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I am a student of mathematics. I am greatly interested in the subject, but it seems as though my peers opine quite uniformly that I totally lack any sort of talent for it. To give you a few examples:

  • One professor suggested in front of a tutor that I was mentally ill and suggested that I find a psychiatrist
  • Another professor said (while I was standing at the blackboard in front of the entire class) that a five page paper was the upper limit to what I could understand
  • and a third professor said that I was often asking questions that made plain to him that my mathematical ability was rather restricted and that I would one day work in the industry ("You are not the kind of person who would one day win a Fields medal.")

and there were several other such incidents, some of which I may have now forgotten. Nonetheless, my interest in mathematics has led me to consider questions in sieve theory, and I wrote them up and converted them into PDF files.

I sent the first one to a professor, whom I didn't know, but he refused to take a closer look because of what according to him amounted to an "abundance of typographical mistakes" (in all fairness, I have since discovered some). Then I sent it to an appropriate journal (here the Bulletin of the Hellenic Mathematical Society), but this is a normal journal without a fast-track option (at least none that I'm aware of), and judging by the other articles, it takes several months for them to check it.

Now my question is this: Given my extremely bad standing at my maths department (which is thus that even my fellow students fling the door into my face when I visit the department's library), how can I obtain any short-term feedback, preferably from an expert?

EDIT: I have recieved many answers, but some of them seem to be asking for more information. Therefore, let me state these things.

  • I have repeatedly and unsuccessfully tried to call upon the university's institutions, which was mostly being ignored. In fact, these institutions seemed to have been biased against me, stating on one occasion without evidence that I was a liar.
  • I am an outspoken atheist who has made his opinion public on several occasions, including writing an opinion piece in the university's newspaper.
  • I am a member of a centre-left student association that stands for election in the university's parliament.
  • I publicly played the Jazz piano in the old style, which was largely developed by the black population of the United States.
  • The maths department in my university seems to be quite powerful; one of the professors told me at one of the three conversations we had (which were all quite unpleasant) that his salary was so large that discussion among staff about me had resulted in net losses for the university "in the hundreds of thousands".

Let me also, however, take the opportunity to sincerely thank many of you for your feedback. Even though I might certainly argue about some specifics, I had pondered several of your suggestions myself. On occasion, I would, however, be pleased if opinions might be formulated somewhat more diplomatically. I laughed very hard at the reference to the Dunning–Krueger effect. Perhaps you allow me then to cite the Online disinhibition effect.

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    Slightly off topic, but right now my screen is telling me that the question was asked 10 hours ago, and that Ben's answer was posted 11 hours ago. Does Ben have a time machine, or is there another explanation? Nov 14, 2021 at 10:18
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    @AirOfMystery The question was asked twice, the second time with some identifying details removed, and later both were merged by a moderator. Ben had answered the first version before the second was posted, but the timestamp for the merged question is that of the second.
    – GoodDeeds
    Nov 14, 2021 at 15:22
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    Given that the user's real name can be found in the edits (and it's quite clear from the answers that these edits exist, that's how I stumbled across them), could they either be removed completely or possibly the whole question? Especially if you happen to speak the user's native language, they have way too much information out there, and I am not convinced they quite grasp the impact this may have @cag51 (should have tagged a moderator?) Nov 15, 2021 at 22:07
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    can we at least take this off the hot list? Nov 16, 2021 at 1:27
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    Thanks for the suggestion, this question has been removed from the HNQ list.
    – cag51
    Nov 16, 2021 at 2:29

5 Answers 5

101

Your question follows the pattern of a passenger on the Titanic complaining about their dinner being spoiled by the inconvenience of the ship crashing into an iceberg, and asking how they can still enjoy a nice dinner despite this event. In other words, you have a huge problem, and a small problem, with the huge problem causing the small problem. But you are asking us what to do about the small problem, ignoring the much bigger one that is the underlying cause.

In your case, of course, the small problem is the difficulty of getting feedback about your draft articles, and the huge problem is the fact that everyone in your department seems to regard you with complete disdain and refuses to engage with you about mathematics.

The point here is that there may be a solution to the small problem (hire someone to offer you feedback, go to the ship’s kitchen and insist on your right to eat dinner, etc), but the situation you described about your department is a large, burning red flag that’s simply impossible to ignore. If you want to continue on your mathematical journey rather than sink to the bottom of the academic ocean, you will start thinking about how to address that dire situation. (If you want to add some related details to your question, people here might have some suggestions.) Good luck!

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    @AlgebraicsAnonymous If you want an academic career it will be necessary for other people to engage with you (by collaborating with you, hiring you, inviting you to events or institutions etc) but you have described a pattern where everyone who one would expect to work with you has treated you very negatively. Without understanding why, it is very plausible that the same will happen everywhere you go, which means any attempt at a career will go absolutely nowhere. Whether or not you care about the personal relationships, this seems like a big problem.
    – dbmag9
    Nov 14, 2021 at 9:55
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    @AlgebraicsAnonymous the fact that you care little for being completely isolated from your peers and mentors is surely a part of the problem, and a big reason for how you ended up in this predicament. Someone who cares more would have taken action to correct the situation long before reaching the current state of affairs.
    – Dan Romik
    Nov 14, 2021 at 15:57
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    @AlgebraicsAnonymous: when I was at high school and attended university lectures ... completing half a degree ... the university staff behaved most kindly and respectfully towards me --- As someone who essentially completed a degree in a similar manner (courses for major, not including numerous required electives in other subjects), I feel confident in saying that the attitude displayed would be much more charitable when you were in high school than in graduate school. Nov 14, 2021 at 17:26
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    @AlgebraicsAnonymous At the cost of saying something unwelcome, let me mention that if one wants to have a career in math, one needs the strong support of one's peers. It's not just that your peers need not to hinder you - they need to actively support you and want you succeed. The academic job market is ruthless, and even with strong letters of recommendation and publication record it's hard to get job. Burning bridges in the way you seem to be glibly doing is likely to essentially block your future career. Nov 14, 2021 at 20:33
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    @AlgebraicsAnonymous "I have done no such thing." - which thing? You have apparently done some things that make everyone around you dislike you. The only common factor in all your relationships is you.
    – user253751
    Nov 15, 2021 at 10:50
74

I briefly looked at your papers (linked from a previous version). I am an analytic number theorist who has written and published on sieve theory.

Your work appears technically competent, but I was unable to tell what your goals were, what you achieved, or what the relationship to other work is. It seems that you have interesting ideas but did not manage to frame them in a way that others can easily understand. If I had been the referee asked by the Bulletin of the Hellenic Mathematical Society, this is what my referee report would say.

If you want feedback, then in the long run you will need to adapt your presentation to what others expect. This is frustrating and painful, and these expectations can seem inconsistent and arbitrary. But it is probably the only way to persuade others to engage with your work.

Alternatively, you could happily work alone and not seek feedback. Creative work has intrinsic value, even if you produce it only for yourself.

Good luck!

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    The flip side of working alone without feedback is that it will make impossible to have a career doing math (which I assume is the asker's goal). For good or ill communicating one's idea is the majority of a mathematician's work. Nov 14, 2021 at 14:23
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    Tell that to Newton.
    – SeanJ
    Nov 16, 2021 at 0:40
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    @SeanJ Newton had a reputation for being hard to work with, but he nevertheless corresponded widely with other eminent minds, networked effectively enough to be a fellow of Trinity College, Master of the Royal Mint, an MP(!), President of the Royal Society, had close friends (en.wikipedia.org/wiki/Nicolas_Fatio_de_Duillier) and collaborators (en.wikipedia.org/wiki/Roger_Cotes) to pick a few examples.
    – dbmag9
    Nov 16, 2021 at 10:14
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The fundamental question, here, is why is your department so antagonistic towards you? This is important, not just because it's the "bigger problem" as Dan Romik noted in his answer, but also because the answer changes the answer to your question.

Here are a few possible "bigger problem" explanations, and the resulting answer to your question for each case:


1. You have upset someone in the department with a lot of sway with the rest of the department, who has since spread rumours, etc, about you.

In this case, your first course of action is to reach out to the appropriate anti-bullying body within your institution. Such behaviour is unacceptable, no matter how egregious your action may have been against that person, and the behaviour of the other members of the department are similarly unacceptable. If what you did to upset the person was a real problem, then they should have similarly reported you to that body, not initiated a campaign to destroy you. And if the cause of the upset was completely innocent and minor, then all the more reason to report the situation to the appropriate body.

Once the bullying is addressed, either people begin treating you with basic respect again or you seek to move to a new institution, where the well hasn't been figuratively poisoned. Continuing at an institution in which nobody respects you is not a viable approach, no matter how self-reliant and insular you may want to be.

2. Your own behaviour is causing general upset within the department.

Contrary to the first possibility, this one is indicative of a problem with how you are engaging with the department. In effect, where in case 1 the well is being poisoned by a professor or other person with sway, in this case you are poisoning it yourself (likely without even realising it). If this is the case, there is no realistic method to "get" people to examine your work, etc, without first addressing what it is that you are doing to repel them.

In this case, complaining to an anti-bullying body, or changing institutions, is unlikely to change your experience, at least in the longer term - the same issues that have arisen at your present department will simply reoccur, and this will cause further issues. Even paying people to review your work is likely to only work in the short term, as you will get a reputation quite quickly.

Instead, you need to undertake some self-reflection, to identify what it is that people are responding so badly to. Perhaps you are unconsciously injecting arrogant language into your interactions, or being too flippant to other people when they speak about anything other than your work. Or perhaps you are handling criticism poorly, coming across as defensive and aggressive when people point out flaws. There are many other possible issues, and it is unlikely that anyone here can diagnose the issue - that said, if there is someone who is a little less antagonistic towards you within the department, you could approach them and ask for their perspective.

3. You have misinterpreted signals from those around you.

Sometimes what people say can be misinterpreted. For example, the first professor you mention may have been expressing concern about something, and honestly recommending that you seek mental health support - this is a taboo topic in many places, but there is no shame in seeking such support. And if you are already feeling a lot of anxiety and discomfort about interactions, it can come across as an accusation, rather than an attempt at support.

Similarly, the second professor might have been expressing that you had some weaknesses in your current understanding, and that you were not yet ready for the more complex arguments that are often found in particularly long proofs, etc. This may have been meant as a simple critique, but for a person with anxiety, for example, it can come across as an attack. And the third professor, as noted by astronat in the comments to your question, may have simply been trying to manage expectations - few people get fields medals, and that doesn't mean their contributions aren't worthy.

In this case, I would strongly recommend seeking the mental health support noted earlier. Again, there's nothing to be ashamed of, and seeing a psychiatrist or psychologist doesn't mean you are crazy or unbalanced. Mental health professionals are much like physical health professionals - they treat a wide variety of issues, many of which are quite common and can become debilitating if not kept in check.

In the meantime, self-reflection is again on the cards. Why are people refusing to help you, if there isn't an antagonism issue within the department? The answer to that question will tell you what to do.

4. Their criticisms are sincere and honest.

This is the hardest one for you to contemplate, but it is worth bringing up as a possibility. You may be showing substantial misunderstandings of basic concepts. Note that this doesn't excuse them calling you out publicly, or telling you that it's intrinsic to you (rather than simply being the current state of affairs), but it is still worth considering for yourself.

This could overlap with case 2, in that the Dunning-Kruger effect could be impacting your response to their criticisms. If you do have a fundamental misunderstanding of something key to your field, then it can be hard for you to see it, and hard to accept when someone tells you that you are wrong, because you lack the expertise necessary to understand their criticisms.

This often leads to crank-like behaviour, which can put off those around you as they view you as nothing but a crank. It is not uncommon for people in academia to become extremely wary of cranks, and disengage as quickly as possible. Unfortunately, this then drives those who are simply a little misguided towards crankism.

This, also, will require some self-reflection, but in a different way. Look back at some of the criticism you have received in the past - which portions of the criticism did you accept, and which portions did you reject? Is it possible that the portions you rejected were actually of value? You likely know more now than you did at the time - you may notice that you had rejected criticisms that you now can tell are legitimate.

In this case, your best way forward is to approach someone who may still be a little amenable, and apologise for previous behaviour - then, instead of asking them to review your work, ask for their help with filling gaps in your understanding, using the work to help guide that process.

5. Discrimination is at play.

It saddens me that I need to include this one, but even in academia in 2021, discrimination can be an issue. Are you black in an otherwise-white department? Or white in an otherwise-black department? Are you female, and the professors, etc, are not? Do you identify as trans? Are you vocally atheist or religious? Many of these things can influence how you are treated, sadly.

But keep in mind, this is a two-way possibility. You might be the one discriminating, and they're simply responding. You need to consider this possibility alongside the reverse.

If you are in a department with a discrimination problem, you could try approaching the appropriate discrimination body within the institution, or seek a role in a different institution that you have checked for better diversity. If you are the one discriminating, of course, you should (and I know this keeps coming up) undertake some self-reflection. Either way, the discrimination needs to be addressed before you will be able to get others around you to take your work seriously.


This is not an exhaustive list, but I believe it captures the most likely cases. You will notice that self-reflection is a common thread for most of the cases - this is because of the maxim that "if everyone around you is the problem, maybe you're the problem". I do not provide this as a criticism, but simply a reason why self-reflection may be needed - the only way to tell whether or not you are the source of your own woes is to undertake some self-reflection. And the result of that self-reflection tells you what you need to do.

In any case, as Dan Romik said in his answer, ignoring the bigger issue won't get you anywhere. It might give you a momentary short-term result, but you'll end up right back where you started in short order.

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    This seems to be the most painstakingly compiled, helpful answer in a collection of helpful answers. +1. Nov 15, 2021 at 14:29
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    Honestly, I would believe if it began with 2, moved to 4, 3 on all parties, then 5 and lastly 1. The question reads like there more to the story and this answer hits several good points to consider. As I believe all of these points come into play to some degree at some point over the years it took to get here.
    – David S
    Nov 15, 2021 at 16:29
  • Hello there and thanks for the long and well thought-out answer, which, as I believe, is also one thing I very much appreciate: Diplomatically formulated towards me. I do however want to point out this: That I might have upset people without intending to, or that perhaps my actions were misinterpreted, with intent or no. Nov 16, 2021 at 9:59
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    @AlgebraicsAnonymous Regarding your actions being misinterpreted, to copy AirOfMystery's comment from another chain: "You're writing (and possibly behaving) in a way that makes misunderstandings more likely." If you want to avoid your actions being misinterpreted, then this is something you need to address. Nov 16, 2021 at 11:27
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    @AlgebraicsAnonymous - that would be under case 2. I have no doubt, given how you've described the situation in your question, that you aren't intending to cause upset. However, this is true of most cases in which people upset others. But this is why self-reflection is needed - you need to understand what you're doing that is causing upset, and seek to adjust your approach to reduce it. This doesn't mean fundamentally changing yourself, but adapting to circumstance. One thing to ask is whether you filter your thoughts before expressing them. It's a common source of this kind of problem.
    – Glen O
    Nov 17, 2021 at 1:50
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OK,I'll give you some feedback right now. I'm not an expert in your field at all, but based on the first two pages of "Some asymptotic laws in the theory of primes" I can say the following:

  1. In footnote 1, you say you're using a non-standard name for something, implying that you know better than established experts in the field. This comes across as arrogant.
  2. You mention what I assume is a standard reference in your field, telling us that reading it "might obscure one's understanding". Despite this, you go on to cite the same reference again.
  3. Generally, your writing style contains features I wouldn't expect to see in academic or professional writing, such as the phrase "not really" and the word "NOT" in capital letters.

If you were an established expert with a good publication record, people might forgive some eccentricities and a certain attitude, or even be amused by these things. (I remember reading a paper by Abhyankar and being shocked by his informal, almost flippant writing style. But of course he was already quite famous before he wrote that paper.)

But you say you're a student. Graduate study is not just about technical expertise. It also includes learning how to fit in as a member of an academic community. You need to spend some time learning the community norms and establishing a reputation before others will tolerate behaviour that they perceive as eccentric.

Of course I'm writing this based on just a few minutes of reading your work, never having met you in person. I don't know whether your conversational style or other aspects of your behaviour give the same impression as your writing. If you can give us some more information here, then you might get some more useful answers. Are you currently enrolled as a graduate or undergraduate student? Have you had the chance to attend any conferences, or mingle with other mathematicians outside your institution? Have you been "in bad standing" from the first day you joined your department, or has this changed over time?

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    @AlgebraicsAnonymous But this is a paper on ResearchGate, which has no such requirement. Also, writing in two columns is highly non-standard in mathematics, and simply screams "not familiar with math writing". Nov 14, 2021 at 13:04
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    @AlgebraicsAnonymous it seems to me you have much more to gain from taking AirOfMystery’s general feedback at face value (or that of any of the answerers) than by arguing about the details in comments. However, you have chosen the latter. You give the impression you are unwilling or unable to accept and process feedback because of this and because you have disagreed with and argued against most provided answers, always evading the larger issue (the “huge problem” as Dan Romik calls it). If you give the same impression in person, that might explain the lack of feedback from your environment.
    – 11684
    Nov 14, 2021 at 13:37
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    @AlgebraicsAnonymous No, it doesn’t. However, which feedback of all the feedback provided to you on this page by people who are kindly trying to help you are you going to take to heart and turn into action? Your comment reads as though you are going to ignore my feedback as well - which is your right of course. The fact that you don’t know how this impression arose is kind of the point; it is hard to tell what impression one makes oneself and I’m trying to help you by holding up a figurative mirror.
    – 11684
    Nov 14, 2021 at 13:57
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    @AlgebraicsAnonymous For another piece of non-standard format, you reference Ramanujan using the Hindi alphabet. If someone wants to look this up, they need to copy and paste it, if they cannot read the Hindi alphabet. Unfortunately, even with your paper, copying the name (for me) results in "DZीƒनवास रामानूजन", so someone who wants to find it is out of luck. Transliterate everything into the alphabet you are using to write your paper in (that is not to say that you cannot keep the original alphabets, too). Nov 14, 2021 at 18:35
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    @Džuris My impression is that mathematical writing is usually formal, precise and succinct, which are three fine things to strive for in a text. The phrase "not really" is not formal, not precise, and can often be replaced by the more succinct "not" (as in this case). Nov 15, 2021 at 10:01
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... but this is a normal journal without a fast-track option ... and judging by the other articles, it takes several months for them to check it.

Given the circumstances you have outlined, waiting the standard period for a referee review does not seem like a terrible delay. If you are a graduate research student then you should have an assigned supervisor who will review your work as part of their supervisory role. If you don't have a supervisor (which I assume is the case) then your options are more limited. If you have the money to spare you could pay someone to review your work for you or try to find a volunteer; otherwise you may have to wait for the standard peer review period at the journal.

If you are not having any luck with your professors, you could try forming a study group with some of the other students. Ideally, if you could get some graduate research students interested, you might be able to form a group of people who are willing to do preliminary reviews on each other's work. This is not particularly easy to organise if you don't already have a good relationship with the other students, but it might be worth a shot. You should bear in mind that even PhD students are not proper experts, but they may know enough to look for preliminary issues in a manuscript and "interrogate" some of the reasoning.

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  • I have tried to obtain a supervisor, but my ideas were discarded, and frankly, devalued each time. In fact, more often than not I was ridiculed by the professor whom I asked. Nov 13, 2021 at 22:44
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    Note that if the work is really terrible, it won't take months for them to send a rejection. And, paid consultants set their own prices.
    – Buffy
    Nov 13, 2021 at 22:47
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    The trick here might be a to ask your interlocutors for more constructive feedback on your work. Devaluing your ideas is itself a form of feedback, but it is not particularly helpful. Follow up by asking for details on what the reviewer identifies as the deficiencies in your work. Let them know that you are open to hearing the critical feedback on your paper, but would like some more detailed constructive criticism.
    – Ben
    Nov 13, 2021 at 22:52
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    I agree with your recent comment, but it seems this has gone on too long for much to happen that is constructive. That isn't entirely due to the OP's action, I suspect, but can't really say from this distance.
    – Buffy
    Nov 13, 2021 at 23:00
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    @AlgebraicsAnonymous "How is such a deal struck?" Usually, a business approaches the university (or department within the university) and requests to hire one or more of the professors as consultants for a particular task. "What would be a reasonable price?" Thousands of dollars, usually, for a small task like this one. Millions of dollars for a long-term research project.
    – nick012000
    Nov 15, 2021 at 7:01

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