The twentieth-century research in philosophy of mathematics was mainly focused on foundational studies. Either specific mathematical theories were proposed as ultimate foundations (set theory, category theory, …), or mathematics was imbedded in specific philosophical theories (naturalism, realism, neo-platonism, structuralism, …). All these approaches were focused on the outcomes or "products" of mathematical practice.
Since the seminal work of Imre Lakatos, Proofs and Refutations, however, it became clear that to fully understand mathematics, must also involve an understanding of the mathematical activity itself, as a process.
What is it that mathematicians do when they do mathematics? This conference is aimed at bringing together all kinds of contributions relevant to this question. They include both discussions about the large-scale structure of mathematics (Are there revolutions in mathematics? Is a Popperian, a Lakatosian or some other framework best suited? How does the mathematical community fit into society?), and reflections on the micro-practice of mathematics (What exactly turns a piece of text into a proof? What role do analogies and metaphors play in mathematical practice? What role does mathematical beauty play?).
It has been the aim of the organizers to search for a balance between, on the one hand, theoretical considerations on these issues, and, on the other hand, case studies of specific mathematical problems.
Invited Speakers
- Jill Adler (University of the Witwatersrand, Johannesburg, SA)
- Jody Azzouni (Tufts University, Medford / Somerville, MA)
- Paul Ernest (School of Education, University of Exeter, UK) - did not participate
- Eduard Glas (Technische Universiteit Delft, NL)
- Reuben Hersh (Prof. Emeritus, The University of New Mexico)
- Sal Restivo (Rensselaer Polytechnic Institute, Troy, NY)
- Robert Thomas (University of Manitoba, CA; editor Philosophia Mathematica)