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        As Thurston says? : On using quotations from famous mathematicians to make points about philosophy and education

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        Author
        Hanna, Gila
        Larvor, Brendan
        Attention
        2299/22544
        Abstract
        It is commonplace in the educational literature on mathematical practice to argue for a general conclusion from isolated quotations from famous mathematicians. In this paper, we supply a critique of this mode of inference. We review empirical results that show the diversity and instability of mathematicians’ opinions on mathematical practice. Next, we compare mathematicians’ diverse and conflicting testimony on the nature and purpose of proof. We lay especial emphasis on the diverse responses mathematicians give to the challenges that digital technologies present to older conceptions of mathematical practice. We examine the career of one much cited and anthologised paper, WP Thurston’s ‘On Proof and Progress in Mathematics’ (1994). This paper has been multiply anthologised and cited hundreds of times in educational and philosophical argument. We contrast this paper with the views of other, equally distinguished mathematicians whose use of digital technology in mathematics paints a very different picture of mathematical practice. The interesting question is not whether mathematicians disagree—they are human so of course they do. The question is how homogenous is their mathematical practice. If there are deep differences in practice between mathematicians, then it makes little sense to use isolated quotations as indicators of how mathematics is uniformly or usually done. The paper ends with reflections on the usefulness of quotations from research mathematicians for mathematical education.
        Publication date
        2020-09-08
        Published in
        ZDM
        Published version
        https://doi.org/10.1007/s11858-020-01154-w
        License
        Unspecified
        Other links
        http://hdl.handle.net/2299/22544
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