Mathematics has universal standards of
validity. Nevertheless, there are local
styles in mathematics. These may be the
legacy of a dominant individual (e.g. the Newtonianism of 18 These local
mathematical cultures are scientifically important because they can affect the
direction of mathematical research. They
also matter because of the cultural importance of mathematics. Mathematics enjoys enormous intellectual
prestige, and has seen a growth of popular publishing (including books by Ian
Stewart, Marcus du Sautoy, James Gleick, Simon Singh, Karl Sabbagh and
others). There have been films about
mathematicians ( What is needed is
a re-presentation of mathematics as a human activity, which means, among other
things, that it is part of culture. The
tools and knowledge necessary for this have been developing in recent years. Historians of mathematics have begun to
consider mathematics in its social, political and cultural contexts. Ethnomathematics studies mathematical
cultures, including advanced research cultures, using anthropological
tools. (The chief journal for
ethnomathematics is the US-based In the philosophy of mathematics, there is now a sub-field devoted to the philosophy of mathematical practice. So far, this has mostly emerged in continental Europe, and to a lesser extent in North America. The Brussels-based Perspectives on Mathematical Practice initiative met in 2002 and 2007 and published proceedings. The DFG-funded network PhiMSAMP (2005-2010) was a collaboration of researchers in several countries. The annual Novembertagung on the history and philosophy of mathematics serves beginning researchers in philosophy and history of mathematics. In France, there is a thriving Parisian history and philosophy of mathematics scene, and a mathematics thread in the studies of scientific practice at the Laboratoire d'Histoire des Sciences et de Philosophie (Nancy). So far, philosophy of mathematical practice has not focussed on mathematics as culture. This has prevented it from elaborating one possible answer to the student’s question, “why should I study mathematics?”, namely, “Because it is beautiful, glorious and deep”. Grounding this answer requires an exploration of the value of mathematics and the values of mathematicians, and communicating this answer requires an understanding of mathematics as part of our larger contemporary culture. Therefore, the time is ripe for an interdisciplinary initiative that brings together mathematicians, philosophers of mathematical practice, historians, sociologists, cognitive scientists, mathematics educationalists, popularisers and science journalists to research mathematical cultures, the value of mathematics as culture and its status in culture. Where these disciplines have encountered each other, it has been largely outside the UK and not on the topic of mathematics as and in culture. Hitherto, studies of mathematical culture are have been largely confined to ethnomathematics, and have taken place on a small scale in North America. In view of the interdisciplinary character of the meetings, each participant will be required to include a methodological commentary in the abstract published in the conference programme. The first and second conferences will include round-table discussions of the particular methodological challenges of interdisciplinary research.
1) Create an interdisciplinary, international network of researchers with interests in mathematics as and in culture, with a supporting internet node that will outlive this funded project. Specifically, to connect existing scholarly communities that are separated by national and/or disciplinary borders. I.e. the PhiMSAMP (Philosophie der Mathematik: Soziologische Aspekte und Mathematische Praxis) group in Germany; the Novembertagung group of historians; the mathematical practice group at the Centrum voor Logica en Wetenschapsfilosofie (CLWF) at the Vrije Universiteit Brussel; the community centred on the Italian Mathematics and Culture conference; the Parisian history and philosophy of mathematics scene; the Laboratoire d'Histoire des Sciences et de Philosophie at the Archives Henri Poincaré (Nancy); the Association for the Philosophy of Mathematical Practice; the North American Study Group on Ethnomathematics; The British Society for the History of Mathematics; national and international bodies concerned with mathematics education (including the groups working on the use of history in mathematics education); cognitive scientists working on mathematical learning and cognition; British philosophers of mathematics. 2) Facilitate discussion of the methodological challenges facing the study of mathematics as culture. Mathematics is simultaneously culture and knowledge. Scholars that treat it as culture must respect its status as knowledge; those that engage with it as knowledge must acknowledge that it is a collection of human practices. 3) Explore and map some of the various contemporary mathematical cultures These can be the cultures of professional research mathematicians, but also user groups such as engineers or actuaries, and cultures within education, among teachers and students. Of particular interest are the images of mathematics among reluctant users of mathematics. 4) Explore the rational structure of mathematical value-judgments When
mathematicians award or withhold prizes, scholarships, PhDs and grants,
correctness is almost never the decisive criterion. Rather, the question is whether the work is
worthwhile, interesting, elegant, promising, insightful, 5) Articulate the cultural and educational value of mathematics in a form useful for educationalists and policy-makers The value of mathematics is usually argued either in economic terms, or in terms of the excitement of making rare breakthroughs. There is a neglected middle ground: mathematics as a proper part of the cultural diet of an educated person. 6) Publish as a book and on the internet high-quality scholarship relating to mathematics as culture Speakers at the conferences will be briefed to refer to contributions from other disciplines and (in the case of the second and third conferences) from earlier meetings. When deciding what to include in the book, the density and insight of connections made across disciplines and communities will be a leading criterion.
This project will host three conferences. The The The
The programme panel will invite representatives of the various communities listed under the first aim (see above). In addition, we will invite mathematicians known to have an interest in these topics, the authors of popular books on mathematics and science journalists. At every conference there will be space in the programme for postgraduate students to present their work (if they are in parallel sessions, they will not be timetabled against established researchers) and funds to support their attendance.
The network will be managed by the Principal Investigator, aided by an administrative assistant who will organise the meetings, coordinate publication of the outputs and develop and maintain the website. The PI will share responsibility for inviting participants, judging abstracts of proposed talks and choosing contributions to the outputs with a panel consisting of: - Prof Jeremy Gray, Professor of the History of Mathematics (Open University)
- Dr. Matthew Inglis, Lecturer (Mathematics Education Centre, Loughborough University); Honorary Research Fellow (Learning Sciences Research Institute, University of Nottingham); Royal Society Worshipful Company of Actuaries Research Fellow.
- Dr.
Benedikt Löwe,
**Universitair Docent (UD)**(Institute for Logic, Language and Computation, Universiteit van Amsterdam);**Privatdozent**(Mathematical Logic Group , Rheinische Friedrich-Wilhelms-Universität Bonn);**Professor**(Fachbereich Mathematik, Universität Hamburg); Principal Investigator of the PhiMSAMP programme. - Dr. Alison Pease, Centre for Intelligent Systems and their Applications, (School of Informatics, University of Edinburgh). Convener of the 2010 Symposium on Mathematical Practice and Cognition (http://homepages.inf.ed.ac.uk/apease/aisb10/home.html)
The conferences will be recorded, edited and published on the permanent project website. The conveners will publish near-final drafts of the contribution abstracts some weeks ahead of each meeting and encourage contributors to discuss each other’s abstracts before the meeting (using a discussion list hosted at UH). That way, there will be conversations already ongoing when each conference starts, which may continue after the end of the physical meeting. There will be a twitter stream associated with these conversations and conference announcements. In order that later meetings can build on earlier ones, the conveners will publish as much electronic material (slides, papers, audio recordings) as possible online shortly after each meeting and encourage contributors to later meetings to refer to it. The project will invite to the conferences (and pay reasonable expenses for) representatives of dissemination and impact routes, such as mathematics popularisers, science journalists, officials of relevant government departments, and senior representatives of the National Centre for Excellence in the Teaching of Mathematics (NCETM) and the British Society for Research into Learning Mathematics (BSRLM). The project will publish (as a book) a collection of the best contributions to the conferences. To maximise the value of this output, the density and insight of connections made across disciplines and communities will be a leading criterion in determining which contributions to include. With interdisciplinary capacity-building in view, contributors will be encouraged to reflect on interdisciplinary methodology. |