LaTeX/TeX Vs. Mathematica for Typesetting

Question

I know Mathematica like the back of my hand, but I do not know a speck of $\LaTeX$ or $\TeX$. With regard to mathematical typesetting, is there something significant I can do in $\LaTeX$/$\TeX$ that I can't do in Mathematica? The Mathematica interface for typesetting seems much more intuitive and I already know it. However, when it comes to mathematical typesetting, I know $\LaTeX$ sets the standard.

By the way: I know Mathematica is expensive and $\LaTeX$ is free, but I already own Mathematica and use it for many other things, so will always have a copy of it. So I mean my question to be independent of price.

Answer 1

$\LaTeX$ is not only free like in beer, but free like in speech. There are enormous advantages to using open source standards.

Right now you like Mathematica and are happy with its software. Suppose that five years from now the company decides to put out a new version and break backwards-compatibility. Or the company goes out of business. And suddenly the files you have become useless, because they're stored in a proprietary format that nobody can read.

$\LaTeX$ has a huge community of people contributing code to the standard. Thousands of user-written packages to do specific things that the base code doesn't. Mathematica only has the Mathematica staff.

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Response added to the discussion that appeared suddenly below:

Microsoft Word is great and has huge market share. Before Word there was Word Perfect, that was great and had huge market share. Before Word Perfect there was Word Star, that was great and had huge market share.

You use closed-source software at your own risk. I use Word myself on occasion (it's installed at work, and people send me Word files), but I would never invest thousands of hours of my time in developing expertise in software that will very likely be obsolete in my lifetime. Open-source standards might become dormant, but they are never dead, because the source is still available and someone can bring them back to life.

I'm not Stallman; I'm not suggesting that closed-source is evil and we should do open-source or nothing. However, using closed-source software is a legitimate risk, and one specific advantage $\LaTeX$ has over Mathematica. In a case of mature, full-featured alternatives (such as in this case) I always prefer the open source one.

Answer 2

Sharing documents may not be easy - LaTeX is a standard that almost everybody is expected to be able to use, and is free. Mathematica requires a purchase, and lots of people never saw it.

Answer 3

I use both Mathematica and $\LaTeX$ extensively. While it is possible to make nice looking documents in each, they really have two different aims. Mathematica is mainly about mathematical computing and interactive content. $\LaTeX$ is about typesetting and publication-ready articles with fine language-based (as opposed to WYSIWYG) control of layout.

As such, they really are too different that one can replace or supplant the function of the other. They are more complementary than anything else. I use both: Mathematica to do computation and $\LaTeX$ for typesetting results. The Mathematica notebook can always be published alongside a PDF.

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In light of the controversy with the open/closed source issues described in another answer, I'd like to amend my answer. First, to address the specific question of "what can $\TeX/\LaTeX$ do that Mathematica cannot," with respect to typesetting, the issue is not so much one of specific capabilities, but rather:

1. the ease with which something can be done
2. the extent to which it can be done well
3. the fundamental look of the result.

I am sure you could manage to replicate a lot of mathematical typesetting functions of $\LaTeX$ with Mathematica. But it simply wouldn't look the same. The emphasis of $\LaTeX$ is on controlling the exact placement of objects on a page, not the mathematical meaning of those objects. On the other hand, A Mathematica document can let the user evaluate formulas and manipulate interactive controls in ways that a static document can never allow. But as I said, the two are complementary: Mathematica has a function called TeXForm that takes a StandardForm expression and converts it into $\TeX$ syntax. So you could certainly use it to help you produce formulas to embed in your journal article, for example. But no journal is going to take a .nb and consider it publication-ready, compared to a .pdf of a $\LaTeX$ file. Many journals these days even have their own templates they want you to use, so they can ensure a consistent look across articles.

In my opinion, the closed/open debate is irrelevant to the OP's question, and it doesn't sit well with me to fret over whether some kind of document format will be supported $n$ years down the line as some sort of justification for choosing one over another. Nothing is certain and all standards eventually evolve. The irony is that Mathematica is not much younger than $\TeX$ itself--it has been around nearly as long, and the core syntax and language has essentially remained unchanged. Support for older notebooks and methods to convert them have always existed; and even if a notebook cannot be run, it can still be read. Of all the things to pick as criticisms of Mathematica, I would not choose this issue to highlight. It makes about as much sense as claiming that we should not use C or Python today because the language itself will become obsolete someday.

Answer 4

Luckily, in the open community world GNU TeXmacs can work as standard Office word in WYSIWYG way. BTW, it can be used as front-end for many open alternative scientific computing packs, such as Maxima, a symbolic computing software. You can have it a try.

Answer 5

OP asks: is there something significant I can do in LATEX/TEX that I can't do in Mathematica?

LaTeX

• far better at handling print page layout … for example, 2 column layout, or page breaks, footnotes etc
• some journals/conferences require submissions in LaTeX format
• I am sure there are other benefits! — but much steeper learning curve … though I believe nice front-ends exist (is Scientific Word still around?)

Mathematica

• typesetting is easy (palette graphical entry, keyboard shortcuts, WYSIWYG etc)
• everything in-built - including beautiful mathematical fonts
• output to either pdf, or mma notebooks (which can be read for free on any computer, or through a web browser using the CDF plugin (Computable Document Format).
• can export individual equations to LaTeX: [ I use this sometimes to paste output here at math.SE, and it works quite neatly, but sometimes it needs a manual tweak, for example to decide what goes into fractions, and what lies outside the fraction ]
• can also be enormously powerful and flexible like LaTeX [though this does require knowledge or tweaking with lots of typesetting options]

Both LaTeX and Mma use style-sheets, and use plain text file formats (not binaries) which can be opened in any text editor, and even edited, if so desired (though not necessarily for the faint hearted).

Personal experience

Having co-authored/typeset a 500 page Springer book in Mathematica itself (with output to PDF for the printed book version) … I can say that getting page layouts to be aesthetically pleasing was a VERY difficult and VERY time-consuming task. At the time, I complained bitterly to Theo Gray who was head of user interface design etc at Wolfram … and I suspect that my complaints mostly fell on deaf ears :) Theo Gray was rather forward-looking, and I believe he was just not interested to expend the effort to bring old-school printed page-layout tools to Mathematica (footnotes, columns, proper WYSIWYG page layout etc), … to an evolving world which he clearly saw as moving away from old-skool print and towards live/interactive/virtual/scrolling etc.

Maybe he was right … but doing printed output in Mathematica is still a pain. And I also think that explains Mathematica's focus in moving towards live Computable Documents (live documents where the equations / diagrams etc are live and interactive).

Open-source vs Commercial

The OP specifically noted that he already had Mma, and so price was not a relevant issue for him. I don’t particularly care whether the software I use is open-source or commercial … although, obviously, like everyone else, I prefer getting stuff for free. But on balance, I also try to use the best tool for the job. And if I am going to use it a lot, as long as the price is not unreasonable, … well, one ultimately has to put a value on one’s time, and place the appropriate respect onto what one does. Maybe walking is cheaper than driving, but it is not always the most efficient solution.

Longevtiy

As to longevity, I frankly don’t see any evidence that open-source platforms survive any more robustly than commercial platforms. In fact, the suggestion that people should not use a commercial platform such as Mac or Windows or Photoshop or Autocad or iTunes, because one day it may not exist … seems as far-fetched and extreme as those who don’t want to get out of bed in the morning because one day the universe may no longer exist. I prefer to live in the present, and I try to use the best tools that exist in the present.

Vadim notes: Microsoft Word is great and has huge market share. Before Word there was Word Perfect, that was great and had huge market share. Before Word Perfect there was Word Star, that was great and had huge market share.

Moreover, the biblical proclamations of extinction and sudden death are just not the way the world operates. It evolves and we evolve with it. I cannot think of any new major platform that has supplanted the past, without taking the past with it. MS Word might have supplanted Word Perfect and MacWrite, but you can be sure that MS Word was able to read all those old MacWrite and WordPerfect files. New Macs with Intel processors succeeded because they could read and run the files from older Macs with Motorola processors. Windows succeeded because it could read MS-DOS. No doom and gloom … just evolution to something (hopefully) better.

Answer 6

Basically, Mathematica is designed for calculations, and can do some typesetting too. $\LaTeX$ is designed for typesetting, and can do some calculations too.

So the main strength of $\LaTeX$ here is that if and when you want to add some other common document feature to your math papers, like cross-referencing, bibliography, numbered lists, etc., you'll already be in the right domain, and can do all that by editing the same one file.

Answer 7

One point that seems to have been largely ignored in the other answers is that the typesetting system in Mathematica deals with more than appearance - it deals with semantics as well and this is a primary consideration in its design. Consider the following two inputs and outputs.

In the first, I've typed in the integral in Mathematica's typeset input format. Displaying it in so called InputForm, we see that this typeset expression maps to a specific, valid Mathematica input. If the function f were defined, the integral would evaluate as well. In the second input/output, we see the reverse. Of course, this is a simple example but there are many others.

On the other hand, if you're interested only in typesetting beautiful mathematics, particularly if you hope to publish it, the $\LaTeX$ is the obvious choice.