I don’t have anything to add in terms of mazes or working a proof from both ends, but I am reminded of a classic cartoon that you might want to throw in — the “then a miracle occurs” cartoon. Here is a link from stack overflow, or you could try and find a link at the original artists site https://stackoverflow.blog/wp-content/uploads/2017/02/then-a-miracle-occurs-... Steve -- Stephen Lucas, Professor Department of Mathematics and Statistics MSC 1911, James Madison University, Harrisonburg, VA 22807 USA Phone 540 568 5104, Fax 540 568 6857, Web http://educ.jmu.edu/~lucassk/ Email lucassk at jmu dot edu (Work) stephen.k.lucas at gmail dot com (Other) Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state. (Plato) On Apr 12, 2019, at 10:21 AM, James Propp <jamespropp@gmail.com<mailto:jamespropp@gmail.com>> wrote: I've posted a draft of the essay I plan to post on the morning of the 17th (or maybe the night before) at https://urldefense.proofpoint.com/v2/url?u=http-3A__mathenchant.org_047-2Ddr... I don't expect to get comments from many of you, but all comments will be appreciated and acknowledged. One thing that's missing from the essay is a good reference for readers who want to learn more about modern mazes. For that matter, do any of you know of any good references about how to create proofs that explicitly advocate the work-from-the-outside-in tactic? I've never read "How to Read and Do Proofs" or the many similar books that are out there, but if you think readers of my blog would like a particular book in this genre, I'd be glad to mention it. Thanks, Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg...