TeX mathematics is one of its most impressive features, yet the internal structure of the mechanism that produces it is painfully complicated and (in some senses) pathetically limited. One area of limitation is that one is only allowed 16 "maths alphabets"
LaTeX offers the user quite a lot of flexibility with allocating maths alphabets, but few people use the flexibility directly. Nevertheless, there are many packages that provide symbols, or that manipulate them, which allocate themselves one or more maths alphabet.
If you can't afford to drop any of these packages, there's
still hope if you're using the bm package to support
bold maths: bm is capable
of gobbling alphabets as if there is no tomorrow. The package defines
two limiter commands: \bmmax (for bold symbols; default 4)
and \hmmax (for heavy symbols, if you have them;
default 3), which control the number of alphabets to be used.
Any reduction of the \xxmax variables will slow
bm down - but that's surely better than the document not
running at all. So unless you're using maths fonts (such as
Mathtime Plus) that feature a heavy symbol weight, suppress all
use of heavy families by
\renewcommand{\hmmax}{0}
and then steadily reduce the bold families, starting with
\renewcommand{\bmmax}{3}
until (with a bit of luck) the error goes away.
This question on the Web: http://www.tex.ac.uk/cgi-bin/texfaq2html?label=manymathalph