[pyninja]

> I mean... isn't the point of academic writing to communicate research and results already performed?

Obviously mathematicians don't leave "exercises for the reader" in research papers, but it is common in textbooks or expository writing.

> I always felt that phrase has no place in the internet age, where the concept of a "page limit" is laughable and a simple hyperlink can point me to chapters upon chapters of appendices.

The constraint is not page length, of course, but time. It is a much better use of a mathematician's time to leave easily reproducible proofs to the reader, and focus on the interesting ideas.

Anyway, doing these kinds of exercises is actually very useful in understanding new ideas.

[pak]

>Obviously mathematicians don't leave "exercises for the reader" in research papers

ORLY? I'll leave this right here for you:

http://scholar.google.com/scholar?hl=en&q=left+as+an+exe...

That's >100k hits from what Google Scholar can index alone--a few are from books, but the vast majority are journal articles.

[pyninja]

I looked at the first few pages and saw only a few math papers, and in those the exercises were uninteresting details (e.g. just computation, or the second of two analogous cases where only the first is proved in the paper).

Do you really think anyone would benefit from such proofs in a paper? I would be interested if you could give an actual example of a paper where a reader might be inconvenienced by something being left as an exercise.