Legibility Loss

Without math alphabets, the Hamiltonian formula
H = ò dt [eE2 + µH2]

becomes an integral equation
H = ò dt [eE2 + µH2]

Generally the math alphanumerics substantially reduce the verbosity of markup, although one can construct cases that aren't so verbose. For example, if you had a sequence of bold italic characters, say abcd, you could define markup to express this as <mbi>abcd</mbi>. This is 15 characters and using the math alphanumerics you need 8 UTF-16 codes, since the math bold italic letters are in plane 1 and are represented in UTF-16 by surrogate pairs. This is only about half as many codes as in the markup although in ISO 10646 it's a quarter as many.

But this markup representation is poor for several reasons:

1. it complicates a search for a bold italic a, since the search engine needs to understand the tags and dissect the tag contents,
2. it doesn't tag the characters individually as math identifiers, which is a MathML requirement, and
3. it introduces complexity into the tag model by introducing multiple variable identifier tags. The last of these disadvantages can be overcome by representing the nature of the variables with attributes, e.g., <mi>, but this approach is indeed quite verbose for items as small as math characters. Admittedly this approach is necessary to handle (quite rare) alphanumeric math symbols that aren't included in the math alphanumeric block. Searching for such symbols requires a sophisticated attribute-aware search engine since simple plain-text search engines would yield many undesired search hits.