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I'm currently a first-year Ph.D Student. My field is applied mathematics. Thankfully, I was able to publish my first paper. In our institution, students usually spend two years before having their first article published.

I heard from one of my colleagues, that his supervisor, a professor of pure mathematics in our department told him that that my field of research is "easy" and that literally anyone can have as many papers as they want published.

This isn't the first time I've heard this being said by this professor, and frankly it's beginning to bother me. Especially since I spend so much time and effort in my work. Don't get me wrong, I love my field, but I can't control the way this makes me feel, especially that having this information around the department and in conferences is not a good thing, since academics, other than the ones working in the same area, and especially pure mathematicians in our department, tend to believe whatever they hear, especially when it comes from a colleague-professor. I'm thinking of talking to the professor, in a conference or if I have the occasion, and try to have a conversation with them in the subject and why not convince them that this is not the case.

Is this the right way to deal with this problem?

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    Let's just say that I am a pure mathematician, and I feel more competent to evaluate the research of philosophers and music theorists (okay I have an undergraduate degree in music and and advanced undergraduate coursework in philosophy) than I do to evaluate the research of someone doing mathematical modelling (which I have never ever studied). Feb 4, 2023 at 21:28
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    This just sounds like academic equivalent of ''locker room talk'' or ''trash talk'' to me, I would ignore and just work on what you want to work on.
    – Tom
    Feb 5, 2023 at 15:34
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    Anyone reminded of the way Sheldon (a theoretical physcist) would frequently disparage his engineer friends on The Big Bang Theory? These types of rivalries between theoretical and applied fields are common.
    – Barmar
    Feb 5, 2023 at 20:29
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    Related XKCD Feb 6, 2023 at 11:40
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    Also I just want to add that sometimes this stuff is just there to ''lighten the mood'' and get people on your side, like I remember reading in Asimov's autobiography how he would sit with editors at lunchtime and they would all whine about how stupid writers were, but really it was a kind of bonding exercise. Similarly, it's hard to get a generic pure math talk these days without the speaker throwing in some reference about how dumb physicists/engineers/applied mathematicians are to get a few laughs.
    – Tom
    Feb 6, 2023 at 18:42

5 Answers 5

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The level of difficulty of your work does not imply its value

You don't need to do anything here at all --- just keep researching in your field and publish papers that advance knowledge in that field. Take solace in the fact that the labour theory of value is false, so the value of your research is not determined by the ease with which one can produce papers in that field. If this professor is correct in his evaluation then that just means that there is an unmined area of research where progress and publication of results can be made with relative ease. That is all the more reason that researchers should pursue this area of research, not a reason to ignore it. Since you are just starting out, you should trust that the peer review system in your field will operate appropriately, and if you have a paper accepted for publication then that will generally mean that it is contributing something valueable, irrespective of how easy it was to do the work and get the paper accepted.

As a secondary point to put you at ease, you needn't worry about whether you are as good a mathematician as a senior professor, or working on problems that are as hard as those done by a senior professor, when you are only a first-year PhD student. I'll save you the suspense --- you're not. It is perfectly reasonable for you to do research in this field of interest to you, learn that field, and then move on to other work later in your career in the natural way that research interests evolve over time. You will probably find that, after a decade or two, you will have some good research experience across several areas of mathematics and you will have encountered problems of varying levels of complexity.

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    First, not all papers are equal. Ease of producing papers just means standards for what counts as one paper are different - doesn't mean the field is easier/harder/more valuable/less valuable. Second, in pure mathematics, or in the arts, or in much of the humanities, there is negligible practical value, and most value is aesthetic. Difficulty can certain be part of an aesthetic measure (cf. musical virtuosos), and then a certain version of the labor theory of value comes into play. Of course all of this is irrelevant to the original question. Feb 5, 2023 at 1:02
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    This answer would be improved without the frankly irrelevant reference to the labour theory of value. The professor in question isn't employing the labour theory of value or any related fallacy. Feb 5, 2023 at 3:50
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    @SriotchilismO'Zaic Given how modern economists can not agree on what the words in LTV even mean (especially "value"!), it is indeed a can of worms best left alone.
    – Lodinn
    Feb 5, 2023 at 8:48
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    Imho this answer basically proves that ops problem exists. You believed the professor over op even though he's not even here.
    – DonQuiKong
    Feb 5, 2023 at 9:19
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    I'm going to keep the reference to LTV for now, but I've changed the heading. OP reports that the remark was that his field is easy and anyone can publish papers. To the extent that this is a criticism of working in that field, it does sound to me like it is invoking the idea that if an academic subject is easy then its value is diminished (which is a manifestation of LTV).
    – Ben
    Feb 5, 2023 at 21:12
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My advice is to ignore them and do your own work with supportive faculty. It is a common enough feeling among pure mathematicians (my field) that applied math is somehow "less" than pure math rather than different. The goals and techniques of applied math are not the same so they can't really be compared in that way.

A professor of, say, anthropology could make the same comments and they wouldn't bother you, I'd guess, though a conversation with them might be more fun and you'd learn something, perhaps.

But, you aren't going to convince them. The problem is that they haven't tried it and, perhaps, don't care a lot about applications, or the "real world" in general as a subject of research. Let it go.

My dissertation was so esoteric that I figured it would never be applied to anything useful. Beautiful and fun, but not useful outside pure math. It took about 40 years IIRC to be proven wrong.

As a student you are unlikely to have any positive impact and an argument with a professor isn't a good start to a career. Let the faculty argue amongst themselves about such things.

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I am currently doing my Ph.D. in pure Mathematics and I have frequently heard from professors of pure Mathematics that few fields (not all) in applied mathematics, as well as pure mathematics, are comparatively easy for publishing papers. So, based on that they have formulated their opinions. So, I would simply suggest you stay away from negative comments and look for positive criticism from colleagues. Also, focus on well being of yourself, your work and prioritize your mental peace.

I would also like to share quite opposite experience. I was asked about the impact factor of the journal that I recently published in by an applied mathematics professor and it was around 0.9 since we have journals with less IF compared to applied mathematics journals. They said that since I was at an early stage of my research that it was okay to publish in such journals but try to publish at better places in the near future, say for example in journals with an Impact Factor of more than 3. I was a little bit uncomfortable and try to explain to them that there are not many such journals in my field but they were quite adamant. So, I was a little confused and had a talk with my supervisor who cheered me up and explained to me how there are differences in the ranking of journals field-wise.

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    say for example in journals with an Impact Factor of more than 3 --- Anyone even remotely informed in the mathematical sciences should know better. Indeed, just a few moments of looking over a list of IF's (e.g. see here) clearly shows that such a restriction pretty much excludes virtually all pure mathematics journals. In fact, even a requirement of at least 2 excludes the vast majority, and also includes a few that are not all that highly regarded, so both false negative and false positive aspects are quite large. Feb 4, 2023 at 21:20
  • @DaveLRenfro I tried to explain the same to the professor, but they felt that I was giving excuses. Their work is in applied mathematics but they publish most of their work in multidisciplinary journals as they have high impact factors and they have very little to no knowledge of pure mathematics journals. Now, I am not bothered as that was at an early stage of my research days and now I know better. I had to deal with them as I need their signature in my progress report as they were on my research committee.
    – Hap
    Feb 4, 2023 at 21:46
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    For what it's worth, I was trying to say in a somewhat indirect way (but all that veiled) that you need not worry about what the person said as they're obviously poorly informed about the matter. (And I realize that now you are not worried, although I didn't originally know how long ago this was -- apparently at least a year or two, given your comment.) Of course, needing this person's signature, and perhaps an even more explicit endorsement of your potential, you definitely don't want to convey this impression of how uninformed they are! Feb 4, 2023 at 21:57
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    Yuck! What I wrote yesterday should have been "... I was trying to say in a somewhat indirect way (but not all that veiled) ..." (word "not" was accidentally not included). Feb 5, 2023 at 22:16
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Looking at this from a slightly different angle, you said

I can't control the way this makes me feel

In every field of human experience, the single biggest lesson that any therapist can help their clients absorb is that this statement is wrong and dangerous.

Everyone who is not a sociopath has imposter syndrome to some extent, because everyone devalues their own skills to some extent. (That's not exaggeration, by the way - this is literally part of how sociopathy is defined and recognised.) So the fact you're experiencing this makes you normal. The problem then is that regardless of this being normal, it's unhealthy for you.

You can't control what other people say or think. To some extent you might be able to guide them in other directions, if you have the energy and willpower and they're receptive to it. If you're in a context where there are defined behavioural rules and they go so far as to break them, you can ask other people to intervene. But if you don't or they aren't, you simply can't change what they do.

The lesson from therapists is learning how to put aside criticism from people who don't matter. Does this person's opinion truly matter? Answer: no, not really, because you don't have to work with them. And anyone you do have to work with will be valuing your skills over his. It's not easy to do, because humans aren't wired that way. We're not cats. But it's a key mental health skill.

For myself, I'm an engineer. We've recently had to solve some problems with improving linearity fit methods to position measurements. We needed to work with someone with mad skills in applied maths for this, because they needed to appreciate that this was solving a real problem, with real data which contains errors. We didn't want a theoretician.

The professor is right that you can publish as many papers in applied maths as you want. Where he's wrong is thinking that it's easy. The reason you can publish so many papers is that there are so many real applications which would benefit from your skills, and they aren't easy because otherwise they'd already be solved!

Sure, maybe a purist can look down on this. But at the end of the day, you will have done something that makes a difference somewhere. Can he say the same? Or is he just jealous of the fact that he can't, and putting you down through his own imposter syndrome?

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Don't get me wrong, I love my field, but I can't control the way this makes me feel, especially that having this information around the department and in conferences is not a good thing, since academics, other than the ones working in the same area, and especially pure mathematicians in our department, tend to believe whatever they hear, especially when it comes from a colleague-professor.

There is a lot in this sentence and between its lines.

Looks like you - and your pure math colleague, possible his professor too - haven't really yet made that mental and emotional shift to a graduate school mode of thinking about your work.

Grad school isn't about competing with other PhDs in your school not those in other schools. Grad school is about simply trying to advance your own and the world's knowledge of math in a single application of interest from where you were yesterday.

So:

  1. Stop preening yourself - privately or publicly - on getting a first paper a year ahead of most others. This is just a bit of luck on your part - maybe your area is topical at present, maybe you have a respected supervisor, maybe there was a lull on submissions, etc. If you make odious comparisons, you invite others (and their supervisors) to wait in the long grass for you. Just look at how Dr Jack Welch (3 year PhD, chem eng, steam condensation, Urbana-Champaign 1959) turned out . . . You don't want to be like him, I take it.

  2. Stop using nearby colleagues' apparent progress as a gauge for your own or as emotional/social goalposts: it's time for you to start to build a circle of purely socially friendly acquaintances outside your own school for relaxation, a game of squash, a hike or whatever. We all need external human supports and we all have a desire to support/nurture others in the same way.

  3. Under no circumstances bar abuse of other people before your own eyes should you challenge a member of academic staff. If the mutterings - and make sure they are real, not imagined - get to a crazy point then you go to your supervisor and leave it with him.

  4. Whether as a result of parental/teacher influence, our own inhibitions or just popular culture, we often tend to think that our human worthiness in personal relationships is reflected by our career progress. Of course this is nonsense - but it is a nonsense that takes a bit of determination to refute. It wouldn't be out of order for you to start looking at the faces in the city crowd once in a while and testing your conviction - as a person, not as an ace researcher - in yourself.

Incidentally, I personally believe it's fair to say that pure math is more challenging conceptually than applied is; and this may have implications for the difficulty of publishing papers. Then again, many pure mathematicians may not be stimulated by the human benefits of applying existing concepts in the industry, medicine, social sciences, etc.

Yet, as Buffy alludes, all pure math tends to find application within a generation of its discovery. So pure and applied math need each other for justification and advancement. In such a situation relations between people involved in these respective fields need to have (and sincerely show) more appreciation of the other's challenge.

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  • +1 for the paragraph about not preening one's self. When OP wrote that "students usually spend two years before having their first article published." I was thinking the same thing. However about Jack Welch, "When Welch retired from GE, he received a severance payment of $417 million, the largest such payment in business history up to that point.[1] In 2006, Welch's net worth was estimated at $720 million". Why don't we want to end up like him?
    – Nik
    Feb 5, 2023 at 15:48
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    Because Welch had no consistent management vision, advanced by continually playing up to seniors' desire for bottom lines and turned one of the US's greatest industrial companies into a finance house. Even his anointed successor, Immelt, now sees the lasting damage done by him. His personal life was equally wrecked.
    – Trunk
    Feb 5, 2023 at 16:16
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    @user1271772 Search for why his nickname is Neutron Jack
    – M.Viking
    Feb 7, 2023 at 16:18

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