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In a research field that math is frequently used, while sending a long note/paper, attaching a pdf is of course the best. But for a short email that only involves few equations, a pdf file might be too much I guess (is this correct?). What is the best way to facilitate communication and not scaring the readers to stay away from the content?

Here are some options for writing equation in a short email:

  1. There is chrome extension generating in-line equation for Gmail. But such option is unavailable for other sender's clients and the recipient might face some formatting/loading problem.

  2. Use in-line image like this enter image description here. Again this option might cause massy formatting issues in the recipients' end, even if the sender's been careful

  3. Use uncompiled latex pseudo-code. This is what my advisor and some seniors use, for example: "consider the equation mu(Q)=sum_{n in Q}a_n, we can get...". This option is hard to read but will not usually cause formatting problem accross different platforms.

  4. Use uncompiled real latex code. Since it is the real code (not pseudo code), the code is more rigorous and directly compliable if the receiver likes to. For example: "consider the equation \mu(Q)=\sum_{n \in Q}a_n, we can get..." This could be harder to read than "option 3".

  5. Use pdf regardless of the length of the email.

  6. Write a pdf and then take a large screenshot of the page.

What do you use daily? Please don't hesitate to share us your own tricks!

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    Voting to close as opinion-based. I don't think there's a "right" answer to this question. Commented Apr 6, 2023 at 10:06
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    There is also the, albeit slower version of typing the equation out in ASCII: µ(Q) = ∑ a_n, or even µ(Q) = ∑_n∈Q a_n. Commented Apr 6, 2023 at 18:35
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    @JannikPitt that's unicode not ASCII.
    – Džuris
    Commented Apr 6, 2023 at 19:21
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    The LaTeX pseudo-code being hard to read for short equations seems like an opinion, for sure. It seems like your advisor and others have decided that pseudo-code is the best for them. Commented Apr 6, 2023 at 20:33
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    @dodo I rather misread this when I answered. Are you concerned with writing professors in all areas, or perhaps advanced students and researchers in math, CS or physics? I imagine biology professors will not want to look at mangled latex code. Also, many researchers are not professors. Commented Apr 6, 2023 at 21:30

9 Answers 9

44

I've frequently send and received emails with LaTeX code in them. I don't think I've ever received an extremely short pdf (ie a single line or so). Formulas as image is something I've seen only students do, never colleagues. As such, I feel confident in declaring LaTeX-code-in-emails the de facto standard in my local neighbourhood.

There is no clear pattern in whether it is compilable code, or whether stuff like \ is dropped. For stuff I am writing myself, I'm more likely to write correct code if either the expression is sufficiently complicated that the receiver may want to compile it rather than reading the source code, or if it seems plausible that the expression could eventually be copied into an actual paper draft. I'm less likely to write to write formally correct LaTeX code if I'm in a hurry.

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    Agree. People who write in LaTeX can "visually compile" math mode in their head. And our visual compilers are more forgiving about missing dollar signs and curly braces! Commented Apr 6, 2023 at 20:41
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    Many thanks! Have you encountered anyone using unicode equation like μ(Q) = sum_{n ∈ Q} a_n?
    – dodo
    Commented Apr 6, 2023 at 20:58
  • @dodo: I occasionally use μ(Q) = ∑_{n∈Q} a_n which is both understandable and I believe directly compiles in modern LaTex. I'm not making that an answer because I do not know actual etiquette.
    – fgrieu
    Commented Apr 7, 2023 at 5:55
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    @dodo I have encountered this, but I don't like it. The mixture of symbols and code throws me off balance a bit, and ultimately reading it becomes more difficult for me. Some symbols also look a bit wrong, depending on the font used (\in is a particularly notable culprit here). Also, it is extra work if the goal is to copy it into an actual LaTeX document.
    – Arno
    Commented Apr 7, 2023 at 17:40
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    @fgrieu (The font I usually use in) my e-mail client can display U+03a3 capital sigma Σ, but can't display the character you've used, U+2211 n-ary summation ∑. I'm not quite sure what we learn from that. Commented Apr 14, 2023 at 12:35
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I rarely need to communicate equations except with other mathematicians or statistician, and in those circumstances, I presume (possibly incorrectly!) that they all speak TeX ... so I write the equation in the same way as I would if I were using TeX, LaTeX, or the kind of markdown that Stack Exchange uses.

No one has yet replied saying, "What was that supposed to mean!?"

Added in response to a comment question ...

I type the equation, much as I would in TeXMaker, including the $ and \ marks. My reason for doing so? Laziness! Sometimes I'm just cutting and pasting a line. I know it might sound inconsiderate, but for reasons similar to these, I don't think it is.

And finally ..

Having just read the nice answer by #Vectornaut, I might change my ways.

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  • It should be non-mathematican readable for most people. If you want nice typesetting it can become much less readable, but there is no need for that in an email or message.
    – gnasher729
    Commented Apr 6, 2023 at 12:50
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    Do you use the real TeX code, or use the pseudo code with "\" and "$" dropped?
    – dodo
    Commented Apr 6, 2023 at 13:36
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I often use LaTeX pseudo-code with some symbols encoded in Unicode. For example, I might express the valid LaTeX

\mu(Q) = \sum_{n \in Q} a_n

as the pseudo-LaTeX

μ(Q) = sum_{n ∈ Q} a_n

or the valid LaTeX

\sum_{n \in \mathbb{N}} \frac{1}{n^2}

as the pseudo-LaTeX

sum_{n ∈ ℕ} 1/n²

I know that the more Unicode I use, the more likely I am to hit a character that the recipient's browser or e-mail client can't render, but I can't recall anyone ever telling me this happened to them. Operating system developers have gotten really good at using font fallback and font linking to seamlessly display documents containing wide ranges of Unicode characters.

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  • Perfect answer! I am also worrying about the recipient's end cannot render some characters. All the Greek letters are fine I guess. Do you also use the real subscription and superscriptions instead of "_"?
    – dodo
    Commented Apr 6, 2023 at 20:56
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    @dodo I've found that most modern computers have built-in fonts that will handle most if not all of the math symbols defined by Unicode. For example, Windows systems have shipped with Cambria Math for years. It's not nearly as big of an issue as it used to be.
    – bta
    Commented Apr 6, 2023 at 22:04
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    @dodo, I use superscript characters pretty regularly, as shown in the \frac{1}{n^2} example. I didn't know about the subscript characters until you mentioned them—I'll try them sometime! Superscript characters aren't the best choice for all situations, and if I use carets anywhere in an e-mail, I might use them everywhere for consistency.
    – Vectornaut
    Commented Apr 19, 2023 at 2:00
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If your equations are reasonably short, consider explaining them in plain English, rather than presenting them in maths notation, e.g.:

For a given sequence, consider a set of indices and call the partial sum of sequence elements on this set

(of course, use the correct terminology -- I am not sure what does your equation represent).

If explaining in simple English becomes tedious, perhaps, your email is not so short after all and it is best to write a proper LaTeX or Markdown file and compile it into a pdf.

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    Maybe I've been at this for too many years (English-writing math stuff in ASCII emails), but if it's only two or three equations and such, for me it's quicker to spend 10 seconds quickly typing something like "The mu-measure of Q is the sum of a_n as n ranges over Q" (or whatever mu(Q) should be called; or just write m(Q)) than trying to figure out how to get an image in the email or stop and make a .pdf of some handwritten stuff. On the other hand, when things get a bit long (and I do this every 2-3 days, at least, regarding my contract work-at-home stuff), then I'll handwrite, scan, attach. Commented Apr 6, 2023 at 11:05
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If the math involved is more than three or four short equations then I usually typeset the math, or even the entire letter, using latex. Then I attach the latex and a PDF -- one for quick reading, the other so the other person can edit the equations when replying.

For just a touch of math, I use an unholy (uncompilable) mashup of latex code and matlab code and ASCII art. I will write --> in place of \rightarrow and alpha_2 in place of $\alpha_2$. And finally totally corrupt things like alpha --> [alpha 3; 3 2*alpha] . Lots of extra whitespace that SE will delete.

When I teach math online, this is a real problem. Undergraduates rarely know both matlab and latex. The discussion boards are rather pointless. I tried third party discussion boards with easy editors for tex, but it was a bit of a failure. The solution that was best was for students to write using pen on paper and use their phone to make a PDF.

2

Personally, I use any and all of the following, depending on how much of a hurry I'm in and who I'm communicating with.

  1. Avoid email and use a messaging service that supports LaTeX.

This is the best option if you can convince people to use such a messaging service, which admittedly won't be the case with everyone you want to mail. The one I like is Zulip. It's free to set up a reasonably small server and the functionality is similar to Slack or Discord, but it supports LaTeX (or rather KaTeX, an alternative to MathJax) out of the box. There might be other good alternatives, this is just the one I know.

  1. Use images

Personally, I think your email is much more likely to be read and understood if the equations are legible, so I think this is much better than the pseudo-LaTeX-code option. I think the main reason people don't do this is because it's a bit of a hassle, but if you set up a good workflow it's not so bad.

I don't know about other platforms but on the Mac there is an app called LaTeXit that allows you to just type the LaTeX code and view the resulting equation, without all the boilerplate of setting up a document. Then you can do shift-option-command-4 to screenshot part of the screen and place it in the clipboard, so you can then just do command-V to paste it in the email. I've never had an issue with someone not being able to see the images.

I never use an image as an inline equation though - I always put each image on a line on its own. That ought to avoid the vast majority of formatting problems that you might otherwise run into on the other person's email client.

  1. Use unicodeit

unicodeit.net is a simple web site where you can enter (pseudo)-LaTeX code and get unicode output. It's great for writing simple inline things like x ∈ ℝ, which I got by typing x \in \mathbb{R}.

  1. use Markdown

There are many Markdown-based text editors that let you use MathJax and export the result as a pdf. What I do is write the email in such an editor, then both paste the Markdown source into the email body and attach the pdf with the LaTeX rendered. That way the recipient doesn't have to open the pdf just to see what you wrote, but they have the option to if they want to see it with the equations rendered properly.

  1. write LaTeX pseudocode directly in the email

To be honest I do this quite often, but only if I'm feeling lazy and/or in a hurry, and if I know that the recipient won't have trouble parsing the pseudo-LaTeX and will take the time to do so.

2

TL;DR Don't use images. Use PDFs if complex.

I don't know much about the math side of things, but based on my experience in end-user email (and everything else) support across many different platforms, I highly recommend against using images. Depending on the destination email system, software (whether local such as Outlook or Thunderbird or online webmail of various types), device (smart phones often different from desktop and laptop computers) and other factors, images are not a reliable way to convey critical details in an email message:

  • Size - depending on many factors, an image that looks "normal" on the sender's computer might appear tiny (and nearly unreadable) or huge (and unprintable) on the recipient's system.
  • Access - Due to bandwidth issues, spam issues and other reasons, some systems block images, some allow images only after confirmation and some block remotely hosted images (some sending systems will automatically turn attached images into hosted images without a non-expert sender realizing what is going on). So using images can sometimes result in the recipient not actually seeing the intended content at all.
  • Printing - Some email systems will reliably print images inline with the text of the message, some will not or will do so but too small/too large.

I have dealt with this so many times that I actually wrote a system - picturepdf.com - to handle it. I have some customers who receive images occasionally from many different sources and in many different sizes and who can't be easily trained to open up attached images in Paint.NET or a similar program to resize them and print them. Send an email to [email protected] and it will send back a PDF of the included images, one per page. Once they have the PDF, they can print that easily or forward it along to someone else, etc. (I don't make any money on this - the value to me is in not having to help customers every time they get an image that they can't print properly. Saves me time and saves them frustration.)

I agree with using various methods of spelling out an equation, depending on the situation, including plain text, pseudocode and LaTeX. I have not used LaTeX myself (I am not a mathematician) but I done similar things with snippets of code as needed.

But when it gets complex, use LaTeX or whatever system you prefer and turn it into a PDF and attach it.

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  • Many thanks! Do you think unicode characters like ℝ, μ will be well-supported?
    – dodo
    Commented Apr 9, 2023 at 18:50
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    In general, I would expect Unicode to be better supported than images. Images present a ton of bandwidth, formatting and security issues that Unicode does not. That being said, there are still some older email clients (e.g., Eudora) that don't handle Unicode very well. Commented Apr 9, 2023 at 19:07
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Another option is to use links to SE posts

I would typically just use attached pdf for communicating mathematical material with colleagues, students, etc. However, one alternative that you don't list is for the student to post their question on https://math.stackexchange.com/ or https://stats.stackexchange.com/ (both of which have LaTeX facilities for mathematical notation) and then send the professor the link to their question. For professors who use SE, they can answer directly on the site, but even for professors that don't use SE, they will at least be able to see the question set out using clear mathematical notation.

This option is obviously not suitable for every occasion, but you can add it to your options. Typically it is useful to use a linked SE post when you have a question of a general nature that may also be useful to a wider audience, you have a professor who either uses SE or doesn't mind viewing linked questions on the network, or you want to attract answers from a broader audience of experts in the field. It is typically not suitable if your question is too narrow to be appropriate for the network, or if your professor is averse to this method of communication.

0

If you need to communicate equations to someone outside a field where LaTeX is common you might want to use the embedded equation features of Office or Google Docs. Typesetting systems knowledge is mostly limited to a subset of hard science and engineering fields and anyone outside of them can still use equations and citations but only through such GUI tools.

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  • Will "embedded equation features" cause some problems on some clients?
    – dodo
    Commented Apr 6, 2023 at 19:54
  • I think providing two options sorta implied universal compatibility might not be available. Each office suite has it's own equation system.
    – davolfman
    Commented Apr 6, 2023 at 20:12
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    @dodo I find that both Office and Google docs mess up fonts when the sender is on a different OS. Sadly, the symbols are the most common to be messed up. Always print to a PDF and attach that as well. Commented Apr 6, 2023 at 20:15
  • @TerryLoring You mean the "embedded equation feature" is messed up on emails or do you mean that the unicode equations will be messed up?
    – dodo
    Commented Apr 6, 2023 at 20:47
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    @dodo I have no idea. When people send me equations and symbols in a word document they are often corrupted. No idea why. Commented Apr 6, 2023 at 20:58

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