As a rider to the stackexchange discussion: TeX/LaTeX did indeed have competition in the early days from, for example, troff. However, the eqn filter for troff was designed to generate troff macros; some knowledge of troff is required to use it effectively, and (speaking as someone who worked in a UNIX techpubs team for a few years in his mis-spent youth) troff is not a terribly elegant or user-friendly language to say the least.

I was curious how troff/eqn and TeX syntaxes compared, and didn't find any nice side-by-side examples, so here's a quick translation of one from the troff manual (http://www.troff.org/prog.html#eqn):

    .EQ
    G(z) ~=~ e sup { ln ~ G(z) }
         ~=~ exp left ( sum from k>=1 { S sub k z sup k } over k right )
         ~=~ prod from k>=1 e sup { S sub k z sup k /k }
    .EN

In TeX mathematical notation:

    $$G(z) = e^{\ln G(z)}
           = \exp \left( \sum_{k \geq 1} \frac{S_k z^k}{k} \right)
           = \prod_{k \geq 1} e^{S_k z^k / k}$$

The TeX is a bit more terse, especially in using ^ and _ for super/subscript instead of sup/sub. That can make a big readability difference in things like simple polynomials; a^2 + b^2 = c^2 is just that in TeX, but a lot more wordy in eqn. The troff/eqn looks a bit less like line noise, though, especially in things like "from" in the summation, and >= for \geq.

Though really I'd guess that TeX's math notation caught on as the de-facto standard for "ASCII math" because TeX as a whole caught on, rather than because of its ASCII-math representation being better.

> The troff/eqn looks a bit less like line noise

Not necessarily a feature. The eqn syntax does contain more letters and less symbols, but that gives it very low contrast, making it hard to scan the equation and "see" the math symbols through the formatting. When writing a large equation, it helps to have a large contrast between words/symbols and formatting commands. The TeX punctuation helps with grouping and delineation.

Furthermore, the LaTeX syntax makes it easier for the computer to parse the document and distinguish actual text from equation symbols.

It depends on the meaning of 'easier', I think. In both cases, 'the computer' can do it, meaning the program `troff` or the program `(la)tex`, and I'm not sure it's reasonable to call one or the other of those programs 'easier' for the computer; but perhaps you are thinking more of something like syntax highlighting?

In that case, I would argue that it's not easy at all with (La)TeX. The obvious difficulty is people mucking about with cat- and char- codes; but, even if that's not happening, you've got things to worry about like old-style `$ $` and `$$ $$` delimiters. I've never seen a highlighter handle `$\text{$math$}$`, or even `\(\text{\(math\)}\)`, correctly.

How does troff handle Greek letters and other exotic symbols? The simplicity of \gamma and friends was what won me over to TeX in college.

You can simply type them in (at least in the Plan 9 version of troff).

LaTeX is easy to read. I want to write a little story from my life as an example.

While I was working at one firm I got own department. I wrote LaTeX class for them to support corporate style. After 1-2 weeks they noticed it was the same if not better than MS Word for documentation.

The same reason a lot of file/language standards become popular. They suck less than everything else when they were created and then large amounts of material became tied up in their continued existence ( i.e. academic papers ).

Existing papers do not really force new papers to be typeset in LaTex, since end products are just PDFs.

I don't know of any alternative solution that is as easy to use and produces a high quality document.

Some disciplines wound up having lots of handy LaTeX macros written to handle things that are common to the kinds of papers that get written, as well as there formerly being the requirement that papers be submitted as LaTeX documents. More the first reason, I think, tended to encourage LaTeX usage for a while. Once you got used to it, LaTeX really made it faster to get what you want without having to fiddle too much with the formatting.

I know I spent a lot of time with qtree, gb4e, and pstricks.

A big factor was/is the prestige of Knuth.

A Markdown extension that turned latex formulas to MathML would be nice...

This is one best directions with the available technology. We're trying to do this at Hoot with what we call "Smart Chat." We've taken the markdown editor and adapted backticks (`) to wrap a simplified subset of Latex, so that the language is more accessible to a wider audience by providing immediate rendering and feedback. In our case the uses are much more simple than the troff example above (https://apps.facebook.com/hootapp/?sid=5Yyt797Jg), but are still very applicable. I think our most common use is by highschoolers and college students for calculus, where ideas such as integrals and summations are easily described in plain english:

`integral cos(x)*e^(2x) dx` or `sum (x^n) / (n!)`

edit: added simpler examples

I use python_markdown with MathJaX, and it works pretty well.

see pandoc http://johnmacfarlane.net/pandoc/

troff is for me far harder to read by eye ... TeX and LaTeX are far easier to read and more versatile. Its just a personal thing, I'm sure, but I found taking to TeX an instantly productive thing to do.

Modern TeX/LaTeX packages for distros these days are huge though, in comparison to the stuff that came on a single floppy when I first learned to use it.