The <MATH> element is used to include math expressions in the current line. HTML math is powerful enough to describe the range of math expressions you can create in common word processing packages, as well as being suitable for rendering to speech. When rendering to fixed pitch text-only media, simple text graphics can be used for math symbols such as the integration sign, while other symbols can be rendered using their entity names. The SGML SHORTREF capability is used to provide abbreviations for hidden brackets, subscripts and superscripts.
The design of HTML math owes a lot to LaTeX's math mode, which has been found to be effective for a wide variety of mathematical typesetting. Where practical, HTML math uses tag names matching LaTeX commands, e.g. ATOP, CHOOSE and SQRT act in the same way as their LaTeX namesakes. Of course, SGML and LaTeX have quite different syntactical conventions. As a result, HTML math uses the ISO entity names for symbols rather than the TeX names. In LaTeX, the character command ^ sets the next character as an exponent, while the character command _ sets it as an index. If the exponent or index contains more than one character then the group of characters must be enclosed in curly brackets { }. This syntax is inappropriate for SGML, so HTML math instead treats _ and ^ as shortref characters for the SUB and SUP elements which are used for indices and exponents, respectively.
I can't find the ISO entity names for the _ and ^ chararacters!
HTML math has been designed to be both concise and comparatively easy to read. In practice, formulae will be a little longer than in LaTeX, but much shorter than with other math proposals for SGML, for instance EuroMath or ISO 12083. This simplification has been achieved through the power of the BOX element, which replaces many elements in other proposals, as well as the simple conventions for binding the SUB and SUP elements and their use as generic raising and lowering operators. HTML math differentiates terms e.g. binary operators, variables, constants, integral signs, delimiters and so on. This simplifies rendering and reflects the assumptions adopted by LaTeX. It further allows the same raising and lowering operators to be used for many different roles according to the term they apply to. HTML math doesn't provide direct support for multi-line equations, as this can be effectively handled by combining math with the TABLE element.
Example - the integral from a to b of f(x) over 1+x
<MATH>∫_a_^b^{f(x)<over>1+x} dx</MATH>
which can be rendered on a fixed pitch text-only medium as:
b
/ f(x)
| ------- dx
/ 1 + x
a
The example uses { and } as shortrefs for <BOX> and </BOX> respectively. This is used for invisible brackets, stretchy delimiters and integral signs, and placing one thing over another. The shortref characters "_" and "^" are used for subscripts and superscripts respectively.
HTML math follows general practice in mathematical typesetting by rendering functions, numbers and other constants in an upright font, while variables are rendered in an italic font. You can set particular terms in a bold face, and for chemical formulae, you can force the use of an upright font. Limits for symbols like the integral and summation signs are placed directly above (below) the symbol or to the immediate right depending on the symbol.
Spacing between constants, variables and operators is determined
automatically. Additional spacing can be inserted with entities such as
  &sp; and &quadsp;.
White space in the markup is used only to delimit adjacent variables or
constants. You don't need spaces before or after binary operators or
other special symbols, as these are recognised by the HTML math
tokeniser. White space can be useful, though, for increased legibility
while authoring.
I need to check on the ISO entity names for
spacing!
The following elements are permitted within MATH elements:
The following links are underconstruction ...
The expression is rendered in three steps:
Note: In practice, only a limited range of font sizes are suitable, as a result, deeply nested expressions like continued fractions can't use ever smaller fonts. This is simply handled by a parameter to the ParseExpression routine that sets the font size to be used for that expression. ParseExpression is called recursively for nested expressions and uses the next smaller font until it bottoms out with the smallest font available. The size parameter corresponds to an enumeration of the available font sizes.
For the MATH element, CLASS can be used to describe the kind of math expression involved. This can be used to alter the way formulae are rendered, and to support exporting the expression to symbolic math software. The class "chem" is useful for chemical formulae which use an upright font for variables rather than the default italic font. For example:
<math class=chem> Fe_2_^2+^Cr_2_O_4_</math>
2+
which is rendered as Fe Cr O
2 2 4
Otherwise, the conventions for choosing class names are outside the scope of this specification.