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I just started my freshman year of high school, and one of the electives I'm taking is a year long research project where we can choose any topic, do an experiment, and write a paper about it. I chose to do a research project with mathematics, specifically a really cool subject called class field theory.

I understand the topic, most of the current papers and literature I've read on it, and I have done an experiment on a certain cause/effect. The problem now is to analyze the data I've gotten and write a paper. It looks really promising, but I will occasionally have questions on certain topics that are really hard to research online. For this, I usually try to contact a researcher who is knowledgeable in the subject I'm researching and just ask if they would be interested in giving some of their time to answer some of my questions.

For example, the way I structured my last email (that spurred this question):

Hello Dr. *****,

My name is *****. I'm 14, and I live in South Carolina. Recently, we were assigned a year-long research project, which I chose to do on Hilbert class fields of global function fields. In one area of my research, I encountered a problem with [short, general topic of problem].

I see that you have taught a lecture on class field theory (including Hilbert and ray class fields). I have studied the lecture notes and it has given me a lot of clarification, but I still have a few questions that I feel most of the resources out there do not address.

I've also read some of your work and it seems right up my alley. I appreciate your concise yet poignant and very understandable way of explaining things. I was wondering if perhaps we could start a short correspondence to help me understand what I'm writing about, and to gain more knowledge of class field theory.

With gratitude, ****

The response I got to this, and unfortunately to the majority of responses I get to similar emails, is condescending in tone and treated me as a child. Of course, I understand this, as I am a child, but in this specific area I would not like to be treated as one. I tried to just not tell my age, and I got much more enthusiastic reactions, but what was suggested to me was to "talk to my advisor" or cited other resources that are not available to me as a highschool student.

Is there something I'm doing wrong in my emails? I've never been part of the whole "academia culture", so this is just me trying my best to sound professional. In any case, what can I include in my correspondence or generally do to be respected as a young researcher?

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    Do you have an advisor? The people you contact seem to help you very well, but it sounds as if your questions can be answered with the material available/published, or they are of 'common knowledge' to people experienced in the field (such as an advisor in normal cases). – Mark Sep 14 '17 at 0:03
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    Too many embellishments and irrelevant information, go straight to the point of your real questions. – Patrick Trentin Sep 14 '17 at 4:22
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    Second of all, if you do end up emailing them, be specific, concise, and to the point. In your case, I would just ask one of the questions, and include a brief explanation of why I think it relates specifically to their research, and give no introduction of myself. Ask a question that can be stated briefly, is closely related to their research, and is most likely to demonstrate sophistication on your part, so that you will build credibility with them and they will be more likely to want to continue the discussion. Then in future emails you can ask more of your questions. – Tom Price Sep 14 '17 at 4:42
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    Why not try reaching out to a grad student instead? In my experience they can be flattered by the attention and are (marginally) less busy than your average professor. – Azor Ahai Sep 14 '17 at 16:09
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    Have you tried asking on mathematics.stackexchange.com ? Always better to ask people who want to answer. – Paul Sep 15 '17 at 11:34
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Researchers tend to be very busy advising their own students, and often don't have much free time to commit to supervising others. Recognize that you are asking someone who is very busy to spend some of their limited time on something that (1) may or may not be interesting to them, (2) is not part of their "official" professional responsibilities, and (3) is likely to take time away from their "official" professional responsibilities. (That is why "talk to your advisor" is a common response; they aren't brushing you off, so much as they are redirecting you to someone who is personally responsible for helping you, and has committed to investing that time in you.)

For this reason, emails to researchers asking questions that they don't feel personally responsible for answering, often go unanswered.

You also wrote that you believe the answers to your questions are not going to be immediately obvious, even to an expert:

I have frequent contact with a professor at my local university, who has taught a class on this subject but has not published any papers or done any research in this area. He and I worked on a few of my questions and were able to solve them, but he couldn't figure out any of my other ones. Although that doesn't preclude "common knowledge to any expert", I am pretty sure it isn't.

which suggests that you are asking for a fairly substantial time investment.

And you are asking for an open-ended commitment in your email:

I was wondering if perhaps we could start a short correspondence to help me understand what I'm writing about, and to gain more knowledge of class field theory.

I would be extremely reluctant to say "Yes" to this without any clue of how advanced you are in the topic, what you are expecting from me, and whether it would be an interesting or useful correspondence for me.

It would, however, be appropriate to send a short, actionable email, on a question that is directly related to the researcher's published papers. For example:

Hello Dr. *****,

My name is *****. I'm 14, and I live in South Carolina. I am working on a research project related to Hilbert class fields of global function fields.

I was wondering if you could answer a question about your paper, [name of paper]. [Specific question that you are looking for an answer to.]

With gratitude, ****

P.S. Would it be OK if I asked some further follow-up questions on this subject?

See

for additional suggestions

For questions that are not related to a specific paper, but are more general questions about the field or your own work (that you and your advisor are unable to answer), I suggest Mathematics Stack Exchange. People are more likely to invest time in answering a stranger's questions for no professional benefit on a platform where that's what they do.

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    Yes, researchers are very busy. In physics, some researchers have been known to ignore emails from graduate students (vs. professors) as a matter of course. – Obie 2.0 Sep 14 '17 at 5:10
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    I'd also leave out the part about the age. (I'm 14..). It does not seem relevant to the rest of the email and could provoke some of the 'condesending' reactions that OP spoke about. – Dylan Meeus Sep 14 '17 at 13:21
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    +1 for suggesting Mathematics Stack Exchange as a better place to ask than a random researcher – Pere Sep 14 '17 at 14:14
  • @Obie2.0 the shock implicit in your use of italics is unwarranted. Some professors have been known to ignore emails from other professors as well, and even from their department chair. But that's simply a sign that they're overworked (and that they're human and sometimes have human flaws just like everyone else). – Dan Romik Sep 14 '17 at 17:57
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    Yes, don't waste an email to ask if you can ask a question! That introduces all kinds of uncertainty. Just ask. – Matthew Leingang Sep 15 '17 at 9:16
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The sentence "I understand the topic, most of the current papers and literature I've read on it, and I have done an experiment on a certain cause/effect." does not inspire confidence. How on earth would one do an "experiment" on a "cause/effect" in class field theory? I'm a professional mathematician who knows something about that subject, and I'm scratching my head right now.

I think you're focused too hard on "respect". I personally don't deal with undergraduate students as equals, and I almost never interact with kids who are younger than that. I think you should dial back on your expectations.

The suggestion that you speak to your mentor (which you've admitted you have) is a good one. While sometimes faculty are willing to answer technical questions from strangers (if they have time and the questions are sufficiently interesting), it is unrealistic to expect them to devote a lot of time to mentoring you. If you've really exhausted the resources available at your school, I would talk to your teachers and the professor who is already mentoring you and ask for introductions to people who could help you. Approaching strangers by email is rarely a useful strategy.

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    "Cause/Effect" is a bad word. I use that term because that's what the project specifications make me frame it as, but it's really just studying maximal unramified extensions of global function fields and how it "affects" a certain space associated with it (because each extension of a function field corresponds to subgroups of the function field that form a cool space with some interesting properties), – TreFox Sep 14 '17 at 1:36
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    @TreFox: OK, that sounds more reasonable. I suggest describing it like that in the future; you are more likely to be taken seriously. – Andy Putman Sep 14 '17 at 1:39
  • And you're right, I'm setting my expectations way too high. Due to my inexperience in academia, I never really considered the pressure and lack of time researchers have. Sadly, I live in a relatively small town where no one in our universitiy's math department can really help me past the basics. – TreFox Sep 14 '17 at 1:40
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    @TreFox: What I suggest then is that you make more of an attempt to learn the kinds of things that your local mathematicians are willing to teach you rather than focus on learning advanced topics. I can't imagine that they are really incapable of teaching you new things (though they may not be the specific things you want to learn). At your age, it is more important for you to develop your mathematical maturity and problem-solving skills than to learn any particular topic (and certainly becoming active in research can wait; that's just not a good use of time at your level). – Andy Putman Sep 14 '17 at 1:51
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    @TreFox There's nothing wrong with setting your expectations high, as long as you accept that high expectations are hard to fulfill. Though this answer is certainly correct in saying that most of the time emailing strangers doesn't work, that's not to say it can't work. I've done it in the past and gotten a ton of "no"s, but also every once in a while a "yes" comes along. – wgrenard Sep 14 '17 at 20:10
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Good luck with your research project, it sounds really cool. I'm a math professor and occasionally get emails from people asking me for help, and in fact recently entered a brief email correspondence with a high school student who asked me some questions. So I think I may be able to offer some useful insights in connection with your question.

Is there something I'm doing wrong in my emails?

No, I think the email is very well written. I can't think of any way it can be improved (except maybe tone down the flattery a bit, but who knows, that might appeal to some recipients). Certainly, as you may already realize, lying about your age or misrepresenting your circumstances to try to get people to give you a more helpful answer than they would be inclined to give otherwise is a very bad idea, and is likely to backfire in some unpleasant and potentially damaging way.

In any case, what can I include in my correspondence or generally do to be respected as a young researcher?

As I said, I can't think of anything else you can do in your correspondence that you're not already doing. But if I'm reading between the lines of your question, I get the sense that you have an expectation that your doing the right thing should somehow guarantee the positive outcome you are wishing for. That is not the case.

Let me explain: the reason professors aren't taking you up on your offer to enter a correspondence has nothing to do with you doing something wrong, and everything to do with the fact that professors are very busy people, who aside from having almost all their professional time occupied with their teaching, research, and other duties that simply cannot be ignored, are also constantly getting bombarded with unsolicited emails from complete strangers asking for advice, help, or trying to interest them in various projects. No matter how exciting or interesting each individual offer is (and trust me, most of them aren't), there simply isn't enough time in the day to give each one the amount of attention it is asking for.

In addition to time being a very scarce resource for a professor -- much more scarce than my 14-year old self could have ever imagined, so I will assume you will find it difficult to imagine as well and hope that you will not find this assumption condescending on my part -- there is also eye strain and physical fatigue to consider. Myself and most of the professors I know spend much too much of our days typing on a keyboard and staring at screens. It is unhealthy and leads to physical discomfort and sometimes pain or even injury, and yet we continue to do it, because (a) much of our work duties that we simply have to do involve those activities; (b) we really enjoy our work and are passionate about it; and (c) after finishing our work we also enjoy doing other things that normal people do on a computer (like facebook, chatting with friends, posting on StackExchange etc).

Now let's go back to your situation. When viewed in the context of what the life of a professor looks like as I described above, do you see how an offer to enter an email correspondence with a 14-year old to help him or her understand an advanced area of mathematics, which is something that would be very difficult to explain even in person to an adult with plenty of background, simply isn't appealing, and is not something that the typical math professor would consider an efficient use of his/her time and other limited resources? It's really not your fault, it's just the way things are.

Let me conclude with some positive advice to offset the somewhat pessimistic opinion above. I think there are in fact plenty of people who would be happy to talk to you in person, at least for a limited time, if you could find an opportunity where you are both physically present in the same place. And moreover in many parts of the U.S. there are all kinds of programs catering to talented youth who are interested in mathematics. I'm not very knowledgeable about this subject (and specifically about South Carolina) so I'll leave it to others to comment about, but generally speaking I think you are on the right track, and in particular the idea of talking to professors at a local university near you, as you seem to already be doing, should be a very good way to help you and connect you with useful resources. Good luck!

3

Your draft dwells on your motivations. Try to appeal to the other person's interests. This is general advice from Dale Cargenie's How to win friends and influence people, a book that helped me.

We assume the professor is proud of their teaching and wants to help students into their field, but is a busy person who can't commit to a ongoing correspondence.

Perhaps

Dear Professor X,

Your lecture notes in super theory were a great help to me—I'd love to take a course of yours in person one day. After re-reading, there's a couple of intricacies that still elude me. No doubt you could explain them clearly.

Can you help?

...

Thank you for reading.

That gives the professor opportunity to confirm their reputation by answering your questions, without committing to an ongoing correspondence. If they don't reply, it must simply be that they are busy.

If you respond gratefully and sincerely "Thank you so much. This helps with my work on Z [now you can mention it]. I appreciate your time", you've built rapport so that you can write to them again in future (perhaps for advice on admissions?). If you bother them too much, they will stop replying.

Best sleep on the message before sending it. In my experience, at the point I finish writing an email to a professor—or just after I send it—I realise my error in understanding!

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    The x-men are real?! – will Sep 14 '17 at 18:46
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I think the main problem is this line:

I was wondering if perhaps we could start a short correspondence to help me understand what I'm writing about, and to gain more knowledge of class field theory.

Despite the word "short", this sounds like a huge endeavor -- I'm happy to send a few one-off answers, but I don't really have time or interest in committing to a lengthy correspondence. It may be better to just put your top 1-2 questions right in the initial letter; this may lead to a correspondence, or he might just answer the initial questions; either way, it's a better outcome.

This line also rubs me the wrong way:

I've also read some of your work and it seems right up my alley. I appreciate your concise yet poignant and very understandable way of explaining things.

This is a bit vague (why is it right up your alley?) -- try citing a particular reason why you chose this professor -- they are very unlikely to reply unless they think that you really need to talk to them in particular, rather than just any math professor (the concise/poignant is a good start, but a technical reason would work better).

Finally, I would be a bit more concise -- in the sciences, brevity is an art form. Maybe something like this:

Dear Dr. *****,

My name is *****. I'm working on a project involving Hilbert class fields of global function fields. In one area of my research, I encountered a problem with [short, general topic of problem].

I read your paper about **** and found it very helpful. I was hoping I could ask you for a few clarifications -- I'm still in high school, so no one at my school really knows anything about this. My main questions are: (1) **** (2) ****

I'd really appreciate any insight or advice. With gratitude, ****

Finally, you will likely have much better luck at local or less well known schools than at "famous" top-10 schools.

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It is somewhat surprising that this is occurring in mathematics, where there are a lot of prodigies running around!

There might be a few things you could do differently in your emails to people working in the field:

  • If you are attending a well-known "magnet" school in math and science, this could be mentioned.
  • You could explain in a bit more detail why you chose your topic.
  • Alternatively, you could explain the problem in a bit more detail.

All of these would be to get the reader to realize that you aren't wasting their time with a "crank" email, but are seriously asking them for assistance.

0
  • Make your enquiries specific, clear, relevant (to the academic's academic research, or to a past publication), and concise. In the subject line of your message, ensure that the nature of your enquiry is clear (e.g.: "[research enquiry] clarification on X in your article '[name of article]'").
  • Ensure your message addresses the academic with appropriate formality: a salutation such as "Hi" or "Hello" is inappropriate; you should use "Dear Prof. [surname]," and close "Yours sincerely".
  • Show the academic that you have already "done your homework" (e.g.: "I have already read A, searched online resource B, but could not find clarification on point X"), and ask him/her whether he/she can point you to any relevant literature you have not already read (explain that you do not JSTOR access &c., but that you are willing to buy a few relevant texts if they are highly recommended).
  • Show the academic that you are genuinely knowledgable and interested in the subject (your credentials, or lack thereof, are less important than tangible engagement in the field: if, for example, you find a mistake in someone's paper, people will take you seriously no matter what your age).
  • It is probably better not to mention that you are minor, although you should acknowledge any limitations in your knowledge of a topic.

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