Talk given at International Association for Computing and Philosophy – Annual Meeting 2016 (University of Ferrara).
Abstract Within the philosophy of mathematical practice, the collaborative Polymath-projects initiated by Timothy Gowers have since their start in 2009 attracted a lot of attention (Van Bendegem 2011, Pease and Martin 2012, Stefaneas and Vandoulakis 2012).2 As this field is concerned with how mathematics is done, evaluated, and applied,3 this interest should barely surprise us. The research-activity within Polymath was carried out publicly on several blogs, and thus led to the creation of a large repository of interactive mathematical practice in action: a treasure of information ready to be explored. In addition, the main players in this project (the Field-medallists Timothy Gowers and Terrence Tao) continuously reflected on the enterprise, and provided additional insight on the nature of mathe- matical research, and large-scale collaboration (Gowers 2010: §2). This led amongst others to the claim that the online collective problem solving that underpins the Polymath-projects consists of “mathematical research in a new way” (Gowers and Nielsen 2009: 879).
In previous work (Allo et al. 2013a;b) we relied on formal models of interaction, mainly from the dynamic epistemic logic tradition, to develop a theoretical basis for the analysis of such collaborative practices, with the explicit intent to use logic to understand the practice instead of using logic as part of the foundations of mathematics. In particular, we argued that focusing on available announcement-types (public vs private announcements) leads to a finer typology of scientific communities than the models used in for instance Zollman (2007; 2013), and is better suited to model collaborative enterprises.
The present paper further develops this work by supplementing it, on the one hand, with a computational/empirical study of all the Polymath-projects (the latest project was initiated in February 2016) that allows us to apply methods from social network analysis to the totality of interactions that took place within 11 Polymath projects and 4 Mini-Polymath projects, and, on the other hand, with insights drawn from Dunin-Keplicz and Verbrugge’s (2010) work on logics for teamwork. The upshot is to integrate data-driven and logic-driven (a priori) methods for the study of scientific collaboration in general, and ICT-mediated massive collaboration in mathematics in particular.
