Collective Discovery Events: Web-Based Mathematical Problem-Solving with Codelets - Computational Creativity Research: Towards Creative Machines - page 363

Chapter 18
Collective Discovery Events: Web-Based
Mathematical Problem-Solving with Codelets

Petros S. Stefaneas, Ioannis M. Vandoulakis, Maricarmen Martinez
and Harry Foundalis

Abstract While collaboration has always played an important role in many cases of
discovery and creation, recent developments such as the web facilitate and encourage
collaboration at scales never seen before, even in areas such as mathematics, where
contributions by single individuals have historically been the norm. This new scenario
poses a challenge at the theoretical level, as it brings out the importance of various
issues which, as of yet, have not been sufficiently central to the study of problem-
solving, discovery, and creativity. We analyze the case of collective and web-based
proof-events in mathematics, which share their temporal and social nature with every
case of collective problem-solving. We propose that some ideas from cognitive archi-
tectures, in particular the notion of codelet—understood as an agent engaged in one
of a multitude of available tasks—can illuminate our understanding of collective
problem-solving, and act as a natural bridge from some of the theoretical aspects of
collective, web-based discovery to the practical concern of designing cognitively-
inspired systems to support collective problem-solving. We use the Pythagorean
Theorem and its many proofs as a case study to illustrate our approach.

All authors contributed equally to this chapter.