercial arithmetic can be connoted as ‘democratic’ mathematics: the former was a guarantee of equal distribution, whereas the latter was identified with moneyed economical exchange, as opposed to non-moneyed, nonquantified, status-dependent transactions, which had traditionally been dominated by aristocratic value systems.1 Aristotle, himself a supporter of oligarchy rather than democracy, even put forth what we could call a mathematizing theory of monetary exchange, where the value of a thing can be, in principle, completely reduced to a number, and transactions to arithmetical operations.