# Journeys in Mathematical Landscapes: Genius or Craft?

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## Abstract

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 “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.

## Notes

### Acknowledgements

We thank Dave de Roure and Pip Willcocks for helpful discussions, and the referees for their thoughtful comments. Support from the UK Engineering and Physical Sciences Research Council is acknowledged under grants EPSRC EP/K040251/2 (Martin, Lane, Tanswell), EP/J017728/2 (Murray-Rust) and EP/P017320/1 (Pease).

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