One thing which regularly annoys me is how difficult it is to find
mathematics on the Web at the level I'm interested in. One can easily
find a lot of undergraduate-level stuff, and a lot of research papers,
but there seems to be a gap between the two at which there is little
available material online. For example, just now, I wanted the
precise definition of a Gorenstein ring (or a Gorenstein
singularity, or whatever: it's the word Gorenstein
which
interests me, in any context). Now there are tons of research papers
which deal with resolution of Gorenstein singularities or
classifications of them, or whatever: but they never bother to recall
what a Gorenstein singularity is, because everyone is supposed to know
that (in order to make any sense of the paper or to have any interest
in it). And on the other hand, this is way too advanced for most
online courses: what I would need is a general treatise on
Cohen-Macaulay rings (such as this book by Bruns
and Herzog, of which I have a copy at my parents' house but none
where I am now).
Of course, there is MathWorld, which is often
useful (especially when it comes to formulæ of kinds): here it gives a
definition of a Gorenstein ring (I won't link to it because I don't
wish to Google-feed it), but I can't make heads or tails of it —
I'm sure they omitted something. And this isn't just bad luck in this
particular case: it's really quite typical of their definitions in
relatively high-brow domains. When there is an entry in the Wikipedia, it's usually more
useful, but, unfortunately, the word Gorenstein
doesn't appear
in the Wikipedia (I guess I'll have to write the entry when I find out
precisely). In general, the Wikipedia isn't very good when it comes
to mathematics because there isn't a convenient way to typeset
mathematical formulæ in it.
(That's what research libraries are for, you say? Yes, but it is presently 4AM, and all research libraries I have access to are closed. And how can I go to sleep without knowing the correct definition of a Gorenstein ring? Now you understand my dilemma!)