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I am a graduate student in math. I am coming up on the end of my masters, and multiple classes require LaTeX submissions. These classes are all very difficult by default, and spending multiple hours doing LaTeX only to submit an incomplete homework assignment feels non-constructive to me. I am getting better at LaTeX efficiency, however, I have found options like https://mathpix.com/ which will let me upload PDFs of my handwritten work, and then their AI will output LaTeX code which I can copy to overleaf and tweak for accuracy and formatting. Is this act that I have described plagiarism, or some other (commonly) punishable academic offense?

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    Could this be the most brilliant guerrilla marketing campaign ever? ;)
    – Ian
    Feb 8 at 23:55
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    Just a lowly student swimming in a sea of Tex.
    – SBJ
    Feb 9 at 0:02
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    You tagged this with generative-ai, but AFAICT, the tool this is about is not generative AI, which is also crucial with respect to plagiarism issues.
    – Wrzlprmft
    Feb 9 at 11:20
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    @Wrzlprmft I don't know in this specific case, but I think generative AI could reasonably be used in such a tool. It's not just about being able to match squiggly lines to LaTeX commands, the software would work much better if it incorporated a LLM trained on math formulas. For example some symbols might be impossible to read correctly unless you can guess which field the formula is from and being able to predict likely following symbols giving a prefix of a formula would also be immensely useful.
    – Nobody
    Feb 9 at 12:11
  • 2
    If you are struggling to write quickly in LaTeX, maybe you should try out Typst. I felt a noticeable jump in my productivity when I switched to Typst. It also has a free local compiler available here.
    – mhdadk
    Feb 9 at 13:57

14 Answers 14

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Overall, no. The tool you use to write something hasn't got the same status as another author. I think it definitely would be treated differently if it was "found out".

One thing, be careful that any text generated isn't accidentally lifted from another document (I think this is unlikely), that can be plagiarism. So just use AI to help generate it, then edit it, check it, and its fine. I think on the whole that's a fair way to look at this issue.

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  • I only intend to take generate Tex from my own handwritten work, so that shouldn't be an issue.
    – SBJ
    Feb 9 at 0:08
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    @SBJ I think the concern here was that the AI might have been trained on other people's work, so even if you only show it your work, it might introduce traces of other people's works in its output. As an extreme example, imagine you write an equation that is somewhat similar with an equation in someone else's work that the AI was trained on; it's conceivable that the AI might put that other equation, instead of yours, in its output. But you have to check the output for mistakes anyway, so everything should be fine.
    – Stef
    Feb 9 at 13:17
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    @SBJ As another extreme example, imagine you write a complicated handwritten equation; there is a straightforward-but-complicated way to write this equation in latex, and a very-creative way. If the AI has been trained on someone else's work, the AI might use the very-creative way, and that could be considered plagiarism even if the resulting equation is the same (but the resulting latex code is not the same). But that's a somewhat extreme example, and writing latex code is not an extremely creative endeavour, so it's fine.
    – Stef
    Feb 9 at 13:20
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    @Stef Assuming the work is being graded on the mathematics as conveyed in the PDF and not on the LaTeX coding itself, I don't think even that situation would count as plagiarism. (I certainly wouldn't count it as plagiarism in my classes.) What you're suggesting feels to me like it's getting close to saying the authors of every piece of software you use should be credited as coauthors of your work. Feb 9 at 14:53
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    @Stef Yes, I get your point. The difference here is that (I assume) the student isn't turning in the LaTeX code, just the compiled PDF. If they are turning in the LaTeX code itself, and especially if they're being graded on the LaTeX coding, then I agree with you completely. Feb 9 at 15:11
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A very interesting issue! Although I do pay a bit of attention to various tech advances, I was not aware that there was any mechanism/app/device that could convert handwritten to TeX.

If any of my math grad students told me that they were using such a thing, I'd probably congratulate them for being ahead of the curve. :) But/and also advise them to double-check! :)

But, yes, many situations would declare that this was not ok... So, you have to ask in advance. I don't think it's "plagiarism" per se, but just maybe "against the rules".

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    Also, be sure to acknowledge "spell-check" in your bibliography. :) Feb 8 at 23:58
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    As we all should!
    – SBJ
    Feb 9 at 0:09
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    Would they? This is just OCR but outputting TeX instead of Unicode. As long as the output matches the input and isn't "corrected" along the way, I see no difference between this and OCR, which I'd be surprised if it were considered bad. Feb 9 at 0:27
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    MathPix is new to me, but Maple has a cell phone app that can read my handwriting and convert it to nice looking math---I was introduced to that at the JMMs a few years back. Though this MathPix thing looks like a major improvement, as it seems to be intended to handle things at a more document level. Feb 9 at 0:28
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    many situations would declare that this was not ok - I'm curious about your point. OP is writing their own equations, only that instead of a keyboard, they are using paper, pencil, camera and a bunch of processors to eventually put their own thoughts into Latex. Why would this be problematic? Mathpix is practically an advanced OCR, not a generative language model building on millions of previous thoughts. The only things it knows are reading formulas and writing TeX. Unlike LLMs, the output contains exactly the same info as it's input, only in a different format.
    – Neinstein
    Feb 9 at 8:26
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Copying the output of a Large Language Model might be cheating, depending on the rules of the game you're playing, but unless the LLM itself is reproducing the work of a human author, then copying the output of the LLM cannot be plagiarism by any usual definition of the word (see final note, below). Plagiarism requires a human on both branches of the plagiariser/plagiarised fork.

If you are being tested or examined on your ability to write LaTeX, then having a machine produce the LaTeX for you would be considered cheating in the same way that the use of a calculator would be looked upon as cheating if you were being tested on your ability with mental arithmetic. It doesn't sound as if that is an issue in your case.

I have experimented quite a lot with using an LLM to produce LaTeX code, either from my handwriting or from a scanned (printed) document that has been poorly typeset. Here are two examples from handwritten material. The "mathematics" is of course complete junk but the results are impressively useful even if not completely correct.

Example 1

In this first example, I am interested in whether the LLM can get the basic structure of the equations correct. Integrals and exponentials This is the LaTeX code that the LLM produced. \[ \int_{-\infty}^{\omega} N(\eta) \, d\eta - \int_{-z}^{p} e^{-i3\zeta} \, d\zeta \] which is set as

compiled from AI

Example 2

In the second example I was interested in whether the LLM could correctly align the equations and also how much of the details (e.g., the bar over one of the digits) would be correctly produced. Alignment. This was the LaTeX code ... \begin{align*} \sin x &= \sqrt{1 - \cos^2 x} \\ &= 27 \times \Omega \\ &= 2.6 \end{align*} which is set as

compiled from AI

As you can see, the results aren't perfect but they are nonetheless very useful.

My advice? Check the rules of the game. Are you being tested on your ability to do mathematics, or on your ability to typeset mathematics? If it is the former, and not the latter, then go ahead and use the LLM. It will potentially save you an immense amount of time (initially) and you will very quickly become familiar with the idiom of LaTeX so that:

  1. You no longer need to rely on the LLM to the same degree but will be able to type your LaTeX directly, and
  2. You will be able to give more nuanced instructions to your LLM so that it can set the mathematics in exactly the way that you want.

Note: ... from the Cambridge Dictionary of English. "plagiarism: the process or practice of using another person's ideas or work and pretending that it is your own"

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    Minor technical point: mathpix.com does not appear to use an LLM, but a different AI/ML technique that does image/handwriting recognition.
    – James_pic
    Feb 9 at 11:09
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    LLM, like pretty much all machine learning techniques, rely on training data. In most cases, this training data was created by humans, so it can very much be plagiarism if you try to pass the LLM's output as your own, and the LLM's output has recognisable traces of someone else's work.
    – Stef
    Feb 9 at 13:37
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    I'm sorry but your point about plagiarism is just wrong, and not supported by various other dictionaries and sources (1, 2, 3,4). Plagiarizing is the act of presenting work you did not do, work that you had no hand in creating, as though it were yours. Arguing that you cannot plagiarize a machine is missing the entire point of why plagiarism is wrong.
    – terdon
    Feb 9 at 14:21
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    The links I gave were the result of just a few seconds search. Just because the author of one dictionary used the unfortunate term "person" doesn't mean that you require the author to be a human being. All it takes to plagiarize is to pretend you produced work that was produced by someone other than you.
    – terdon
    Feb 9 at 14:22
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    Agree with @terdon, the definition of plagiarism here seems too narrow. Suppose you copy an essay off the internet and submit it as your own work. I have a hard time accepting that it is impossible to tell whether that wholesale copying of text and false representation of it as your own is plagiarism or not, unless we also know for certain whether the original text came from a person or LLM. In an age where LLMs can pass the Turing Test, it's not even possible to tell whether something was written by a person or machine, meaning "I copied an LLM, not a person" is always an available defense. Feb 9 at 15:46
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As many answers have already pointed out, this would not be plagiarism. However, you should be aware that by using an AI, you turn over your data to them- that is, future users might plagiarise you. Using the example provider that you linked, here is their privacy FAQ (emphasis mine):

New and different images allow Mathpix to improve current recognition features and add new recognition features. If you allow Mathpix to use your images, anonymized versions of your images may be chosen for algorithm training purposes by our QA team. Regardless of if an image is selected by QA or not, all images in the QA database are permanently deleted after 60 days.

So while your use might not constitute plagiarism, others might plagiarise using the future trained model of this AI. If it's just homework it is probably okay, but a Master's thesis could already be something worth pursuing in a PhD.

In this case, the provider suggests that you can opt out. This would be something to always check when you use an AI provider, and proceed with caution.

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Here is a good rule of thumb to understand what constitutes plagiarism.

Plagiarism is - in spirit - about claiming intellectual credit for yourself that you did not do, but copied from someone (or had someone do for you).

[That's why self-plagiarism is called "plagiarism", although it's a bit controversial naming. The use of that latter term focuses not so much on the aspect of stealing credit from others (which regular plagiarism also implies), but on claiming credit that you don't deserve (because you already received it earlier).]

Back to your question: Under above interpretation, as long as the AI does not carry out any intellectual work that you are supposed to do, you should be fine.

For instance, if the course involves actually learning to use LaTeX, it would be plagiarism. If the course only involves somehow typesetting the material in whatever way is suitable, you could ask the tutor if it is legitimate to use an AI helper for that purpose and to cite it if relevant.

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    "Plagiarism is - in spirit - about claiming intellectual credit for yourself that you did not do, but copied from someone (or had someone do for you)." And looked at this way, the problem is completely solved by being fully honest and open about what you've done: that's why citations and quotation marks help. In this case, OP is probably asked to fill in some sort of (digital) form at the time of submitting the work, and will have an opportunity on that form to declare this as "use of an automated translation tool" or similar. Feb 9 at 13:40
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    @DanielHatton Indeed. Though, nobody will put quotes around all words they looked up in the dictionary or which was fixed by Grammarly. With the increasing power of tools, the boundaries where external work needs to be acknowledged will become increasingly blurry. Had your human assistant typeset your math, you would probably acknowledge and thank them for typesetting, but not cite them, or mention them as co-author. Feb 9 at 15:08
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    @EspeciallyLime I used also to fall for that trap, but then I understood where it comes from. The word plagiarism has two aspects and they are linked, but not equivalent: 1. "taking undeserved credit from others", 2. "claiming undeserved credit for oneself". Self-plagiarism gets the "-plagiarism" epithet not because of 1., but because of 2. Of course, that implies that credit is a quantity to be "counted", but in a publication-beancounting society, that's pretty much is given. Feb 9 at 15:58
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    @EspeciallyLime Not that I know of, but I kept wondering why the term self-plagiarism took hold and is so persistently used. That's the explanation that I came up with to explain it to myself. Feel free to disagree, to me that made it finally make sense. Feb 9 at 16:31
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    @DanielHatton Apart from that, I did not criticise the word self-plagiarism, but I saw many people criticize the choice of word. As a consequence, I wondered, as I said, why people used it. And this was the explanation I came up with for myself. Feb 11 at 12:53
8

Ask the person teaching the course

Only they know whether the (secondary) goal of the course is to teach you LaTeX skills or not. If it is, using an unapproved tool might circumvent that didactic goal. If it isn't, it's still up to the teacher to decide which tools are ok to use for their course and which aren't.

And don't ask about plagiarism. That's not the issue here. Ask whether you are allowed to use that tool for your coursework.

Since these AI tools are fairly new, there is no "established consensus" on this issue, so be prepared for answers ranging from "Absolutely not!" to "Sure, why would you even ask?" to "Uh, no idea, I need some time to think about that"¹.


¹ Next week on academa.SE: "Should I allow my student to use an AI tool for LaTeX markup?"

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    Oh shoot, I wish I would have seen your comment sooner. I asked specifically about plagiarism this morning. All of them seemed to echo "that's not an issue here".
    – SBJ
    Feb 9 at 20:23
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I'm going to go against the consensus here and argue that what you are doing is self-defeating, whether or not it is technically plagiarism.

I'm sure your lecturers aren't asking for submissions in LaTeX in order to torture you. It's possible they are doing it for their own convenience (because well-written LaTeX is much easier to read than handwriting); but it seems much more likely that training you to use LaTeX is part of the course goals – LaTeX is, like it or not, the "industry standard" for typesetting mathematical documents and so being able to write in LaTeX is a necessary skill for a mathematician. If so, then using a fancy OCR program to generate TeX from handwritten math is cheating.

It's really not that hard to pick up; with a little practice, you can get fluent enough that you can even take notes in lectures directly into LaTeX in real time ("live-TeXing"). Unless you have a disability which prevents you from using a normal keyboard (or something of that sort), then I suspect that in the time it's taken you to find this handwriting-recognition website, learn to use it, then fret about whether it's allowed or not, you could have sharpened your LaTeX skills to the point where you don't need to cheat any more.

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    I agree with your main point (+1), but actually from the examples in this thread the LaTeX it generates is better than a lot of the code I see from human authors. So playing around with this tool and looking at the code it produces might be an efficient way to learn LaTeX. Feb 9 at 11:40
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    > LaTeX is, like it or not, the "industry standard" for typesetting math. Well that depends what industry you work in. If you’re an academic whose business is writing papers in math or physics or comp sci, then I’d agree. If you’re writing mathematical documents in industry, or you’re a high school math teacher, or you’re an academic in engineering or economics, then (like it or not) MS Word and Google Docs are more widely used.
    – bubba
    Feb 9 at 12:45
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    Regarding "being able to write in LaTeX is a necessary skill for a mathematician", that may be true currently, but it's unlikely to be the case for long given that there are already tools that do a really good job of generating the LaTeX. I would argue there's nothing self-defeating about not learning a soon to be redundant skill.
    – cigien
    Feb 9 at 12:53
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    If you are a whiz in LaTeX, probably you will keep honing this skill. However, if you want to write math instead of worrying how to move characters into the right position, then such a tool is for you. Personally, I enjoy coding a lot, but dedicated and clever LaTeX manipulation to get the typesetting right, not so much. Feb 9 at 15:10
  • Thanks for your consideration. Yes, I agree with your main point. However, I have done LaTeX for multiple years and 100+ hours, and it still does take me multiple hours to code up an in-depth assignment. Consider me behind the curve or whatever you want, but it took me about 15 minutes to figure out the website, and another 24 hours to really realize how useful of a learning tool this could be for me, and the colleagues of mine who struggle with LaTeX more than I do. I talked to my professors also, and none of them considered this "cheating", as the point of each class isn't learning LaTeX.
    – SBJ
    Feb 9 at 20:18
7

This question, like most questions of the kind "Is X plagiarism" can easily be answered by going back to the fundamental reason(s) why plagiarism is considered such a grave offense against academic integrity in the first place.

Traceability of ideas

The primary and most important reason why plagiarism is a Bad Thing™️, is the importance of traceability of ideas in academia, science, research, culture, art, music, …, and really, society in general. But specifically in academia.

Imagine, you find a flaw in someone's argument. Or, since you are a mathematician, imagine, you find a flaw in someone's proof. It's a subtle flaw that took a while to spot, so, there have already been new papers written by other authors, relying on the theorem.

Traceability guarantees that it is possible to find every paper relying on the theorem and see if the flaw affects them or not. If the author of the original paper got the idea for the proof from somewhere else, then traceability guarantees that you can find the root cause of the flaw, and find other papers that might have picked the flawed idea up from the original source.

Plagiarism is a problem because it breaks the chain of ideas, so an idea can no longer be traced backwards to its original source or forwards to all the other ideas that build on it. This means that any flaw discovered in the idea cannot be fixed: it cannot be fixed at the root, because you don't know where the root is. It often cannot be fixed by the plagiator, because, well, they "stole" the idea and there is a chance they don't actually understand how it works!

Even if there isn't a flaw in the idea, there is still a problem: say, you want to build your idea on top of someone else's idea, but there is some detail you don't quite understand. So, you contact the author and ask them about it. If that author plagiarized the idea, there is now a possibility that they don't understand the idea enough to be able to answer your question. In the unrealistic best case, they will admit to plagiarism and point you to the original source. The probably more realistic case is, they just ghost you. The worst case is, they make up something, and it is convincing enough that you don't notice right away and go off and start building your idea on top of this made up answer, potentially wasting a lot of time, resources, money, and effort, until you notice there is something wrong.

Traceability is also one of the reasons why self-plagiarism is a thing: it still "breaks the chain". If you use the same idea in two different papers without properly referencing and citing it and someone looks at one of the two papers and finds a flaw, they have no way of knowing that there is a whole other paper out there with the same flaw. Other authors may have cited only one of the two papers, so there may be whole separate chain of papers all built on the flawed idea that nobody knows about.

Recognizing contributions

The reason that is often cited as the most important or even only reason, but is actually secondary in my opinion, is that contributing good ideas should be recognized. An author, group, or organization which advances the field should get credit for this advancement. In other words, the giants whose shoulders you stand on, should be rewarded for carrying the load.

This is another, although admittedly much weaker, argument for why self-plagiarism is a thing: you get twice the recognition for one idea. However, I find this a pretty weak argument, and I can see how people don't get why self-plagiarism is a problem if the idea of plagiarism is merely presented as "stealing someone's credit". That is why, in my opinion, focusing on the traceability aspect is important.

Conclusion

I think it should be obvious when applying the two criteria above that what you are doing is not plagiarism.

However, as pointed out in other answers and comments as well, it might still be academic misconduct in other ways. In particular, if demonstrating proficiency in LaTeX is part of the course goal, then it might be considered cheating. Or, it might be considered clever use of available tools.

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  • I really like the traceability argument and generally your description of why plagiarism is a problem. However, in the specific case of OP, the thing you consider secondary, is actually the primary, namely getting credit. This is a class, and thus the original contribution of OP is at essence here. Also self-plagiarism - I agree with your take on it where it comes to taking credit from others; however, the problem specifically for a student is getting undeserved credit (whether through work of others or through cloning of one's own work). Feb 9 at 15:17
  • In the professional realm, I agree that the argument against self-plagiarism is weaker. It's about not getting credit counted multiply for oneself, but it is only a problem because it's fashionable to count papers rather than value insights. Feb 9 at 15:18
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This isn't really an answer to your question but too long for a comment. (Largely an elaboration on David Loeffler's answer.)

In my math graduate courses I require all of the homework to be typed. I don't require the students to use any specific software, but I encourage them to start using LaTeX if they aren't already. I would not consider the use of AI tools that you describe to be plagiarism, or any other kind of cheating in my classes.

However, there are three reasons I require the homework to be typed:

  1. So that it is legible.

  2. When students take their handwritten scratchwork and type it up, they go through another round of thinking about their arguments (in my experience, more thorough than when they just recopy by hand) and end up with better reasoned (and more likely to be correct) work.

  3. They will all eventually need to be able to use LaTeX fluently, and it's better to start learning sooner rather than later.

Your system partially defeats the second and third reasons. Only partially, since you're still typing up the text part yourself, plus reading and tweaking the AI's LaTeX output. So I get, and don't fully disagree with, your choice to do things this way at this stage, when you are pressed for time and focusing on learning the math. But although as I said I wouldn't consider what you're doing to be cheating, I see it as not really in the spirit of the requirement.

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    2. is an excellent reason. 3. is also great. Moreover, I always found that every tool to speed up things LaTeX-wise ends up wasting even more of my time. Frontends for bibliography cease to work at critical moments, or are incompatible with my collaborators; auto-completions end up messing up with the code, etc... In the end, it is better to just bite the bullet and type LaTeX directly. (I never used these AI tools, but I suspect they are still at this stage where they are more of a waste of time) Feb 9 at 17:01
  • Regarding #3: I’d say it’s pretty unlikely that the average undergrad in the average math class will end up in a job where LaTeX fluency is required.
    – bubba
    Feb 13 at 6:57
  • @bubba Agreed. Which is part of why I don't have that same requirement in my undergrad classes. For the PhD students, they'll at least need LaTeX fluency for writing their theses, regardless of their post-degree employment. Feb 13 at 16:54
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In my opinion there should be no issue in using such methods for mechanistic conversions (as opposed to generation of text, solutions, ideas, etc.), assuming you check the output for accuracy, of course. In spirit, it is the same as using OCR. Further, I am not aware of anyone having objections to use of Detexify, which also uses a machine learning method. I see no clear reason for why it would be OK to use machine learning methods to recognize one symbol at a time, but not entire equations or sections... That said, Mathpix's marketing leans heavily into the AI angle so it may be a likelier target of overly broad policies. Finally, the data security concern raised in this answer is worth taking into account.

As some answers have mentioned, courses and assignments where the goal is to learn using (La)TeX can be different in this regard from cases where (La)TeX is just used to typeset documents, and it's worth asking the instructor about both rules and advice. Jumping straight to automation tools like this may mean you overlook learning useful structures and how to effectively read TeX. However, at the same time, personally I tend to think that such courses should introduce useful tools like this (and, e.g., various editors, online table generators, and the TeX StackExchange!) that help overcoming the (often exaggerated) entry barriers to learning (La)TeX. Having to constantly flip through tables of symbols until you learn a sufficient number of commands for math symbols was frustrating, but hasn't been necessary for a while now, and courses ought to reflect this reality.

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    Heck, using Word’s spellchecker is using a fairly primitive LLM and I doubt, aside from elementary school spelling class, that anyone cares. And one does need to check the suggestions at times, particularly for technical terms.
    – Jon Custer
    Feb 9 at 14:11
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    If you entered a spelling competition it would be cheating. If there was a competition for “most beautiful latex output of complex formulas” it would be cheating. Since what you do is producing maths it’s not.
    – gnasher729
    Feb 11 at 8:40
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I saw handwriting input for equations years ago. It was used with Word, but used a TeX-like format at least as an intermediate step. That required using writing on a graphics tablet rather than scanning, but fundamentally it's the same concept (and akin to a cleverer version of automatically generating bounding boxes round characters and feeding them to detexify).

So this is an improved input tool. It's not plagiarism.

That doesn't mean it's not cheating in a LaTeX course, where the goal is to learn to write your own code. But there are also click-and-place equation generators for TeX and I'd see those in the same light.

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I think you should talk to the prof, as it's possible that learning LaTex is one of their educational objectives.

That said, IMO, if you use a tool to turn your handwritten notes into LaTex, and then prominently cite the tool and say in the submissions how LaTex was generated, then this is NOT an academic honesty problem (with the caveat that there may be language in the syllabus saying that it IS an academic honesty problem -- maybe "all turned in work must be your own" or some such -- in which case, it assuredly is). This way, you haven't claimed, in any way, personal provenance over work that isn't yours. You may certainly lose points for not doing it "right", but that doesn't make it an honesty issue.

2

What is the assignement about?

Is the evaluation based on the quality of LaTex code?

If yes, and learning LaTex is part of the course and therefore an essential part of the hand-in? -> don't use it!

If not, and it is about the content, and the format is simply required to be LaTex? -> No problem!

Why this is not a problem

(stated well in other answers)

Assumption: as stated, the tool does not do anything generative. Even if other sources were used to train it, so have other sources been used to train humans -> the tool should cite sources used, but this doesn't mean that there is content in there.

Plagiarism applies to ideas and content. You could cite the tools you use (in academia, that would surely be the right way), such as LaTex itself, maybe a compiler etc. But if you use handwritten text as a base, Word and a converter, whether you use a keyboard or voice promts to write: it's irrelevant.

0

plagiarism - no

other academic misconduct - no, unless one of the purposes of the course or the assignment is for you to learn LaTeX, in which case, you would be cheating.

If not certain, you can always ask your instructor.

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