U.C. Berkeley

Contemporary work in scientific explanation has pursued to a great extent the project of a
single unified account of the nature of explanation. Unfortunately, the drive towards unfication
has also left by the wayside an important number of phenomena. In particular, many theories of
scientific explanation do not address mathematical explanation, either because they rule
mathematical explanations out of court from the outset or because they hold that their account
of explanation automatically takes care of mathematical explanation. In this paper we begin
by providing evidence for the claim that mathematicians seek explanations in their ordinary
practice and cherish different types of explanations. We go on to suggest that a fruitful
approach to the topic of mathematical explanation would consist in providing a taxonomy of
recurrent types of mathematical explanation and then trying to see whether these patterns
are heterogeneous or can be subsumed under a general account. We maintain that mathematical
explanations are heterogeneous. However, neither giving the taxonomy nor arguing for the
previous claim is what we have set for ourselves in this paper. Rather, we would like to
provide a single case study of how to use mathematical explanations as found in mathematical
practice to test theories of mathematical explanation. This can be seen, as it were,
as a case study of how to show that the variety of mathematical explanations cannot be
easily reduced to a single model. The case study will focus on Steiner's theory of
mathematical explanation and Pringsheim's explanatory proof of Kummer's convergence
criterion in the theory of infinite series.
## Friday, May 2, 2003

SST 777

3 pm

*Refreshments will be served*

©

SST 777

3 pm

©