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.
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?
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.)
 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.
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.
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.
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.
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.
> (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, 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 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?
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.)
> [...] (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).
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_...
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.
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). (See also the Ascii to MathML converter that has already been mentioned in another comment.)
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.
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.
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.
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.
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?
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.
Igalia had already been improving WebKit's  MathML renderer and they had a fundraiser for the Chromium MathML work for a long time. Now they seem to collected enough to start with it. It's one of the great advantages of open source that a small company like Igalia can just go and improve multiple rendering engines used by billions of people.
"The NativeMML output processor uses the browser’s internal MathML support (if any) to render the mathematics. Currently, Firefox has native support for MathML, and IE has the MathPlayer plugin for rendering MathML. Safari has some support for MathML since version 5.1, but the quality is not as high as either Firefox’s implementation or IE with MathPlayer. Chrome, Konqueror, and most other browsers don’t support MathML natively, but this may change in the future, since MathML is part of the HTML5 specification."
"The advantage of the NativeMML output processor is its speed, since native MathML support is usually faster than converting to HTML-with-CSS and SVG. The disadvantage is that you are dependent on the browser’s MathML implementation for your rendering, and these vary in quality of output and completeness of implementation. MathJax relies on features that are not available in some renderers (for example, Firefox’s MathML support does not implement the features needed for labeled equations). While MathJax’s NativeMML output processor works around various limitations of Firefox/Gecko and Safari/WebKit, the results using the NativeMML output processor may have spacing, font, or other rendering problems that are outside of MathJax’s control."
wxMaxima is something like jupyter notebook but developed with wxWindows by a solo developer.
?? is help for command
I just copy pasted:
(%i2) ?? mathml;
-- Function: mathml_display (<form>)
Produces MathML output.
<math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>mlabel</mi>
<mfenced separators=""><msub><mi>%o</mi> <mn>2</mn></msub>
<mo>,</mo><mi>done</mi> </mfenced> </math>
(it helps to have the LaTeX Computer Modern fonts installed locally, which for some reason aren't imported on this page)
ascii2mathml was the first compiler I ever wrote (and have written since). I wrote it because I wanted authors from a non math background to be able to write short expressions in forums or comment threads without having to know latex. I tried to make it as intuitive as possible. Even going as far as making `1+2 / 3+4` a different expression from `1 + 2/3 + 4`. But I know some people started integrate the library in their notebook apps, mainly used by math students taking notes in lectures in a markdown format (writing the expressions in ascii2mathml). Ascii2mathml might be a better fit then then the original asciimath for that purpose as the original is no expressive enough to capture advanced math expressions.
I bailed on it a couple of years ago because it looked like MathML was a dying. Chrome wasn’t going to implement it. Also I haven’t been using it for anything either. Perhaps it is now time I revisit it and give it some love.
With mathml supported by Chrome, you could instead of the whole Mathjax renderer use only a lightweight "latex/asciimath to mathml" translater and let the browser do the rendering job.
For instance, as a user, if you want to scale the equations by some amount or use a different maths font, it's a couple of lines of CSS, using exactly the same method you'd use to make any other changes to the appearance of a web-page. (Yes, you can easily do the former with MathJax, but I don't think the latter is possible user-side).
As a developer, if you'd want to interactively highlight parts of an equation, for educational purposes, it'd be trivial with MathML, but rather hard to do nicely with MathJax (statically coloured elements are possible with MathJax, with the "color.js" extension, but not dynamically coloured ones — and no, swapping out the entire equation to make colour changes is neither nice nor scalable). Alternatively, if you want to embed equations in a diagram or a graph, it's pretty easy with MathML, but would be difficult otherwise.
Lastly, I think a common standard for math representation is valuable for the same reasons "official" <section> and <article> elements are valuable: They offer a common data model that tools, extensions and search engines can work on to provide extra functionality. A "de-facto standard" like MathJax doesn't provide this, because there is no requirement that two different sites use the same representation. The only requirement is that they put up something which the particular version of MathJax they embedded can understand. This makes things a lot harder for tools.
 not that "niche" websites like nLab should be disregarded, since the web was originally designed to help scientists...
That's why we can't have nice things.
If MathJax or KaTeX is too slow for some purpose, someone should try to compile a more streamlined TeX renderer to wasm.
I dunno. Looking at the math rendering torture test at https://mdn.mozillademos.org/en-US/docs/Mozilla/MathML_Proje...
I prefer the MathML version in 15 of the examples and the LaTex in 11. (No preference in the others.)
This would be a fairer comparison if they saved the LaTeX as SVG outlines, or as a higher resolution bitmap. As it is the LaTeX version looks fuzzy on my high DPI display.
Second, it is first class. "cross-browser-inconsistent" is not an argument that it's not first class, tons of things are inconsistent (JS features, CSS implementations, etc).
Third, you missed the whole idea that the proposal is about enhancing the rendering, and also has buy-in from Mozilla people.
>If MathJax or KaTeX is too slow for some purpose, someone should try to compile a more streamlined TeX renderer to wasm.
That's not even wrong. It's beyond right and wrong, into the realm of crazy.
> The syntax is an irrelevant part of the feature
This viewpoint explains a lot about web technology. The syntax doesn’t matter. The visual output doesn’t matter. Practical adoption by users doesn’t matter. All that matters is ticking features down on a checklist somewhere.
"First class" in computing terms means strictly "built in", "supported as a native object" -- it doesn't say anything about quality (as opposed to e.g. "first class" airplane seats).
>This viewpoint explains a lot about web technology. The syntax doesn’t matter. The visual output doesn’t matter. Practical adoption by users doesn’t matter. All that matters is ticking features down on a checklist somewhere.
Sounds like a generic lament.
What matters here is: (a) performance, which is and always will be better than some plain-js implementation.
(b) being native (which means it will eventually be on all browsers, without asking the users to load anything extra, and will mean writers can just depend on it), (c) the visual output will be better (for one, it will be native vector fonts laid out, not a canvas drawing which is not infinitely zoomable or non-math aware SVG where it's just pretty pictures), (d) it will be able to interact with all other browser capabilities better than any pure-JS implementation.
The syntax is irrelevant, as it can be a target for any other syntax one prefers. In fact MathJax already delegates to MathML rendering where it can.
I am in favor of bundling MathJax's MathML implementation in browsers though.
Yeah, because moving 1/100th of web rendering (the math rendering part) to JS is going to make things more secure...
Use-after-free is a C thing, not a C++ thing. Granted, C++ makes is super easy to code in C, but that's an organization problem that is already solved in any sane project.
They are already tied to static analyzers, which is how they were found. What do you think the: "Sanitizer: address (ASAN)" or "Issue 938699: AutotestPrivateApiTest.AutotestPrivate getPrinterList failing on ASAN/LSAN" in the bug reports means?
The word "static" refers to compile-time; a static analysis reports errors or warnings based only on the source code of the program.
Sanitizers are dynamic analysis based on instrumentation. https://github.com/google/sanitizers/wiki/AddressSanitizer
The tool consists of a compiler instrumentation module
(currently, an LLVM pass) and a run-time library which
replaces the malloc function.
As Dijkstra said, Program testing can be used to show the presence of bugs, but never to show their absence.
Does anybody know if this will translate to chromium based web toolkits (eg QT), and MS Edge (soon to be based on chromium), and therefore, React-XP