HTML-Math is a format for representing mathematical expressions within HTML documents. The representation allows an expression to be rendered or interactively edited using standard notations in common media, and for subexpressions to be interchanged with computer-algebra systems. What is represented is notation rather than semantics, but authors are free to define and/or use macros which they consider to have (private or conventional) semantic meanings.
HTML-Math is human-readable and writable, and in many simple cases follows conventional syntax for written or typeset mathematics. Authors can modify or extend the syntax according to descriptions in separate documents and/or within the document that uses it.
The structure expressed in HTML-Math generally corresponds to that which is likely to affect the human interpretation of a typeset expression -- that is, it generally specifies the identity and relative size of symbols and their approximate relative positions (e.g. "above and somewhat to the right") in a 2-dimensional medium. In some cases, "higher-level" (or more "semantic") structure can also be expressed (at the option of the author) as an aid to the interpretation of expression meaning when this would otherwise be ambiguous; but even in such cases there is still a well-defined "2-D presentational structure". [More specific low-level information for certain renderers and media might be specifiable in the document or in style sheets, but the nature and extent of this remains to be discussed.]
There is a standard way for an author to specify a string (e.g. a URL) intended to define the semantics of the HTML-Math expressions in all or part of an HTML document, but the HTML-Math standard does not address the structure or interpretation of such a string.
HTML-Math expressions can be viewed in any medium supported by HTML browsers. The standard will suggest appropriate rendering algorithms and parameters for the on-screen or printed 2-dimensional graphical formats. Rendering into other media (such as speech) is expected to communicate, essentially, a "mental picture" of the 2-dimensional form of an expression. (Rationale: since almost all mathematics is conventionally expressed in 2-dimensional graphical form, most notations in that medium have no standard version in other media.) Individual viewers can add their own rules or macro definitions (via style sheets) to alter the rendering of specific expression patterns.
HTML-Math is intended to encourage the representation of sufficient expression structure for structure-based WYSIWYG editing of expressions, and for copying of subexpressions into computer algebra systems when the notations used have a standard meaning in such systems. Specifically, the portions of HTML-Math text which correspond to subexpressions will always be well-defined.
Many features of HTML-Math are incrementally author-extensible by means of style sheets. [Exactly which, how much, and how, remains to be decided. In some manner, this will allow authors to define new, typically higher-level, operators, along with an equivalent form for rendering them -- i.e. to define "macros".]
HTML-Math expressions can appear within any HTML text, and can be designated as either "in-line" (displayed as if replacing some words of text) or "out-of-line" (displayed as if replacing some paragraphs of text).
HTML-Math expressions can include most other HTML elements in place of individual math-expression terms. Specifically, they can include links and anchors. [The details of how these might be used for making possible automatic equation numbering, or viewer-controlled relabeling of equations and other referenced objects, remain to be discussed, as does the precise set of allowed included elements.]
HTML-Math is SGML compatible to the extent that this doesn't conflict with its other design goals. Specifically, every HTML-Math document will conform to the HTML DTD, and any conforming document will be renderable; furthermore, an author will have the option of writing any HTML-Math expression in a fully expanded but equivalent form in which each subexpression is a separate SGML element, facilitating document processing by existing SGML-based software tools. (Furthermore, it will be straightforward to write filtering tools which transform any HTML-Math expression into its fully expanded form, by adding appropriate markup. Such tools may also expand macros, but this is a distinct operation.)
Issues to be discussed (but note that some of these may be addressed in some of the more specific position papers):
Whether authors can define macros using newly-made-up SGML tags, and if so, whether they must do this in an SGML-compatible way (by using the SGML feature allowing individual documents to extent the DTD). (Note that there are reasonable macro schemes which don't require this. I'll provide details of one such scheme later.)
Extent of specification of precise appearance (layout spacing rules and relative font sizes) of HTML-Math in 2D graphical media. E.g., do we document (as TeX does) the precise amount of horizontal spacing between symbols appearing in a row (which can affect the viewer's perception of operator precedence)?
Extent of ability for author modification of precise layout rules. (E.g., do we provide layout primitives (typically for use in macros) which allow authors to specify the precise coordinates and relative font sizes of subexpressions of an expression?) [In the conference call of 2/29, the only opinions expressed were "no", but I am aware of potential opposite opinions which were not represented, so I think this issue will need further discussion. Furthermore, if HTML itself is evolving towards allowing such specification for text and graphic elements in general (which I don't know), then we should keep track of such evolution in case it ought to be integrated with HTML-Math.]