Proofs in expository writing — Some examples from Bourbaki's early drafts |
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| Authors: | Liliane Beaulieu |
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| Institution: | (1) The University of California at Berkeley, USA |
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| Abstract: | Conclusion The stories told above exemplify the ordinary as much as they document the extraordinary. In the practice of expository writing, definitions play as important a role as mathematical proofs. Also, specifying notation and vocabulary is usually at stake in the writing of textbooks. Although the making of concepts and conceptual settings puts an emphasis on definitions, proofs are in no way absent from this process: in the case of Bourbaki's treatment of Stokes' Theorem, proofs may have acted as a spark in the search for better settings. In the case of filters, the discovery of new concepts simplified some proofs and enabled the results to hold in a more general context. But the motivation for new concepts to be defined did not rise exclusively from a dissatisfaction with proofs that were deemed not rigorous enough. Moreover, the close interplay between the members' own research and the group's expository task tended to relegate proofs to a heuristic in the background of the group's preoccupations. |
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