Reasoning and symbolism in Diophantus 345
elite-educated, literate form, Diophantus chose to produce not Euclidean
algebra, but Diophantine algebra.
I note in passing that the character of Diophantus – as intended for elite
literate culture – is in my view not in serious doubt. Th e material does not
conform to elementary school procedures; it is ultimately of great complex-
ity, suitable only for a specialized readership. It had survived only inside
elite literate tradition; and, as is well known, it quickly obtained the primary
mark of elite literate work – having a commentary dedicated to it (that of
Hypatia). 17
In other words, I suggest that Diophantus is engaged primarily in the
rearrangement of previously available material into a certain given format,
of course then massively extending it to cover new grounds that were not
surveyed by school algebra itself. Th is is very much the standard view of
Diophantus, and I merely wish to point out here what seem to me to be its
consequences. Let us agree that Diophantus is engaged in the refi tting of
previous traditions into the formats of elite writing sanctioned by tradition.
Th en it becomes open to suggest that he belongs to the overall practice of
late antiquity and the Middle Ages which I have elsewhere called deutero-
nomic: the production of texts which are primarily dependent upon some
previous texts. 18 Typically, deuteronomic texts emphasize consistency, sys-
tematicity and completion. Th ere is an attention to the manner of writing
of the text. Th is means that they bring together various elements that
might have been originally disparate. Th e act of trying to bring disparate
17 Th e evidence is the fl imsiest imaginable – a mere statement in the Suidas (Adler IV:644.1–4:
Yπατια... εγραψεν υπομνημα εις Διοφαντον) which, however, if not proving beyond doubt
that Hypatia wrote a commentary on Diophantus, makes it at least very likely that someone did.
18 Virtually everyone, from Tannery to Neugebauer onwards, has agreed that Diophantus was
acquainted with many arithmetical problems deriving from earlier Mediterranean traditions
and was therefore at least to some extent a systematizer. Some, such as Heath, had thought
that Diophantus’ systematization of earlier problems may not have been the fi rst in the Greek
world, making comparison with Euclid as the culmination of a tradition of writing Elements
(I doubt this for Euclid and fi nd it very unlikely for Diophantus). Th e dates are fi xed, based on
internal evidence, as –150 to +350. What else is argued concerning Diophantus’ dates is based
on scattered, late Byzantine comments which are best ignored. Th e e silentio , together with
Diophantus’ very survival, suggest – no more – a late date. (Th e silence is not meaningless,
as it encompasses authors from Hero to the neo-Platonist authors writing on number.) A late
date was always the favourite among scholars (not surprisingly, then, the thesis of an early
of Book I, Propositions i .8–10 and ii .5, respectively – most likely derive from a classroom
context). However, the bulk of papyri fi nds with mathematical educational contents are
diff erent in character, involving basic numeracy and measuring skills or, in more sophisticated
examples, coming closer to Hero’s version of geometry. Th e impression is that, in antiquity
itself, Euclid was fundamentally a cultural icon, which occasionally got inducted into the
educational process.