Traditionally, there has been a deep divide between philosophy of mathematics dealing with foundational issues (questions about mathematical ontology, connections between logic and mathematics, and the proper axiomatic framework) and sociological and didactical approaches to mathematics deadling with a description of mathematical practice (including mathematics education and related matters). Currently, we witness this picture undergoing considerable changes.

In the tradition of the *Grundlagenkrise*, philosophy of mathematics was
focussed on the battles between the schools of Platonism, intuitionism, and
formalism - approaches that have entirely lost their lustre. In the past ten
to fifteen years, however, new viewpoints entered the philosophical debate,
viz., naturalism (e.g., Maddy), structuralism (e.g., Shapiro), and social
constructivism (e.g., Lakatos, Tymocko, Hersh). All of these approaches to
mathematical thinking have in common that they focus on mathematical practice,
take seriously linguistic usage in the community of professionals, and
emphasize (naturalism in a weak sense, social constructivism in a very strong
sense) the social embedding of mathematical practice and therefore of the
epistemic prerequisites of mathematical research. Accordingly, Corfield in his
2003 monograph *Towards a Philosophy of Real Mathematics* demands more
attention to the areas of mainstream mathematics and criticizes the fact that
philosophers of mathematics disregard everything since GĂ¶odel's theorem
as a kind of footnote to mathematics, irrelevant to their loftier concerns.
But not only the philosophical community has started to discuss mathematical
practice. A (now famous) joint paper by Princeton mathematicians Arthur Jaffe
and Frank Quinn on rigour in mathematics incited the so-called "Jaffe-Quinn
debate" in mathematics (published in the *Bulletin of the American
Mathematical Society* in 1993). In its wake many working mathematicians
have discussed the practical consequences of the social conventions in the
mathematical community, most famously Bill Thurston in a reply published in
the same journal in 1994, who describes a view of mathematical practice that
focusses much more on the social acceptance mechanisms of the community than
on formal proof.

All these developments question the special character of philosophy of mathematics as traditionally conceived. Our workshop is devoted to developing this line of development further, putting special emphasis on the epistemological issues involved.

Last changed: November 4th, 2005