I guess this is one of the best tips in terms of general structured writing.
You realize that definition should be before chapter 5, but in which chapter? 1, 2, 3, or 4?
You have to review each chapter (probably in reverse order) to determine the latest position it should be in.
Additionally, as you add that definition you find out that there's even more that needs to be shifted. Do you reorganize the whole thing, or leave it as is? You'll end up spending as much time reworking the text as you did writing the original.
Really, this is a philosophical thing. In the spiral approach you end up reviewing things early and realizing what's missing and where they should be moved. In your approach, you don't get to do the review until late. Is it wrong? No. But it can create a less flexible document that requires more effort (and not less) to correct.
This is very similar to the argument in lean software development of keeping batch sizes low (small number of changes at a time) but running them more frequently. Versus the waterfall approach which has large batch sizes and takes much longer to do it all, with a big review near the end.
which seems a bit more nut-and-bolts. This post seems a good compliment.
If the linked text is too long, you might enjoy his shorter piece "Mathematics as Creative Art" .
Also well worth a look is Serre's "How to write mathematics badly": https://www.youtube.com/watch?v=ECQyFzzBHlo
The committee was authorized by the Council of the American Mathematical Society in August 1968; the last appointment to it was made by Oscar Zariski, then president, in March 1969. The charge was to prepare "a pamphlet on expository writing of books and papers at the research level and at the level of graduate texts."
In May 1969, two months after the committee was completed, one of its members resigned. He said he thought the project was too interesting to leave to a committee, which would never get it done properly, and he said he wanted to be free to write and publish his version independently. Norman Steenrod (the chairman) declined to accept the resignation, preferring to allow the member the freedom he sought. This left the exact membership of the committee up in the air.
The work of the committee proceeded mainly on Steenrod's steam; he wrote to the other members (in triplicate), and occasionally they would write an answer (to him alone). The committee met only once (for an hour, at the Eugene meeting in August 1969, with three present). The result of the correspondence and the meeting was the decision to present to the Council, as the product of the committee, four separate essays, one by each of the four members, with the recommendation that the Society publish them, together, as this book. > > A year later (in August 1970) Steenrod had at hand only one essay. A year and six months later (in March 1971) that essay was published. (L'Enseignement Mathématique, 16 (1970), 123-152.) Even so, Steenrod was still hoping; he set August 300, 1971 as a target date for the receipt of all the essays. The solution he proposed for the problem created by the already published essay was to reprint it as is, as part of the AMS publication, provided the editors and publishers of L'Enseignement Mathématique agreed. They did.
Steenrod died in October 1971, before quite completing his own essay. Before he died he asked, through his wife, that his nearly finished work be prepared for submission to the council and presented together with the others. That was done.
J. A. Dieudonné
P. R. Halmos
M. M. Schiffer
Really. And he’s gonna teach us to write about math?