I read a lot of math too and the points you raise are good ones. I bought a Kindle DX in hopes of jettisoning a large part of my hardcopy math library; thanks to TeX, a huge swath of math literature is available by PDF (most of it free, if you have university access). I guess I wasn't prepared for how cumbersome it would be. Flipping back 10 pages to check a lemma takes, well, 10 seconds. It really detracts from the study experience.
That said, if I may play devil's advocate for a second, another way to look at the linear structure imposed by print is as a useful constraint for conveying thoughts in an effective manner. Every once in a while, I come across a "classic", math or otherwise, where the author has put so much thought into structuring her argument that I don't need to flip around. Invariably I absorb more from these rare gems than I would from a sort of hypertext arrangement, simply because somebody thought hard about the best way to learn the material.
It's funny you mention Apple because this strikes me as a very Apple thing to do--impose something on its users which initially seems quite cumbersome (one-button mouse, no floppy, one-button cell phone, no CD/DVD, hell the whole HIG), but actually turns out to be a clever mechanism for enhancing usability.
I totally know what you mean, I appreciate the craftsmanship too that went into such gems. It's like knowing you are in "good hands" ;-)
Still, I would appreciate if the form would give me the option to "mess" with it sometimes, e.g. suppressing some stuff that I may or may not come back to later after a first glance; or generating quick links between passages (for example, a proof uses a previous result, can I quickly link back to it); or when I point at a technical term, can I see the formal definition from the text. etc etc. That would be amazing.
It occurs to me, you could submit a feature request to Amazon... "while reading, type CTRL+5 to go forward 5 pages, ALT+5 to go back" or something like that.
Of course this would be cumbersome on the keyboardless models, but they are designed purely for novellas et al anyways.
I'm not a fan of ebooks generally, but would love to have a tablet that could replace a bunch of technical books and papers. Any of the e-ink readers refresh too slowly to really allow skimming, but maybe the iPad or Android tablets would be better. Something like a split pane view for PDFs where you could 'dock' a bunch along an edge for quick reference, or even have multiple papers open at once. I don't know that current devices are either quick enough to render pages quickly, or have enough memory to cache the current page +- 10 others.
That said, if I may play devil's advocate for a second, another way to look at the linear structure imposed by print is as a useful constraint for conveying thoughts in an effective manner. Every once in a while, I come across a "classic", math or otherwise, where the author has put so much thought into structuring her argument that I don't need to flip around. Invariably I absorb more from these rare gems than I would from a sort of hypertext arrangement, simply because somebody thought hard about the best way to learn the material.
It's funny you mention Apple because this strikes me as a very Apple thing to do--impose something on its users which initially seems quite cumbersome (one-button mouse, no floppy, one-button cell phone, no CD/DVD, hell the whole HIG), but actually turns out to be a clever mechanism for enhancing usability.