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Mathematical Practice, Crowdsourcing, and Social Machines

  • Conference paper
Intelligent Computer Mathematics (CICM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7961))

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Abstract

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend.

The Study of Mathematical Practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question-answering system mathoverflow contains around 40,000 mathematical conversations, and polymath collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of “soft” aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal.

Crowdsourced mathematical activity is an example of a “social machine”, a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.

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Authors and Affiliations

  1. Queen Mary University of London, UK

    Ursula Martin & Alison Pease

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  1. Ursula Martin
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  2. Alison Pease
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Editors and Affiliations

  1. Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Jacques Carette

  2. School of Informatics, University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, Scotland, UK

    David Aspinall

  3. School of Computer Science, University of Birmingham, Edgbaston, B15 2TT, Birmingham, UK

    Christoph Lange

  4. Faculty of Informatics, Department of Computer Graphics and Design, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic

    Petr Sojka

  5. Johannes Kepler University Linz (JKU), RISC, Altenberger Strasse 69, 4040, Linz, Austria

    Wolfgang Windsteiger

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Martin, U., Pease, A. (2013). Mathematical Practice, Crowdsourcing, and Social Machines. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds) Intelligent Computer Mathematics. CICM 2013. Lecture Notes in Computer Science(), vol 7961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39320-4_7

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  • DOI: https://doi.org/10.1007/978-3-642-39320-4_7

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