I've been writing an algebra editor analogous to Vim/Emacs. Unlike English, maths is too slow to re-type while you perform algebra. Instead, insert expressions once then use keyboard shortcuts to edit and combine existing expressions.

It is interesting because it's the only algebra system in which the user actually performs the algebra. With practice, edits are as fast as maths on paper, but without all of the redundant re-writing. Similar to the sense of flow you get when programming with Vim, this leads to a sense of immersion in the maths.

A small, fast executable *.jar, check it out at: http://sourceforge.net/projects/ket/