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I write many telegraphic reviews of monographs and textbooks.

Occasionally I see certain books do something I think should become an industry standard, namely tagging nearly every theorem, lemma, definition, example, exercise, etc. with some short mnemonic nickname, so readers need
not depend solely on a numbering scheme for cross-references, etc.

Examples of books that employ this laudable practice (and just happen to come to mind) include Epstein's Word Processing in Groups and Thurston's Three-Dimensional Geometry and Topology.

My question: what author and/or publisher initiated this practice?

(I'd like to cite the original source as a comparison when I feel the visual design of a book makes it difficult for browsing.)

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Another example is Edelsbrunner's Geometry and Topology for Mesh Generation (Cambridge University Press, 2001). –  Joseph O'Rourke Nov 3 '11 at 11:58
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Shoenfield's 1967 book "Mathematical Logic" uses names rather than numbers for most (but not all) theorems. But that's only for theorems; exercises (which contain much of the content of the book) are numbered as usual. I found the lack of numbers on most theorems to be a hindrance when I needed to find the statements, but I imagine you're referring to an arrangement where theorems have both labels (to stimulate the reader's memory) and numbers (to facilitate searches). –  Andreas Blass Nov 3 '11 at 13:30

1 Answer 1

First a comment. I recently wrote an intro level text on group representation theory with such tags. One of the reviewers found the tags annoying and said it seemed like I was sharing my latex labels with the world. I had to convince Springer to let me keep them. So it may be a matter of taste.

To answer your question partially I doubt any publisher started this. I think it is an author thing. Notice both books you mentioned have Thurston and Silvio Levy involved. My advisor tended to name theorems so that one could have something to refer to them by. I think many of his students picked this up.

I doubt it originated with one person.

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Some people don't have a taste for seat belts, but their proper use demonstrably saves lives. So I'd wager that a double blind study would actually show that tags and/or other features of visual design will tends to get self-studiers to digest monographs more quickly, stay with them longer and retain more. In the computer world, no one considers well-commented, top-down, spaghetti-free code a matter of taste anymore. In this era of camera-ready copy, mathematicians ought to figure out collectively what really works and pass along the principles to their graduate students. –  David Feldman Nov 3 '11 at 13:28

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