We look at how Anglophone mathematicians have, over the last hundred years or so, presented their activities using metaphors of landscape and journey. We contrast romanticised self-presentations of the isolated genius with ethnographic studies of mathematicians at work, both alone, and in collaboration, looking particularly at on-line collaborations in the "polymath" format. The latter provide more realistic evidence of mathematicians daily practice, consistent with the the "growth mindset" notion of mathematical educators, that mathematical abilities are skills to be developed, rather than fixed traits.We place our observations in a broader literature on landscape, social space, craft and wayfaring, which combine in the notion of the production of mathematics as crafting the exploration of an unknown landscape. We indicate how "polymath" has a two-fold educational role, enabling participants to develop their skills, and providing a public demonstration of the craft of mathematics in action.
Section 1 PreludeIn 1993 Andrew Wiles announced the proof of Fermat's Last Theorem. A subsequent interview by the US PBS [Wiles, 2000] plays to the popular notion of a lone genius, waiting for inspiration to strike, and highlights the "passion and emotion" of mathematics, lingering on the moment where Wiles says And sometimes I realized that nothing that had ever been done before was any use at all. Then I just had to find something completely new; it's a mystery where that comes from, followed by a dramatic pause.
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