How do mathematicians gain the adherence of their audience?

Who is the audience? Who are the addressees of a mathematical paper?

  • The reviewers (and the editors)?
    They

    • Check the correctness (see the entry on “proof”)
    • Decide about the relevance
  • The readers of the journal?
    • The abstract and the classification of a paper are means to ‘attract’ readers, to make them aware
    • The selection of the paper to be published is already a matter of advertisement, authority and trust
    • Reviewers/editors can be considered judges as well as priests.
  • The ‘universal’ audience? Everybody?
    • In ‘principle’ mathematical results, mathematical statements are considered to be ‘true’, which means universally acceptable and the publishing of a mathematical paper might be seen as informing ‘everybody’ about this result.
    • Should the ‘universal audience’ be reduced to the appropriately educated? The hidden assumption which is probably a main pillar of most mathematician’s self-image of mathematics is, that after an appropriate preparation (or ‘education’) everybody should have to recognize and accept the necessity of each mathematical proof. It is a universality for a specialized audience and it is absolutely not clear why the process of becoming a specialized audience and of interfering – as a member of such a specialized audience – with mathematical items, is not considered an integral part of the universality, or even of the ‘unity’ of mathematics.
    • The above text induces a new problem – about specialization. There is the distinction between research articles written for a small number of narrowly specialized readers and so-called expository texts which are usually longer. But there are different levels of expository texts. Are the expository texts the ones which are written for the ‘universal audience’? No! They are just for a less specialized audience. These texts should, but not always do, clarify in their introductory part which level of specialization is expected from the reader in order to ‘get the message’.
    • The ‘lowest’ level of texts are so-called ‘textbooks’ or expository texts named ‘Introduction to …’ but here again the expected audience needs some level of specialization. How should a truly introductory text look like?

Different levels of specialization induce different values, different habits and above all different kind and duration of training. They induce also different kind of absolute presuppositions, of habituated attitudes, of forgotten previous modes to approach a mathematical text.

Is anything said above specific for mathematics?

Testimonials:

J-P. Serre (source: ‘Writing mathematics badly’ video part 3 http://www.dailymotion.com/video/xf88g3_jean-pierre-serre-writing-mathemati_tech#.UT06hleiHvh 3:38 – 3:56 ):

A proof is something which is accepted by experts. A ‘Bourbaki-proof’ is accepted by non-experts. And of course I favor the second choice.

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