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This question is a little vague, but I'd like to ask total number of math symbols in TeX (or we can say amsmath?).

I cannot find information in ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf document, and http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Symbols link gives approx. 290 kinds of math symbols.

I know that math symbols are treated as a sort of fonts in TeX, but does it have any information in common?

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    For LaTeX, there's a comprehensive list with 5913 symbols.
    – texnokrat
    Feb 1 '14 at 14:14
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    There are many symbols that have more than one command.
    – Sigur
    Feb 1 '14 at 14:16
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    the answer depends on what you consider a symbol. do you, for instance, consider a greek letter a symbol? amsmath is really irrelevant -- while symbols are used in math, beyond the basic set defined with the "tex core" (as created by knuth), they are provided by font-related packages; amssymb is a package that gives names to symbols in the font collection amsfonts. with the availability of "unicode" fonts, the number of symbols (including what unicode calls the "mathematical alphanumerics") reaches several thousand. Feb 1 '14 at 15:42
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With standard TeX, the theoretical maximum number of different math symbols is 256⋅16, that is 4096. There can be as many as 16 math families, each corresponding to 256 symbols.

The maximum can't be reached, though, because math families from 0 to 3 are preempted and, in particular, the font in family 3 has many slots corresponding to character extensions, so symbols that can't be directly used. Also commands such as \mathbf, \mathsf and \mathtt preempt a math family as soon as they're used in a document; other packages may occupy a math family for their symbol font.

So the maximum is the number of free math families times 256.

With XeLaTeX and LuaLaTeX the limit is the sky, because both allow 256 math families and each family can fully use an OpenType or TrueType font.

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