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I got an opportunity to collaborate writing a mathematics paper with some professor at my university, but I'm suspecting my role won't be much more significant except doing menial work in the form of writing dozens of lines of code using Mathematica and helping my professor computing things. I can probably get in my name as a possible collaborator, but I am wondering is it really worth putting in the effort into it to do so?

While I'm aware that research experience is taken into account while considering grad school applications, I am also aware that putting into papers in which I had menial contribution into my CV might even carry negative weight, in the sense they might suspect I'm trying to game the system without really doing anything substantial.

Is it worth pursuing this project instead of, say, learning some new math by myself (not under the supervision of someone)? Even if I do, what are some ``red-flags" to notice for, which can indicate this might not be a great idea?

[PS: I don't want to go into details regarding the subject matter of the paper, but it's a relatively advanced topic that requires a fairly good mastery of the core undergrad curriculum to understand. I believe I have such an understanding, but I'm not sure if my role in writing the paper would reflect that/I would have the opportunity to use my understanding, especially if I'm not considering the professor as my main recommenders for grad schools].

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    Why do you want to go to grad school if you are not interested in solving/working on research math problems? – lalala Mar 4 at 9:17
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    @lalala "Solving/working on research math problems" is very different, from what I understand, from "helping a professor who is working on a research problem by doing some computations for them" – noobie Mar 4 at 10:08
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    Whats the (big) difference? The computations are still part of the research problem. I do not think you can be a master while skipping the apprentice step. – lalala Mar 4 at 10:15
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    You should not be thinking exclusively about applications. Do you want to do research? Do you think you will learn from working with more senior people? I expect you to get a lot of experience from that, but you may have a better idea of what you will be doing and how helpful it will be to you. – user2316602 Mar 4 at 16:19
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writing dozens of lines of code using Mathematica and helping my professor computing things

That sounds like normal undergraduate research to me. It's probably not a menial contribution. Very few people can write a dozen lines of Mathematica code.

If you do a good job, this could be a big help to your graduate school applications and even later career.

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    Yeah, doesn't really sound like "scut work". Just not "glamorous". :) – paul garrett Mar 3 at 22:14
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    > Very few people can write a dozen lines of Mathematica code. Isn't this a gross understatement? – noobie Mar 4 at 4:12
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    @noobie If you work in a group where everyone uses Mathematica, it might appear that everyone everywhere uses it. In reality, while there are plenty of people who could use it, as AP points out its use is not widespread at all. – awjlogan Mar 4 at 9:40
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    @noobie From my experience in industry, sponsoring university research (at PhD and post doc level), the number of academics who can write good quality and reliable code is zero, to a first order approximation. – alephzero Mar 4 at 12:21
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    @alephzero That said, if that's true (and I don't think it is, personally), it also seems unlikely that noobie would qualify as being able to write code, according to your definition. – xLeitix Mar 4 at 18:15
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If you have holes in your knowledge then a course might be (marginally) better, but any involvement in a research program is a plus. You want to arrange it so that you get an acknowledgement in the paper for your work (assuming co-authorship is impossible). Then it is a line you can put in your CV. I doubt that it would be seen in a negative light, but a formal ack is important. And, if the PI later turns out to be one of your letter writers, perhaps they can mention it also for reinforcement.

Beyond how it looks it is a good thing do do in itself, as it gives you an idea about research "as it is played". Even programming "at the edges" should give you a deeper insight in to the problem at hand. And insight is the real goal.

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    Even if you do not make it as a coauthor to the paper this still can be in the CV as research experience. More so if you do a good job you will have a professor who can write a recommendation letter for your application about real work you did and not only about your lectures or GPA. – JennyH Mar 4 at 8:34
  • "And, if the PI later turns out to be one of your letter writers, perhaps they can mention it also for reinforcement." This should be a when not an if! Working with a professor on an individual basis like this is a perfect and rare opportunity to get a letter of recommendation that speaks directly to your ability to do graduate-level research. – Max Mar 5 at 8:54
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The level of involvement you describe is what admission people will expect when they see that an undergraduate student coauthored a mathematics research paper with a professor. In the rare cases where an undergraduate contributed more significantly, it would be up to the professor to explain this in their letter of recommendation. Thus, there is no reason to feel that you'd be claiming more recognition than you deserve.

Of course, having a publication on your CV makes it a natural topic for questions during admissions interviews. The idea here would be that a curious and smart person will pick up enough about a project they are contributing to to have an engaged conversation about it.

Having contributed to a mathematics research project is a strong plus for a PhD application, because it means that you have at least a faint idea of what mathematics research is, and your decision to engage in more of it is thus better informed. Mathematics research is quite different from learning pre-existing math, and not everyone who enjoys and excells at the latter will also do so for the former.

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I just want to clarify something: writing the code that will solve the problem your professor wants solved should NOT be considered "scut work". This needs to happen anyway regardless of who does it, and is actually a meaningful contribution. This code will most likely be part of the final research document that gets reviewed, and as such can probably be considered a critical part of the paper. It's important that this code does exactly what the algorithm in the paper describes, and being able to correctly transcribe these formulas into Mathematica code shows domain knowledge in both the research domain and Mathematica. This is valuable knowledge for the time when you're doing your own research projects and don't have someone under your tutelage to do this work for you. And who knows, you might be able to suggest improvements to your professor and provide an even more meaningful contribution beyond just converting their work to a computer-readable format.

REAL scut work would be manual data entry: thoughtlessly transcribing thousands of lines of data that were unable to be read in manually for whatever reason, with no domain knowledge required and no option to even consult with the professor for potential ways to optimize things that may or may not be possible and change your contribution to something that rises above menial labor.

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