Collective Discovery Events: Web-Based Mathematical Problem-Solving with Codelets - Computational Creativity Research: Towards Creative Machines - page 380

ligent enough to cope with hard mathematical problems, is replaced in Web-based
problem-solving by the image of a “collective” mathematical mind, which is more
efficient to handle difficult problems in shorter time. The new picture is vividly
outlined by Nielsen [ 13 ], as an epoch-making type of “networked science”.
Collective intelligence in Web-based problem-solving is characterized by open-
ness, i.e., unrestricted sharing of ideas and intellectual property among codelets,
peering of codelets and joint goal-directed action. Thus, collective intelligence can
be understood as an emergent distributive property over numerous codelets of a
“collective mind” that uses a set of flexible and adaptable tools from a Web-based
repository in facing mathematical problems.
Such tools have a double nature: on the one hand they are objects readily available
to be used for any specific purpose, i.e., they are objects “ready-to-hand” (to use
Heidegger's terminology), just lying there; on the other hand, when these tools are
activated (for instance, when Mathematica is used) they may initiate processes and
produce contributions that even a prover might fail to reach, although they lack the
intelligence of a prover. From the latter standpoint, they act as (intelligence-less)
codelets, insofar as they actively work on data and follow the architecture of the
Web.
18.8 Conclusion
A system for Web-based cooperation among people for the handling of proof events
andmathematical problem-solvingwas proposed in this paper. Themain advantage of
this approach over the more traditional proving methods is the interesting possibility
that mathematical problems that are far too complex to be solved by a single person
might become solvable by a community of mathematicians who cooperate following
the system outlined in the present text. It is our firm belief that the limits of group
thinking and cooperation among members of a community lie far beyond those of
individuals, and that such limits need to be further explored.
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