MathML in Chromium (opens in new tab)

XML is faster and far simpler to parse than TeX. To the extent that you need to (if for whatever reason you don't want to rely on a LaTeX to MathML or Ascii to MathML converter) you can make the quadratic equation MathML slightly more readable, by not using hex entities, but unicode for − and ±, and the named entity for ⁢.[0] Furthermore, you (and I!) are just far more familiar with TeX, which makes the comparison in readability not particularly fair. Finally, much of the invisible, seemingly redundant mark-up, such as ⁢ or ⁡, can help you avoid some of TeX's ambiguities — e.g. is $ f(a+x) $ the function $f$ acting on $(a+x)$ or $f$ multiplying $(a+x)$?[1] If you were to omit this mark-up (and if you're converting from TeX to MathML and don't want your converter to engage in guesswork, you have to) the MathML would be even simpler.

Using the same format for equations as for the rest of the document (i.e. HTML/XML) is advantageous (in addition to the parsing benefits). In particular, you can use the same mechanisms for styling and transforming elements, as you can for the whole document. For instance, you could easily style parts of an equation, provide pop-ups that explain what each symbol means, when you hover over it, or interactively change the equation. (Much of this hasn't actually been done, outside experiments, because only Firefox properly(-ish) supports MathML, so it would have been wasted effort.)

[0] https://gist.github.com/aplaice/266b092bc48afbbdd46cdbd0ca81...

[1] Presentation MathML is still obviously not semantic, but it can be better in this respect than default TeX — there have been proposals for semantic TeX, but none of them have really caught on.

MathML was created as a human-readable interchange format. It was never intended to be written by humans. Much like how HTML is often generated from markdown nowadays.

It was specifically created to avoid TeX being used on the web, because TeX is ill-defined, loosely structured and lacks basic functionality such as Unicode support.

It is true that the LaTeX ecosystem as a whole is a mess of packages and macros. But most of its mathematical typesetting comes from the underlying TeX (and a set of macros maintained by the AMS), and it's fairly small and consistent. The Detexify you mention is only for looking up specific symbols provided by various fonts (packages), and has nothing to do with mathematical typesetting or LaTeX macros in general: TeX/LaTeX engines support Opentype fonts now and if you want to use one of them, you can just type ∞ instead of \infty or ℝ instead of \mathbb{R} (actually you can do this regardless with unicode-math), bypassing the need for looking up symbols-a4 or Detexify.

Encoding the aesthetics of good mathematical typesetting is not trivial, and Knuth and others have spent decades on it based on studying and absorbing all the tricks that hot-metal typesetters had come up with over centuries. It would be foolish to throw away all that hard-won knowledge and implement half-baked solutions from scratch: those working in the field understand this (though the original MathML proponents perhaps did not), which is why the linked post mentions “math rendering based on TeXbook’s appendix G”.

More generally, in this conversation (and in any discussion about MathML), several things get conflated:

1. What syntax the user types to get their mathematics. I think it's beyond dispute here that no one wants to type MathML by hand (and even the MathML advocates do not propose it AFAIK). Also, so many people are familiar with TeX/LaTeX syntax that it must be supported by any complete solution, though alternatives like AsciiMath or some interactive input are still worth exploring.

2. How the mathematics is actually encoded in the HTML file, or delivered to the browser. Frankly I don't think this one matters much because it's invisible to the user; any of raw TeX syntax, or MathML syntax, or fully-positioned HTML+CSS, or SVG, will probably do.

3. Who does the rendering and typesetting / layout. The promise/dream of MathML is that a standard will be specified and all browsers will implement it; though this is yet to become reality. Meanwhile, typesetting can already be done server-side (someone runs TeX/MathJax/KaTeX/etc before sending it to the browser) or client-side (MathJax/KaTeX running in the user's browser) instead of being done in the browser's native code.

4. The quality of the typesetting/the algorithms used. I already mentioned this in the second paragraph above so I won't reiterate it, but this has been mostly underestimated/ignored by those advocating MathML. The decisions made by TeX reflected the best journals of the early 20th century and have in turn become the shared aesthetics of the mathematical community; “so-so” typesetting will not do.

5. What the result/output of all this rendering/typesetting/layout will be, in the web page's DOM. This affects things like usability (being able to copy-paste), scaling/zooming, styling individual parts of formulas, etc. Again, already (La)TeX+dvisvgm supports SVG for this, and MathJax supports HTML+CSS, MathML or whatever. Anything other than raster (PNG etc) images is probably fine here.

The main new/useful thing I can see with MathML is with (3); the browser doing the typesetting. But that's hard, and it has a lot of other challenges to overcome too. And as MathJax/KaTeX/dvisvgm demonstrate, the facilities provided by the browser for layout (HTML+CSS for example) are already sufficient for print-quality typesetting.

If Latex can be rendered in HTMl, than the world you dream of could become reality.

Nobody wants to learn a new type setting language. Latex is much less hard to learn and use than you imply

I mean just look at MathML https://en.wikipedia.org/wiki/MathML#Example_and_comparison_...

While LaTeX might be hard to learn and inconsistent in its entirety, the formula is quite consistent and a lot easier to write by hand than MathML.

Most people who write for the web probably do indeed write in something like markdown, which means they probably sprinkle in a bit of HTML for the parts which markdown doesn't natively support. I imagine a lot of blog posts written in markdown contain a few <table> elements, for example. Anyone writing math content for the web using markdown will have to either write the mathml directly, or write the math expressions in another language and manually compile it to mathml which is copy/pasted into the document. Maybe the CMS they happen to use will some day add native support for compiling latex, but that sounds rather unlikely.

I do write the raw HTML actually

>\sum has no way to specify what is being summed over

I could usually tell you what was being summed over by reading the _ subscripts and ^ superscripts. However the thing written under the sigma is not always formal, nor should it be: oftentimes it will be an abbreviation of a fairly elaborate conditional that is described elsewhere in the text. Please, don't treat typesetting languages like they're programming languages where the computer has to be able to execute the formulas you write, we want to keep our close interweaving with natural language.

This comment sums up perfectly why it is such a failure. We don't want to run the frigging formulas! Typesetting is the point! Stop making it do everything, it will end up doing nothing!

There are two variants of MathML: semantic MathML (which does capture enough structure of an equation, and sees very very little use) and presentational MathML (which doesn't, but is much easier to author, and accounts for almost all MathML usage). There's no real difference in usefulness between presentational MathML and TeX.

> Does TeX semantics have something that MathML does not yet have?

It does not. In fact MathML captures much richer information than TeX.

> MathJax works with both MathML and TeX. Is there difference in the rendering when using different markup with MathJax?

There shouldn’t be. MathJax internally converts TeX input into an intermediate MathML AST before rendering.

Even users on Firefox only get to see the SVG images per default.

MathJax is a unified way to render mathematical formulas in browsers. So that only leaves "native".

Why is it desirable to have "native" implementation? The usual answer is performance, but I am not aware of much performance complaint of MathJax. If not performance, how does it make sense to add more C++ code to browsers to be exploited, when memory safe JavaScript implementation is already available?

arXiv.org uses MathJax. https://arxiv.org/help/mathjax

It’s not first class. It’s cross-browser-inconsistent garbage layout largely unsuitable for anything but the simplest mathematical expressions, and a horrible markup syntax for authors.

If MathJax or KaTeX is too slow for some purpose, someone should try to compile a more streamlined TeX renderer to wasm.

Yes, because JS is superior to C++ in terms of security.

I am in favor of bundling MathJax's MathML implementation in browsers though.

Having first-class tex/postscript support in the browser would certainly be better than having to support the MathML monstrosity.

You can render Mathjax offline for non-interactive purposes (ie most use-cases) using 'mathjax-node-page'. I recently implemented this for my website; now pages like https://www.gwern.net/Embryo-selection display math instantly (instead of requiring ~5s - it's a big page), and also no longer require the MathJax JS, just the fonts/CSS.