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I am trying to find a professor to do my first research under his/her supervision. I am a high school student. However I have already self-studied all the BSc and MSc (Pure Mathematics) books [based on Melbourne Uni]. But I haven't done any research and I need to have some professor to help me to choose a topic, access to non-free-papers, publishing, etc. Most probably I won't need for the learning part, i.e. to ask professor on more understanding the texts (i.e., tutoring). Although not asking for teaching Mathematics to me may result in much less taking professor's time compared to professor's student, but professor prefers to not spend on someone off the street asked him/her to do research with.

I already have asked two professors to do research under their supervisions and in reply I have been rejected, saying "I would prefer to supervise my students" or similar, (one was just yesterday).

I am interested in doing research on Real Analysis and I know there might be some other professors to be interested in guiding me even a lot but they are not specialized on Real Analysis.

I should also add here what I am saying when approaching:

  1. As I quickly rejected in the first try by emailing, I decided to go to a professor's office in person with no previous meeting time; the result was a bit better in the beginning but no success.

  2. I speak: "As I found Mathematics the most supreme beauty, a true Paradise, I started and committed to Mathematics. I had a consecutive study plan and I have studied ... [name of books]. As I was keen to have a big impact on Mathematics, so I decided to analyze books (like what a critic does with a paper to publish) rather than studying. I know that I need a lot to learn before doing research (which I don't know what to study next) and afterwards I don't know how to proceed in research. It would be a great honor if you please help me in my journey..."

My questions are: What's wrong with my actions and speaking? and, what should I say or do in order to 'win' a professor's heart?

PS - I took your kind and helpful advises in the other question, and I decided not to be isolated from 'the system'. However, it's not that easy to find my way on my own. By the way, I truly appreciate for all your guidance.

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    Professional and academic networks are complicated things. People know people who know people... When you approach the teachers, phrase it as asking them for advice and help. Also, don't be impatient. You may need to work with one of them for weeks or months to convince them of your ability, before they will bet their network reputation on you. – Patricia Shanahan Jun 13 '15 at 15:53
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    Also, I see a lot about what you have read, but not much about what you have written. Writing mathematical proofs is a skill that needs practice. I do hope you are doing the exercises in the books, and writing out the proofs, even if you have nobody to check them. – Patricia Shanahan Jun 13 '15 at 17:18
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    In all honesty, "the most supreme beauty, a true Paradise" ...makes me really want to stop reading. – Mehrdad Jun 14 '15 at 9:45
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    I'd also recommend against opening with the beauty of mathematics. One reason is that it's trite. This is the one thing every pure mathematician believes, and you wouldn't be seeking this opportunity if you didn't agree, so saying it explicitly adds nothing. It can actually give the wrong impression: some people like talking about the beauty of mathematics more than they like actually doing mathematics, and others feel a need to say something but can't think of anything substantive to say. You don't want the reader's first reaction to be wondering whether you fall into one of these categories. – Anonymous Mathematician Jun 15 '15 at 5:15
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    @MKR maybe I am not a real scientist, but "the most supreme beauty, a true Paradise" is something that I would advise my students to NEVER say. – StrongBad Jun 15 '15 at 9:00
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+50

As I found Mathematics the most supreme beauty, a true Paradise, I started and committed to Mathematics. [...] As I was keen to have a big impact on Mathematics, [...]

This is quite off-putting. What you say here is essentially that you want to be a great mathematician. Since there is no a priori reason to assume that you are better than many other students the professor you address has, such a statement is a little presumptuous.

I had a consecutive study plan and I have studied ... [name of books].

This is good. You give a more or less objective description of your abilities and show that you actually have done serious work.

What's missing is a description of your actual interests. If you say you are interested in mathematics or real analysis, you essentially say that you have not found something that really intrigues you. As research is largely internally motivated, this is not a good sign. Note that I do not say that you have no special interests, but that what you write in your question and what you state as your approach to a professor says so.

So a letter which should attract the attention of a professional mathematician could be the following:

I am (description + why you have no direct contact person).

I have read the following books.

I am fascinated by (special topic), because (honest reason). In particular, I would like to understand (something you are really interested in).

Can you recommend me further directions for my studies, e.g. textbooks dealing with (whatever)?

If you get a reaction like "read XYZ", and after half a year you pose a question which shows that you have worked through this book, you will probably be taken seriously.

  • +1. Thank you very much esp. for your first paragraph (excluding beauty of Mathematics as off-putting). – MKR Jun 15 '15 at 2:52
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    @MKR - You really should listen to the recurring advice here: your flowery spiel about the beauty of mathematics is not going to help you open any doors, and it's quite likely to elicit some eye-rolls during an introduction where your audience is probably guessing you're out of your league. If you want to prattle on about the "true Paradise" of mathematics, save your eloquence for when your work is underway and you've established some credibility. As a footnote, if you want to cement a professor's disinterest in working with you, simply exhibit an inability to listen – that'll do the trick. – J.R. Jun 15 '15 at 10:02
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    I would argue strongly against "I have read the following books.", as opposed to focusing on the specific technical topics that you find interesting. Focus on the substance, not on the packaging. (And especially, as others have said, leave the flowers at home.) – JeffE Jun 15 '15 at 15:32
  • What do you mean by "why you have no direct contact person"? Sorry, I didn't understand that at all! Thank you. – MKR Jun 16 '15 at 10:50
  • @MKR: The professor will ask himself is "Why do you ask me?", and he is looking for an honest answer. So "Because you are famous" is not the right thing to say. "A student/a friend/someone else told me about you" would be good, if it was true, but "because I have noone else to turn to" is probably the right thing to say. In a face-to-face this is probably not an issue, as the professor already knows your name and your basic situation. – Jan-Christoph Schlage-Puchta Jun 16 '15 at 14:37
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What's wrong with my actions and speaking?

Nothing's wrong with your actions, although they are not likely to lead to success. As for your speaking, the paragraph you quote is not ideal, but I don't think that's why you are getting turned down. Instead, the problem is that the system is just not set up to provide research mentors for high school students. I regularly turn down requests for high school research supervision, for several reasons:

  1. Like many faculty at research universities, I have more local students who would like to work with me than I have time to supervise. This is particularly true for undergraduate research, and I end up turning away many undergraduates because of a lack of time. The ones I end up working with typically have very strong backgrounds, and I'd be reluctant to turn more of them away to free up time to supervise high school students.

  2. It's much easier to vet local students. If they have never taken any of my classes, I can ask my colleagues about them. By contrast, it's much harder to evaluate high school students. It's already difficult to quickly gauge mathematical talent and background, and that's not even enough: I'd also want to know how hard working someone is, how overcommitted they are with other activities, etc.

  3. I don't think high school research is particularly important, and I question whether it's even worthwhile. For the vast majority of high school students (even ones who are exceptionally talented), spending a few more years studying the mathematics that's already known is at least as worthwhile as doing research. The number of people who have genuinely reached the stage where they should be doing research, but who are not yet prepared to go to college, is minuscule. By contrast, there are lots of people whose main motivation seems to be that doing research at a young age looks impressive, and I'm not eager to encourage this.

Of course not everyone will share these reasons, but I think they are reasonably widespread. To maximize your chances of success, you should keep these issues in mind.

The most straightforward one to address is how to evaluate your background and talents. You need external evidence, such as a letter of recommendation from a faculty member, ideally combined with some feedback and advice. You could try taking an advanced course at a local university, or attending a summer math program for high school students. Another possibility is strong performance on a math contest. (That's less meaningful, since it measures only a limited form of talent and doesn't come with feedback/advice, but participating in a contest is less expensive than taking a course.)

It's worth applying to research programs specifically aimed at high school students, such as RSI. There aren't very many of them, and they don't admit many people, so you may not have any luck with this. If you target individual faculty members, you may have better luck if you choose people who have supervised high school students in the past, since you know they are in principle open to the possibility. (You can sometimes tell this from their web sites or CVs.) Faculty members at schools that don't have particularly strong undergraduates may be more excited by the idea of working with a great high school student, while faculty at Princeton have plenty of top undergraduates to work with.

If your search for a research supervisor works out, that's great. But if it doesn't, you shouldn't worry that it's a negative judgment of you. You're trying to do something the world basically isn't set up to facilitate.

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    +1 for point 3, I cannot agree more. There is so much left to study still - the only reason why people seem to be doing this is because they have heard that it looks impressive to do research at that age (which does not make sense at all). – dreamer Jun 14 '15 at 8:55
  • @Anonymous Mathematician: Is it alright that at the beginning I don't talk about my original intention, i.e. to do a research under supervision of some professor, but I just ask to attend him/her classes then after a while I ask for doing a research? (By "alright" I mean: 1- more effective, and 2- ethical). Thank you. – MKR Jun 16 '15 at 5:32
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    That sounds reasonable to me, assuming you are genuinely interested in attending the class and wouldn't just quit if the professor later declined to supervise a research project. I don't know how likely it is to lead to a research project, but it is worth doing in its own right (the class could be valuable either way) and taking the class will give the professor more insight into your background and talents (which could increase the chances of supervising a research project). – Anonymous Mathematician Jun 16 '15 at 15:14
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It does not sound as though you are supplying any evidence of your ability beyond your own claims. You need to fix that.

I suggest working on your relationship with the teachers, especially the mathematics and science teachers, at your high school. A letter from one of them saying they have a brilliant student who needs more challenge then they can give might work better.

What grades are you getting? If not straight A, what can you do to change that? The most efficient use of the time in high school is to first learn the material it is supposed to teach, so you already have that before going to university.

If straight A, try asking your mathematics teacher for more difficult assignments. Would one of your teachers be able and willing to grade exercises from the textbooks you have been reading? That would give the best cross-check that you really are understanding the material, as well as giving them objective evidence of your ability that they could use in a letter of recommendation.

A letter from a teacher saying "MKR has correctly completed exercises from each chapter of books X, Y, and Z. Here is a sample of MKR's mathematical proof writing." would be far more impressive than your claim to have read books X, Y, and Z.

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    +1 for a letter from a current teacher who knows your potential – Luigi Jun 13 '15 at 17:15
  • Trying to find connections through teachers didn't help a lot, as I was expected. But I will get some letter from a math teacher as he promised to write it later, and thank you very much for your informative advice. I find a very nice guy doing his PhD who already helped me a lot and would like to guide me more. – MKR Jun 15 '15 at 2:31
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    @MKR I certainly did not expect it to produce results within hours or days, rather than weeks or months. – Patricia Shanahan Jun 15 '15 at 13:16
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As a math professor, I also find your intro a bit off putting. You need to sound more serious - if you are.

I would start with: "Hi. I'm a high school student. I read ... and ... and got interested in ... I tend to be attracted by combinatorics/geometry/algebra... especially ....

Could you suggest something I could read and study, and maybe some interesting problems I should look at?

  • Thank you very much for very helpful advice. Though short but I believe it should be enough and more effective than my talk. I will remember that. – MKR Jun 16 '15 at 4:33
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There's two colleges near me I do not attend. I've just walked right up to professors, talked to them for a few hours fine. I've even been engaged in research projects, while both not their student, and not attend the college. In many ways, this question is a lot like asking how you get anyones attention; productive talking is effective.

There are things to keep in mind of course:

  • Talking to random professors or about random subjects is not going to go over particularly well. One personal example I have is I deliberately sought out a professor of mathematics, to discuss something mathematical; keep it relevant.
  • Trying to get their attention at bad times is not going to work; learn their schedule and find a time that works. Even better if you can set up an appointment (emails works, in-person has a nice touch).
  • Don't demand. You have no idea how often I've seen this, even from students. It doesn't go over well. Ever!

Good luck!

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Here are a few ideas to get you unstuck.

  1. Start by identifying a university in your area with the right sort of department. Study the professors' web pages to identify people who seem nice, and whose research fields intrigue you. Take a look at some of their papers. Find out if they have regular office hours. You might need to phone the department for this last step. Then take one of your favorite books with you, and go to the person's office to have a chat!

  2. Attend some seminars either in your desired topic or in a nearby topic, and sit in on some university lectures. Approach the speaker, or someone else in the audience, afterwards, and talk about what you found intriguing, and ask a question. If the conversation goes well, lay the groundwork to continue contact with the person -- ask if you may follow up with an email for some advising.

  3. Make an appointment to speak with an advisor.

Note, in all of the above, just be yourself. You need not blow a bugle announcing your age or your current educational level. You can share all of that later, once you have established a human connection with someone.

Comment to some of the others who have participated in this question: a bit of social awkwardness is not as much of a hindrance in mathematics as it might be in some fields. Also, please take into account that English has lots of variants in different parts of the world. So please don't be so critical of the OP.

  • Thank you very much for your very informative advice. And I think attending in a seminar is an effective way to 'build a network'. – MKR Jun 15 '15 at 13:00

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