70 A History ofMathematics
since Cicero’s time (first centurybce). Briefly, this is that the Romans in contrast to the Greeks
made no contribution to mathematics, and that any works of theirs which contain or use it, such
as Vitruvius’ architecture, are trivial in comparison with the Greek achievements. The charge has
some basis in fact, as Cuomo acknowledges—‘I would be hard put to adduce a Latin equivalent
of Euclid, Archimedes or Apollonius’, she admits (p. 194). This seems like an understatement;
where are the Latin equivalents of Heron or Nicomachus? True, these second- or third-rate
mathematicians worked under Roman rule, and may have been, like St Paul, Roman citizens.
However, they wrote in Greek, and in a tradition which was, and continued to be, overwhelmingly
Greek. The Romans, with better access to the Greek classics than the ninth-century Arabs or the
Renaissance Europeans, never seem to have felt the same need to build on their work and develop
it. And while Cuomo also interestingly makes a historicist point about the class angle contained in
Cicero’s statement (ideas of ‘the Roman’ and ‘the Greek’ were marks of different kinds of prestige,
while many users of numbers, and land-surveyors in particular, were seen as jumped-up technical
upstarts), one is still left with an underlying feeling that it is an ideological statement based on
good factual evidence. The most interesting part of her argument is a broader one, and does bear
serious consideration: that thepracticeof mathematical methods of some sophistication pervaded
the Roman world from top to bottom. Some of her examples, notably the charioteer whose tomb
boasts that he
drove chariots for 24 years, ran 4,257 starts and won 1,462 victories, 110 in opening races. In single-entry races he
won 1,064 victories, winning 92 major purses, 32 of them (including 3 with six-horse teams) at 30,000 sesterces...
(CIL 6.10048 (Rome, 146ce), tr. in Lewis and Reinhold 1990, pp. 146–7)testify to the power of ‘numbers’ to impress rather than to the ability to do anything with them.
However, her study of the practice of the despised land-surveyors (see also Dilke 1971), and of
Vitruvius show how an appreciation, and application of classical geometry underlay their prac-
tice. Perhaps rather than decrying the ‘low level’ of geometry present in Vitruvius’s architecture,
we should think about the fact that it was a Roman, rather than a Greek, who bothered to write
such a treatise; the architects of Greek temples were not, it would seem, given to exposition.
We have different cultures (cohabiting in the same empire) with different ideas of what a book
is for.
Similarly, the famous tunnel of Eupalinus in Samos, dated at 550–530bce, is often cited as an
amazing example of very early practical Greek geometry; how did the builders of the tunnel, who
started from the two sides of a mountain, contrive to meet so accurately in the middle? The answer
is again that we do not know, and no Greek sources seem to have taken the trouble to explain
how such a recurrent problem could be solved. The Roman surveyors, however, organized as a
profession in which a discipline was transmitted by means of ‘textbooks’, both explained how they
did it^8 and wrote instructions whosefoundationis in their training in some derivative of Euclidean
geometry.
This debate is only now beginning; the same applies to the doubts which Cuomo has cast on the
idea that Greek mathematics was ‘in decline’ from (say) the time of Ptolemy, if not before. It is not so
much a question of rehabilitating the Romans (awarding points to individuals or to civilizations for
their excellence in mathematics should not be part of the business of history, though it often is).
Rather, as we saw in Chapter 1 with the pre-OB periods, it is a question of looking at practices- See Cuomo (2001, p. 158) for a surveyor’s account of how he helped the weeping villagers whose tunnel had manifestly gone
badly wrong.