As a fellow mathematician you may then appreciate the fact that local and global maxima may differ dramatically which pretty much precludes true WYSIWYG (not just in TeX) in that you have to settle for one of the two: visual output with suboptimal aesthetics (TeXmacs, and, to some extent, LyX) or perfect results that you have to compile with some delay. It has nothing to do with the computational power available but rather with the occasional highly unstable line breaking. Even in MS Word it is annoying sometimes to see it resize a current line even though it uses a rather lame line breaking routine. TeX does have facilities for almost real time WYSIWYG (SyncTeX was added specifically for that purpose) although they take some effort to set up. As far as concentrating on the work at hand I have written whole papers without compiling the document once before everything was complete. I admit it takes some getting used to but I prefer something I can grep through to a mere pretty picture. I admit if my work was heavy on large commutative diagrams I might have had a different view. One thing I totally agree with you on is that TeXmacs is an outstanding piece of software. I would just prefer to keep my documents in TeX (which TeXmacs can export, kinda).
> visual output with suboptimal aesthetics (TeXmacs, and, to some extent, LyX)
Till now I took the developers word that the aesthetics of TeXmacs is better than the one of TeX and I would be curious to know where the opposite is true (and in case also why this cannot change)
From what I have seen in TeXmacs documentation, they have implemented pretty much every feature of TeX's linebreaking algorithm and more (microtypography, global page breaking, etc) so my claim above was not to say that the documents TeXmacs outputs have suboptimal aesthetics (to be fair, modern versions of TeX have all of these features, as well, although not the original TeX, alas). What I meant to say was there is no (even theoretically) possible way to have a perfect WYSIWYG editor if global paragraph/page breaking is desired. For example, due to global page breaking, one may be editing a line in the middle of the document and its position on the page (and the page number, left/right headers, etc) will be constantly changing---not good for the visual experience. I do not know how TeXmacs deals with these (extremely rare, admittedly) cases but the discussion was about the true WYSIWYG vs not so take it with a grain of salt. Let me say this again: TeXmacs is an outstanding piece of software. If in thirty years, a TeXmacs file format is still readable by the newest version (possibly with some easy tweaks), I will consider switching from TeX :). My other (minor) concern is that the LaTeX files that TeXmacs exports do not render at all as the pdf files TeXmacs produces itself. So as a WYSIWYG frontend to LaTeX, TeXmacs is ... not quite. Which they never claimed to be so I cannot fault them for this.
