[fdej]

I really wish browsers would just render formulas directly from TeX. Let me write <tex>\sqrt{1+x}</tex> or whatever. TeX is the de facto standard for writing mathematical formulas. That browsers don't render it natively just screams of NIH syndrome on the part of browser and web standards developers.

MathML still hasn't caught on after two decades, for three reasons: 1) not working in all browsers; 2) even when it worked, the rendering was often buggy or plain ugly; 3) no one wants to write MathML directly.

MathJax instantly solved all problems, which made it an overnight success. MathML might be able to overcome 1) and 2), but 3) should not be underestimated. MathJax will be around as long as it is the most convenient solution for showing equations in a browser (no user-side compilation required), and rendering times and network traffic will suffer accordingly.

[sharpneli]

MathML is probably the best example of the late 90's early 2000's XML craze when everything was going to be XML and it was the best thing ever.

https://en.wikipedia.org/wiki/MathML#Example_and_comparison_...

Comparison to LaTex is almost hilarious. Showing well how in the end XML managed to combine the properties of Binary and Text formats. It's slow to parse like text format and hard for humans to read, like binary formats.

Personally I'd also really love that they'd just standardize LaTex or something similar. Why invent some non human readable mess when there is already a perfectly functional and widely used notation available?

[aplaice]

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 &InvisibleTimes;.[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 &InvisibleTimes; or &ApplyFunction;, 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.

[sharpneli]

XML and readability are orthogonal concepts in the end. Basic html is easily editable and readable by humans. There is nothing preventing them from making an actually human editable XML markup language for maths. And that is the sad part.

As MathML is not human readable nor editable it’s effectively an opaque image format that can be manipulated from JS side and that scales like vector graphics.

[pvorb]

Yep. MathML is quite similar to SVG in that it's really hard to write by hand and you need editors to make it accessible.

[jahewson]

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.

[conistonwater]

MathML is not human-readable as shown by the example in the wikipedia link, and TeX is supposed to have Unicode support these days, assuming you have a properly configured modern system, that's not a good example.

[phkahler]

HTML was meant to be written by humans.

[felixfbecker]

I'm sorry but Latex is an inconsistent touring-complete mess. Latex commands are far from intuitive, otherwise Detexify wouldn't be so popular. It's a million macros held together with duct type with no consistency in naming and syntax, and always dependent on which age-old package you're referencing. It's good at outputting pixel-perfect printable, non-accessible PDFs, and that's it.

I'm excited by this because I hope that with a proper widely-supported system for math in HTML we can eventually write more papers to be digital-first. An HTML document is so much more accessible, searchable, semantically analysable and flexible than Latex and its PDF output. I dream of a world where the standard for papers is not Latex .pdf but .mhtml or .maff.

[svat]

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.

[aplaice]

This is an interesting, thought-provoking comment!

> (though the original MathML proponents perhaps did not)

FWIW I'm pretty sure that they did. Arguments to authority are pretty terrible, but if you look at the authors of the MathML 1.0 (earliest) or 3.0 (latest) specs[0][1], and google them, you can see that many of them have backgrounds in science or math and have been active in the LaTeX ecosystem.

> but this [quality of the typesetting] has been mostly underestimated/ignored by those advocating MathML.

I don't see any evidence for this, not among its designers, implementers or even general proponents.

Firefox's output (implemented almost(?) entirely by individual volunteers), for instance, is acknowledged to be still considerably worse than LaTeX output in a pdf, though it is competitive with its web alternatives (superior in some respects, worse in others) — do be sure to install MathML fonts[2] though.

> 5. What the result [...] will be, in the web page's DOM.

Have you seen the tag soup generated (by necessity) with MathJax or KaTeX?

[0] https://www.w3.org/TR/REC-MathML//TR/REC-MathML/

[1] https://www.w3.org/TR/MathML3/

[2] https://developer.mozilla.org/en-US/docs/Mozilla/MathML_Proj...

[svat]

I guess when I say “MathML proponents” I ought to be more careful in my thinking to make a distinction (even if they are often the same people) between those working on MathML as a project, and those advocating for its actual use today under current conditions. I have no problems with the former; I wish them good luck and look forward to trying the result when it's ready. For the latter, I can only say that anyone advocating using MathML today despite its problems (poor layout and browser support) clearly cares about something else more than they do about actually communicating mathematics to humans.

No doubt among the authors of the MathML specs there are people who care about typesetting. Though I'll note that being active in the LaTeX ecosystem is not a guarantee of this: the prime example is the author of LaTeX (Leslie Lamport) himself, who makes a pitch for the LaTeX model around (mostly) not caring about the appearance: https://lamport.azurewebsites.net/pubs/document-production.p... — in contrast with Knuth who devotes the largest (despite smaller font size) chapter of The TeXbook to Fine Points of Mathematics Typing. (A blog post by one of the authors of the MathML spec you linked to: https://blogs.msdn.microsoft.com/murrays/2011/04/30/two-math...) In fact some of the worst mathematical typesetting I've seen is by people who wrote in LaTeX and blindly trusted it to produce the best typesetting, and sometimes even ignored the warnings about overfull/underfull lines.

Looking at the MathML sample page in Firefox (https://mdn.mozillademos.org/en-US/docs/Mozilla/MathML_Proje...), there are many that are worse and none that is better that TeX's output (which for some reason is given on the page in low-resolution images rather than high-dpi images or SVG) — and in any case if you feel that some are subjectively better, it's still the case that the aesthetic most everyone wants is “like TeX”. And personally I've seen very little by Firefox/MathML people on their layout decisions (if they decided to do things differently from TeX, why?), while with MathJax I've seen that if their output is found not to match TeX's it is treated as a bug report and a fix attempted. What are the some respects in which you say Firefox's output is visually superior to MathJax's? Is there a page demonstrating them?

> Have you seen the tag soup generated (by necessity) with MathJax or KaTeX?

Yes, and it's not pretty. But (1) among the list of things to care about this is the lowest of the low, as it does not affect what is visible to the user, and (2) the tag soup of MathML, though shorter, has still all the XML ugliness so it's not as if it will ever be readable. (In fact looking at the comparison of different input formats https://en.wikipedia.org/w/index.php?title=MathML&oldid=8864... for sufficiently complex equations even the TeX/AsciiMath inputs become unreadable; the well-typeset visual representation may be the only somewhat readable one.)

[aplaice]

> For the latter, I can only say that anyone advocating using MathML today despite its problems (poor layout and browser support) clearly cares about something else more than they do about actually communicating mathematics to humans.

Much of the reason people are in favour of providing MathML output is that if nobody did, then the likelihood of Chrome getting MathML support would have been near zero (and the risk of Firefox removing its existing (if imperfect) implementation, high). (A chicken and egg problem.) Since MathML is likely (you may disagree — but you must agree that it's plausible that if a JavaScript solution can do it, a native one can probably do it better) to lead to better equation typesetting on the web, once it's properly implemented, people advocating MathML today can very much care about better communicating maths to humans, in the long run. Also, MathML is not incompatible with MathJax — in fact, since MathJax's internal representation of equations is similar to MathML's, converting from MathML (to SVG/HTML+CSS/whatever) is faster than converting from TeX — so it's not as if providing MathML in the document dooms your readers you to its "ugly" output. (And yes, MathML can be both an input and an output for MathJax...)

> [...] (which for some reason is given on the page in low-resolution images rather than high-dpi images or SVG) [...]

That's because the page was made several years ago, when such images were the norm (look at a Wikipedia page on the Archive from even 2016), and hasn't seen significant updates since, because MathML was feared dead (due to Chrome, at the time, explicitly rejecting support) and volunteer effort dried up. Somebody™ should update this...

> Looking at the MathML sample page in Firefox [...], there are many that are worse and none that is better that TeX's output

For the little that it's worth, IMO five are worse, two are slightly better and the rest just as good as the TeX.

> And personally I've seen very little by Firefox/MathML people on their layout decisions (if they decided to do things differently from TeX, why?), while with MathJax I've seen that if their output is found not to match TeX's it is treated as a bug report and a fix attempted.

Far more people work on MathJax than on MathML — MathJax has a two-member team, plus support from AMS, plus volunteers, while MathML has only had occasional volunteers (see above; not that it was much better previously), so it's not a fair comparison. Also the page comparing TeX with MathML was made by the people in favour of MathML precisely because they care about trying to achieve parity with TeX.

> What are the some respects in which you say Firefox's output is visually superior to MathJax's?

For instance the speed with which the output is rendered. Several second latency for better final appearance might be a bargain you want to take, but it's still a visual trade-off. (You can use server-side MathJax, but then you lose some end-user customisability.)

> the tag soup of MathML, though shorter, has still all the XML ugliness so it's not as if it will ever be readable.

How else would you expose the structure of an equation, to the DOM, than with XML ugliness? It's just important that the XML ugliness makes sense (and MathML's does).

[MiroF]

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_...

[felixfbecker]

I think it can be, it's just nobody does it. I don't know what formulas get compiled to though - I would guess PNGs, at which point you lose the benefits over a PDF (at least for equations). With proper browser support for MathML it could always be MathML though, which would render sharp and be readable by a screen reader.

It is unfortunate that MathML is not easily hand-written like the rest of HTML. What I find interesting in the link you posted though is that they embed the Latex or StarMath representation inside the MathML. It should be possible have tooling in text editors such that you only edit that Latex representation and on save the MathML representation is updated automatically.

[pvorb]

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.

[aplaice]

When you write web-pages, do you usually write the raw HTML or do you use something like Markdown or Wikitext and have it converted to HTML? If the latter, then why would having LaTeX as part of the input and MathML as part of the output, be any different?

Also, directly converting TeX to MathML, even client-side, is much easier and faster than MathJax's many-to-many approach (I'm not criticising MathJax — given the constraints, they're doing the best possible job).[0][1][2] (See also the Ascii to MathML converter[3] that has already been mentioned in another comment.)

[0] http://fred-wang.github.io/MathUI2014/demos/7-web-component....

[1] https://github.com/fred-wang/MathUI2014/blob/master/demos/7-...

[2] https://github.com/fred-wang/x-tex

[3] https://runarberg.github.io/ascii2mathml/

[mort96]

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.

[aplaice]

Pandoc and Mediawiki have been able to convert embedded LaTeX to MathML, for a while. Once Chromium supports MathML most CMSs will probably start providing suitable converters, and in the meantime MathJax will still work (and better, since MathJax's Native MathML output is faster than its CommonHTML one[0]).

[0] http://docs.mathjax.org/en/latest/output.html

[ronsor]

I do write the raw HTML actually

[runarberg]

Think of MathML more like SVG. You can write it by hand (and in some cases you should), but in most cases you should use a graphical editor (like inkscape), or a library (like D3).

[qhwudbebd]

This is exactly the property that makes it actively worse than TeX notation. It makes equations a second class citizen compared to text because you can’t write them comfortably without external tools. MathML is a failure - because of its ludicrous verbosity. The correct solution may not be TeX notation, but it can’t be this bad a step backwards in usability.

[aplaice]

How's it worse?

In either case, you can use TeX as your input, and if you do, you have to convert it, client-side or browser-side, into something usable by the browser; it's just that if the browser accepts MathML the rendering is faster and/or more convenient, plus you get other options.

[qhwudbebd]

Sorry, my claim was about the two notations: that the TeX one is writable, and the MathML is not.

I’m not claiming that a JavaScript parser and complete renderer for TeX is better than a JavaScript parser that renders via MathML. The second option may indeed be more efficient - but making the browser parse a sensible notation for maths instead of an XML crapfest would be better than either.

[pvorb]

I don't see why rendering TeX formulas would be slower than rendering MathML. It should be possible to maintain implementations for both variants with similar performance. MathML's parser should be simpler though, cause it's XML, which already has many efficient parsers.

[jahewson]

MathML was created specifically because TeX is not a standard, has no definition, has only one “true” implementation and does not capture enough structure of an equation to be a useful interchange format. Even ignoring syntax, the AST of TeX does not represent the underlying equation particularly well - just enough to use to as input to a typesetting system which behaves exactly the way that TeX does, e.g \sum has no way to specify what is being summed over (it’s irrelevant for typesetting in TeX - though not in general).

Math typesetting is hard and stretchy characters in particular are not an easy fit into the browser layout model. It’s not been a priority for browser vendors. Hopefully that will change.

[whatshisface]

>\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.

[stefan_]

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!

[gsnedders]

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.

[qhwudbebd]

The verbosity of MathML makes it completely impractical to type as working mathematician. It’s not just a small difference; it’s completely ridiculous.

[CJefferson]

While MathJax is great, the biggest problem is that 'TeX' is a very poorly (read undefined) standard, and it's fairly easy to produce things which TeX renders fine, but MathJax and Katex both bork on.

Of course, writing a clean "standard" which covers most of what people expect when they say "TeX", and implementing that, would hopefully produce the best of both worlds.

[saagarjha]

Although that does bring up the question of which subset of TeX browsers are willing to support.

[nabla9]

Markup and rendering+typography should be orthogonal issues.

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

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

[jahewson]

> 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.

[vnorilo]

I write quite a bit of LaTeX, but I shudder at the thought of browsers embedding it. It is one of the more Lovecraftian codebases I've ever witnessed.

[pvorb]

If you hadn't commented, this would be exactly what I'd have written.