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Following the premise that mathematics is an art as well as a science, I want to encourage students to produce not only correct proofs but also to try to find a particular beautiful/elegant proof.

Apart from pointing out particularly beautiful proofs, which strategies for promoting elegant or beautiful proofs do exists? I would be particularly interested in strategies which have been evaluated.

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    $\begingroup$ Have you identified the characteristics of an elegant or beautiful proof? That might be a starting point. $\endgroup$
    – paw88789
    Apr 19 '16 at 12:38
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    $\begingroup$ It takes a long time to develop elegance and beauty in crafting proofs. I think most students need to focus heavily on understanding how to construct rigorous and logically sound proofs, as well as how to formulate useful proof strategies. I would recommend that you include some remarks on elegance in proof writing in class through some well-motivated examples and address elegance/efficiency when appropriate when giving feedback on assignments. But elegance is not something that one can reasonably demand for students who are not fairly strong grad students (or on their way toward that point). $\endgroup$
    – Michael Joyce
    Apr 19 '16 at 17:53
  • $\begingroup$ @paw88789: I think that this is a difficult issue. Although in my experience mathematicians seem to agree (at least in most cases) on whether a proof is elegant it seems to be hard to come up with (hard) characteristics. Would asking for (references for) such characteristics be on topic on this site? $\endgroup$
    – Christian
    Apr 28 '16 at 16:00
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    $\begingroup$ @Christian Because one needs to have a "well-posed problem" I agree with paw88789. And that "this is a difficult issue" is totally besides the point: you have to let your students know, else how are they to understand what you want from them? $\endgroup$
    – schremmer
    Jul 1 '17 at 16:12

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