# Why is LaTeX used as the defacto standard for math equations?

In almost every application I've ever seen that uses math equations, it always supports LaTeX.

If LaTeX does so much more than just math equations, why is it the defacto standard for math equations? Isn't that akin to everyone deciding to use Microsoft Word's Math Editor for math equations?

Related question: Is there a name for the subset of LaTeX that deals specifically with math equations?

• Note: I couldn't choose a better tag due to lack of reputation. Could someone with enough rep please retag this? – Senseful Mar 24 '12 at 8:06
• I think you can still edit your own question. – Leo Liu Mar 24 '12 at 8:12
• @LeoLiu: I'm not familiar with this site, so I'm not sure which of the existing tags would work best. – Senseful Mar 24 '12 at 8:13
• – Leo Liu Mar 24 '12 at 8:21
• Maybe because LaTeX just sucks less than Microsoft Word's Math Editor. – af3 Mar 25 '12 at 13:00

I think it's a survival of the fittest thing. First of all, math notation isn't specific to LaTeX, it's inherent in the TeX engine.

So what do we have:

1. Around (virtually unchanged) since the late 70s.
2. Text-based.
3. Terse.
4. Easy to read and write by humans.
5. Effective: Virtually every mathematical formula can be formulated.
6. Operational: There exists an engine available to everyone to render a graphical representation of the formula.
7. In actual use by millions of mathematicians around the world.

I don't know what `troff` did for formulas (which might have been a competitor at the time), and I don't know whether Knuth invented it all by himself (was'nt there a system named `scribe` he used as a blueprint?), but I can imagine there was not that much pressure to ever develop an alternative aspiring for all these features at once.

You can look at MathML for the result what happens when such a thing is attempted by a committee ;-)

• You should note that MathML is math input format, so though it might compete with TeX as math input language, they do not compete on the actual rendering as TeX can render MathML in a way or another (there are several solutions for that). – Khaled Hosny Mar 24 '12 at 15:14
• @KhaledHosny -- two downers re mathml as far as i'm concerned: (1) it's not really directly human-readable or writable; (2) there's no clear prospect for "content" mathml (as opposed to "presentation" mathml), so it's not easily converted to something intelligible to a vision-impaired user, whereas (la)tex can reasonably easily be given tailored input for that purpose. – barbara beeton Mar 24 '12 at 16:25
• @barbarabeeton each format has its strengths and weakness of course but actually accessibility concerns have been central to the design of MathML from the start. – David Carlisle Mar 24 '12 at 16:42
• I think this: "Effective: Virtually every mathematical formula can be formulated." is the main reason. In the original question, the Microsoft Word comparison can be answered that with MS Word, you can formulate some high school math but nothing more professional. – Vesa Linja-aho Mar 24 '12 at 17:22

As the first two answers have already stated (La)TeX has become the defacto standard in several areas because it is basically good at what it does, fairly natural to author and freely and widely available.

It's also I think instructive to see where (La)TeX did (or has) not become ubiquitous. @stephan-lehmke mentioned MathML. The downside of TeX being so flexible (which is what makes it excellent as an authoring format) is that it is hard to process with anything other than TeX (and hard to convert to anything other than a printed page). Many Journals, even if accepting TeX from authors (to make it easy for author submission) put the documents through complicated and error prone conversions to internal SGML formats (or in some cases simply printed the documents and had them re-keyed in those formats). Having an open widely available format like MathML allows the tooling around an XML/SGML Math markup to be more easily shared (and improved).

MathML (rather than TeX) is part of the EPUB standard for electronic books, the DAISY standard for audible/accessible electronic publication, and part of HTML5. It underlies the Math formatting in OpenOffice and other ODF based office suites and it is supported as cut and paste of mathematical expressions in MS Word and the Math input panel. MathML doesn't compete with TeX in any of these areas as TeX simply was was not considered, primarily as it is just too "different" to fit into workflows that are not totally designed around the TeX processing model.

Conversely when it comes to typesetting MathML, TeX is still probably the best mathematical typesetting system there is.

Probably I should mention in case it isn't obvious, that I have various conflicts of interest here, as a member of the latex3 team responsible for LaTex2e and an editor of the MathML specification, so these comments can't exactly be considered an impartial review

• Full ACK. My snide remark at MathML wasn't really warranted as the purposes are quite different (I was mainly answering the original question). I know TeX math is a horror to parse, which has always been a big disadvantage for TeX2anything converters. If I ever add math capabilities to my DocScape, it will surely be based on MathML ;-) – Stephan Lehmke Mar 24 '12 at 11:50
• @David -- please try harder to develop a really competent "content" mathml. please! – barbara beeton Mar 24 '12 at 16:29
• @barbarabeeton competent at what though?:-) OpenMath may be more your style? – David Carlisle Mar 24 '12 at 16:34
• @David -- competent at conveying the meaning of the math, as opposed to what it looks like. but you're right; i should look more closely at openmath. – barbara beeton Mar 24 '12 at 16:41
• @barbarabeeton MathML/OpenMath is quite expressive enough to encode fully formal proof systems, as has been demonstrated. A system like Maple can also output its internal expression trees in that for, and certainly Maple cares for some meaning of "meaning" not just presentation. This is unlikely ever to be mainstream though as working in fully formal systems is hard, most mathematics is written down using informal notations and proof steps, and that won't change whatever syntax is used. – David Carlisle Mar 24 '12 at 16:49

Besides being a great format to mark mathematics and the production of outstanding output, some other reasons as explained by arxiv.org a heavy user of `TeX\LaTeX`.

TeX has many advantages that make it ideal as a format for the archives: It is plain ASCII, it is compact, it is freely available for all platforms, it produces extremely high-quality output, and it retains contextual information.

It is thus more likely to be a good source from which to generate newer formats, e.g., MathML [namely HTML, or more specifically XML, that handles mathematics correctly -- note that the MathML people plan a LaTeX to MathML translator, but dvi/ps/pdf lack the necessary document structuring concepts]. Possession of the source thus provides many additional options for future document migrations. Using emerging new technology, most of the Postscript generated from the source contains hyperlinks, so that using new versions of PostScript previewers (e.g., the next version of Ghostscript/Ghostview), readers can point-and-click to navigate within the paper, and even over the web itself.

And by archiving the source, we maximize the potential for seamless adoption of future technological improvements. Archived papers can be repeatedly rejuvenated by automated reprocessing.

Simply put, it does a great job and fulfills the requirements of its users.

Leaving aside the power and flexibility of LaTeX, the huge existing codebase coupled with the lack of good conversion tools is a currently an insurmountable obstacle to any move away from LaTeX. I teach university mathematics. Like most of my colleagues, I maintain several hundred teaching related LaTeX documents (plus many other research documents). I would dearly love to be able to generate html pages with MathML equations from the LaTeX source seamlessly in a way that:

1. Supports the full range of LaTeX packages that are widely used for specialised mathematical purposes.
2. Offers a gentle migration path that lets me use my LaTeX codebase to produce typeset material for printing and slide presentations as well as to produce html that I can publish as online materials for students. That way, I could transition to fully electronic publication as the need for paper gradually abates.

At present, this is all a dream. Even if good conversion tools existed, the lack of browser support for MathML means few mathematicians would even contemplate publishing anything this way. So we are stuck with publishing materials in pdf format on web sites, with all of the downsides that entails. So in university mathematics and engineering departments, I would say LaTeX is unlikely to yield much ground in the near future. Anyway, I thought that the perspective of a major and influential segment of the LaTeX user base might be of interest.

As for comparing Word with Equation Editor to LaTeX, well, surely you are joking?

• This doesn't really answer the question. It seems to be closer to its own new question, although I think its not defined well enough for the format of the site. For example, which specific packages should be supported? Anyone hoping to formulate a solution would need to know this at least. – Paul Gessler Jul 23 '14 at 15:26
• `I would dearly love to be able to generate html pages with MathML equations from the LaTeX source seamlessly` you can try tex4ht. – Nasser Dec 13 '14 at 23:26