This post is about some general conclusions held at the end of the workshop recently organised in Athens (Oct 11th and 12th) by the center for history and philosophy of sciences in the university of Athens, with the cooperation of centre Koyré and the support of the French programme “GDR histoire des mathématiques” [argument; program].

I have tried to summarize the main points of conclusion as best as I could – I invite the colleagues who took part in it to complete or correct my account if needed.

***

The discussion began by the quotation of the conclusion of the argument or the workshop [x]: “The aim of the workshop, then, is to make explicit and discuss the purposes and criteria of such comparisons, through the concrete attempt to construct such comparative studies on a limited example,  and the study of secondary literature. This work might help, in particular, to clarify methodological issues for future studies. Depending on the results, it might enable us to prepare a larger international congress on similar questions.”

We therefore discussed briefly (a) what seemed to us emerging issues, that might be dealt with in future meetings, and to discuss (b) the possibility and nature of such meetings, in the present circumstances.

(a) emerging issues.

• Mathematical commentaries: antique and medieval commentaries are much studied in general, esp. for those with philosophical contents for which there is already a huge literature. The specificities of mathematical commentaries, many examples of which were studied in the workshop,¹;  are worth of inquiry. This might be, then, the subject of future workshops and discussions, especially since the HASTEC structure has, as one of its cooperative axis, the very notion of commentary [x].
• Mathematical encyclopedia: again, several talks had to do with encyclopedic forms, like Pachymere’s quadrivium, but also Theon’s particular and intentional way to “capitalize” on various sources, Jean Borrel’s work, and Stevin’s overall conception of the role of ‘mathematical style’ in his works.
• Mathematical series of problems: since some of the contributions, from the outset, stemmed from the collective work done in the corresponding project within HASTEC [x]. There will be a seminar and continuation of it anway, next year in Paris (a more detailed annoucement will follow, around January).
• The application of literary genres to mathematical texts at large: more generaly, the notion that comparing texts not only meant comparing them from the point of view of their contents, but from that of their belonging of a definite genre, was obviously a key issue. This is not surprising, because the theory of genres, as soon as it is question of comparing texts, is a natural tool to use – which is one point and raison d’être made clear in the “series of problems” project [my talk, point 2.2]. This might open toward an interesting meeting associating experts of this theory or of closely related literature, like the astronomical one as we saw with Jeffrey’s talk.
• The nature and reception  of Diophantus’s work obviously was another strikingly emerging issue, for the number of contributions showing one aspect of the other of the re-appropriation of Diophantus: Ianna’s on Theon’s use of Diophantine categories for species of numbers; Jean Marie’s on Stevin’s translation of Xylander; Giovanna on Xylander himself²; Jean and Nancy on Pachymere and Planudes; Michalis on the historiographical discussions about “ancient algebra”, part of which concerns Diophantus up to the present day; myself on Diophantus’s “rhetorical aspects”³. This might become, then, the subject for another meeting, about “Diophantus and company”⁴.

(b) the possibility of future meetings.

We finally discussed more political and financial problems, related to the very possibility of such meetings, which have the great advantage to be relatively informal, based on actual readings, and not focused on publication as it is the case with more formal events. The ground problem is of course to build such opportunities, which are made necessary for the low numbers of specialists of these kind of issues in each country (here the States, the UK, France and Greece).

Some more or less serious ideas were launched, I list them (especially the most serious proposals 🙂 ) as a reminder and white stone:

• consolidating an international group of “personnes de bonne volonté” who would be ready to host in turn informal workshops like this one: once in Athens, once in Paris, once in London, etc. As for funding, finding a compromise between collective and personal contributions.
• organising an international congress, as initially scheduled, for the sake of making more visible the state of the art; the disavantage is heaviness, the advantage is the possibility to build an interdisciplinary argument and invite specialists of various fields, and to gain visibility through publication.
• having Jeff organise a hi-tech session in Indianapolis with the rest of us connected through skype: he would then discuss with a host of different monitors. The advantage is that he could cut short of any argument that would displease him by only pressing a button;
• organising a session in emerging Kurdistan, so as to get as closest as possible to interesting Iranian manuscripts (more dangerous, perhaps we should wait);
• finding a beautiful, poetic and possibly inexpensive place to meet and discuss: a Greek Island, any place lost in the mountains, an isolated farm in the mid-west.

More seriously, one important point (to my mind) that we discussed is the perimeter of such meetings: what seems really interesting is to have experts from various periods spanning from antiquity to the Renaissance (at least) and covering various cultural and linguistic areas, especially the Byzantine, arabic and latin Middle Ages.

1. namely: Ianna’s talk on Theon’s technique; Dora’s on Hero, as far as his meta-mathematical remarks are considered as being a kind of commentary; Michalis’s touching on the precision interpretation of Hero’s commentary on Euclid bookII; Jean-Marie’s insofar as Stevin relied on Xylander’s translation of Diophantus with Planude’s scholia; Jean and Nancy on Planude’s commentary itself [↩]
2. for even though she turned to Borel for reasons related to the advancements of her “SoP” paper, this was her initial project to discuss this text [↩]
3. even tough I finally did not discuss this point as it was planned [↩]
4. as Jeffrey remarked, a good title for getting funds 🙂 [↩]

Alain Bernard

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