MathML in Chromium

118 points by aplaice 7 years ago | 86 comments

fdej 7 years ago |

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 7 years ago | |

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 7 years ago | | |

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.

jahewson 7 years ago | | |

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.

felixfbecker 7 years ago | |

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 7 years ago | | |

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.

MiroF 7 years ago | | |

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_...

pvorb 7 years ago | | |

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 7 years ago | |

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 7 years ago | | |

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.

ronsor 7 years ago | | |

I do write the raw HTML actually

jahewson 7 years ago | |

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 7 years ago | | |

>\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_ 7 years ago | | |

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 7 years ago | | |

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.

CJefferson 7 years ago | |

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 7 years ago | |

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

nabla9 7 years ago | |

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 7 years ago | | |

> 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 7 years ago | |

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 7 years ago | |

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

est31 7 years ago |

It's very good news that this has finally started. Wikipedia, probably the biggest website that displays formulas, still renders them to SVG images.

Igalia had already been improving WebKit's [1] 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.

[1]: https://webkit.org/blog/6803/improvements-in-mathml-renderin...

notthingnill 7 years ago |

You can also use a computer algebra system (CAS) to perform computations and get the output in mathml, for example the free CAS maxima.

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. (%i1) load("alt-display.mac")$ (%i2) set_alt_display(2,mathml_display); <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> (%o2) true

dtf 7 years ago |

Here's an example of why MathML is attractive as a rendering layer (try Firefox vs Chrome, and look at native MathML latency vs MathJax emulation):

https://runarberg.github.io/ascii2mathml/

(it helps to have the LaTeX Computer Modern fonts installed locally, which for some reason aren't imported on this page)

runarberg 7 years ago | |

hmm, here is a project I haven’t given nearly as much love as it deserves.

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.

cotelletta 7 years ago | |

Except MathJax isn't the bar to beat, it's Katex which doesn't rely on a measurement of DOM layout.

SimeVidas 7 years ago | |

I’m getting “main.js:100 Uncaught ReferenceError: MathJax is not defined” in Chrome.

bjoli 7 years ago |

Not in any way affiliated, but Igalia is a cool company. They pay their employees to work on OSS projects as a part of their job. Andy Wingo work(ed?)there and they financed quite a bit of guile development as a way to make him develop his compiler and runtime skills.

sanxiyn 7 years ago |

My personal opinion is that MathML should die. MathJax is here today and works.

75dvtwin 7 years ago |

this is great news.

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 [1] ?

[1]https://github.com/Microsoft/reactxp

mymythisisthis 7 years ago |

I hope MathML gets more support. It is a bit unwieldy, but it seems like a simple solution to displaying maths on a simple HTML page, here is my example.

http://gron.ca/algebra/023.html