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    • Brendan Larvor

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    Project Overview

    Rationale and research context

    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 18th century British mathematics).  Or, there may be social or economic reasons (such as the practical bent of early modern Dutch mathematics).  Sometimes, a local style results from deliberate policy.  For example, in the 1920s and 1930s, Polish officials identified ‘foundations of mathematics’ in the style of topology and real analysis as something that Polish mathematicians should excel in.  Local mathematical cultures can reflect the uneven geographical spread of a methodological division.  For example, in theoretical computer science, there are two main directions: ‘Algorithms and Complexity’, and ‘Logic in Computer Science’ .  In many countries, the split between those areas is heavily uneven. 

    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 (Good Will Hunting and A Beautiful Mind), a novel (Uncle Petros and Goldbach’s Conjecture) and plays (Proof, Arcadia and A Disappearing Number).  However, this same intellectual prestige encourages a disengagement from mathematics.  Ignorance of even rudimentary mathematics remains socially acceptable.  Policy initiatives to encourage the study of mathematics usually emphasise the economic utility of mathematics (see for example the 2006 Science, Technology, Engineering and Mathematics (STEM) Programme Report of the Department for Education and Skills).  Appeals of this sort rarely succeed with students unless there is a specific promise of employment or higher remuneration.  Moreover, the policy response to the STEM report has largely focussed on institutional connections, and has not addressed the unhelpful perception of mathematics as remote and forbidding. 

    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 Journal of Mathematics and Culture.)  There is now an established sociology of science and technology, published in journals such as Science as Culture and the Journal of Humanistic Mathematics.  Mathematics educationalists have begun to draw on some of these developments (particularly historical research). 

    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. 

    Aims and objectives

    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, etc..  If these judgments are not arbitrary, they should refer to some standards or values.  Are these common across all the mathematical cultures explored in (3)?  How are they taught?  How do they evolve?

    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.

    Timetable of Activities

    This project will host three conferences.  The first (September 2012) will explore and begin to map the variety of and connections among contemporary mathematical cultures.  These can be research cultures, but may also include practitioner cultures (e.g. among engineers, economists, social scientists, etc.) and mathematical cultures among instructor and student groups (e.g. primary/secondary/tertiary teachers, school pupils, mathematics students at all levels).  The project will not invite contributions on historically or culturally remote mathematical cultures except as these illuminate contemporary mathematical culture in developed societies. 

    The second (September 2013) conference will articulate and classify mathematical values.  What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, ‘explanatory’, etc.?  What is the rational structure of the deliberations mathematicians use to reach value judgments (in PhD examinations, book reviews, journal referee reports, etc.)?  This conference will build on the first conference by referring these questions to the various mathematical cultures identified at that first event. 

    The third conference (Easter 2014) will discuss mathematics in public culture.  Amongst other topics, it will explore the question “why should I study mathematics?”.  This third meeting will build on the first conference by identifying the contributions from and audiences in the various mathematical cultures.  It will build on the second conference by drawing on the articulations and explorations of mathematical values. 

    Key speakers or participants

    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.

    Management and co-ordination

    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:

    Dissemination

    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.

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