How do I get a fellow mathematician to examine my work when I have a bad standing in my home department?

Question

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.

Answer 1

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!

Answer 2

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!

Answer 3

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:

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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.

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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.

Answer 4

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?

Answer 5

... 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.