Comparison of OpenXML math and MathML
Murray Sargent who was the architect of the new math functionality in Office 2007 has a blog post where he talks more about the design of the Math schema in the Office Open XML formats (http://blogs.msdn.com/murrays/archive/2006/10/07/MathML-and-Ecma-Math-_2800_OMML_2900_-.aspx). Murray has also been active in the MathML community and is even joining the MathML 3.0 working group.
I gave some background information on why we made the decision to support MathML, but not to use it in the Office Open XML formats. We support MathML on the clipboard, and also have XSLTs that go both ways (from MathML into Office Open XML and from Office Open XML to MathML). Murray goes into much greater detail on this in his post. Here is a small snippet from his post:
Naturally there's been a lot of discussion as to why we even have OMML, since MathML is really good. Brian Jones has addressed that issue in some detail in his Open XML Formats blog. The main problem is that Word needs to allow users to embed arbitrary scan-level material (basically anything you can put into a Word paragraph) in math zones and MathML is geared toward allowing only math in math zones. A subsidiary consideration is the desire to have an XML that corresponds closely to the internal format, aiding performance and offering readily achievable robustness. Since both MathML and OMML are XMLs, XSLTs can (and have) been created to convert one into the other. So it seems you can have your cake and eat it too. Thank you XML!