2 ms·
I mean, perhaps; though I've found it does quite the opposite. The idea is proposed front and center, sure (this approach does not preclude that), but far less
by LolWolf 7y ago
I mean, perhaps; though I've found it does quite the opposite. The idea is proposed front and center, sure (this approach does not preclude that), but far less time is spent explaining the motivation and doing mathematical yoga to clarify steps in a proof than is spent providing clear examples and sensible constructions.[1]
I am not, of course, saying that all textbooks (or papers) will be better served by this structure, but I think a surprisingly large amount are. This may also be a consequence of the field I'm in, as well, where most statements I've made have several natural generalizations which are all relatively straightforward to prove, but presenting them all under one large umbrella with a very general construction makes the end result much harder to understand.
Either way, both ways have their merits, but I've (along with several of my peers and editors) found one much harder to work with and read than the other. Though, I will again mention that this may be due to the specific fields I work in.
--
[1] I want to be clear that I'm also not advocating for the "big reveal finish" which many papers (and some terrible textbooks) fail miserably at. Neither of these mediums is a novel. But I am saying that some approach motivating the construction and building the picture in a natural way (instead of a here's the theorem, let's explain why everything is a trivial corollary of it) lends itself to more clear expositions.
Perhaps either presentation can be made clear, but I've found it's very, very difficult to make the latter work in a way that readers can easily understand, while the former falls almost naturally from most research notes I've written and keeps people more engaged.