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I am a high school student who is interested in mathematics. As such I have been emailing several professors from prominent universities. I have been running into trouble when trying to figure out what their research is from their websites (it's either way too specific and jargon-filled, or so general I can't find anything good to ask them.) Would it be a good idea to just plainly say: "I see you research 'area in math.' Would you mind telling me what specifically your research entails?"?

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    What's your end goal in emailing these professors? – Santiago Canez Apr 17 '16 at 1:25
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    Did you try to read some of their papers? If you cannot understand a single word of those than you probably do not have yet the knowledge necessary to even comprehend what their research is about (which is probably normal for an high school student vs mathematics research) so you are only bothering them. – Bakuriu Apr 17 '16 at 10:53
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    + Santiago Canez My goal is to see if they have any recommendations on resources (books, websites, etc.) where I can learn what they are researching about. – Conan G. Apr 17 '16 at 16:07
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    ConanG, sending professors whose work you do not yet understand blind emails is not a good strategy to learn about what mathematicians do. I would recommend taking a phrase near something that looks interesting, and googling it to see if you can find a more accessible resource. Then ask a pointed question not to a professor directly, but at a forum (or similar) where you know people are looking to help you learn math, like on math.stackexchange.com . – Mark S. Apr 17 '16 at 18:46
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I advise you to put yourself in the shoes of the professors reading your emails. Why would they answer you? What's in it for them? They explain mathematics for a living, so your request is a bit like asking a barber you aren't friends with to cut your hair for free.

It's great that you want to learn about math research, but with due respect, you can't understand the specifics of most math research. Not because you aren't smart enough, but because it's written in a language that takes years to learn. It is (or can be) possible to communicate some of the ideas behind a piece of research math to nonexperts, but this is a difficult thing to do, and most researchers aren't inclined to try. This is unfortunate, and it would be nice if there were more resources out there for laymen who want to get a sense of what math research is all about, but emailing professors out of the blue is not the way to go about this.

  • TBH, I'd answer it. – Ave Apr 17 '16 at 9:13
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    "They explain mathematics for a living, so your request is a bit like asking a barber you aren't friends with to cut your hair for free." I think this is a terrible analogy. Professors are supposed to be educators, and part of the mission of a university is to educate the public. If your reaction to an ignorant but genuinely-interested townie is, "What, you want to know things for free?" then a university is the wrong place to work. – Namey Apr 18 '16 at 5:50
  • @ardaozkal I'd also put it on my TODO list. The thing is, it will have such a low priority chances are it will never get answered. – Davidmh Apr 18 '16 at 10:39
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    @Namey If the townie has done their homework enough to ask a substantive question, that's a different story. If no effort went into asking the question, I see no point in putting effort into answering it. – user37208 Apr 18 '16 at 17:34
  • @user37208 I think it is sometimes hard to tell if someone has tried to do homework and failed, versus made no effort at all. Unless the email seems to be downright spam, I will usually at least respond quickly and politely with a link to my website and maybe to one of my overview articles/resources and encourage them to read up on those topics. It's quicker than needing to try to tell the difference, also. If it happened a lot, I'd probably just keep a form-email on hand to paste in and amend if needed. – Namey Apr 18 '16 at 19:40
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Some professors are open to interested/enthusiastic students. However, they are busy people. If you want them to spend their time with you, you have to give them a starting point that gives them something specific to start from, not some generic "tell me what you do".

Better to check out what you would be interested in (e.g. robotics, quantum physics, topology, or whatever), read up on that, and then find a friendly lecturer at a local college who covers that material. If there are none, then you could contact a prof, but be specific with your question, and do not waste their time.

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    As part of the reading, aim to learn enough of the jargon to understand some of the websites. – Patricia Shanahan Apr 17 '16 at 0:13
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    +1. The correct order is (1) learn to understand what the academics (doesn't always have to be professors) are writing (or a sufficient part of it to contribute) and (2) contact them; not the other way round. Good benchmarks: Are you able to find typos in their formulas? Are you able to ask concrete questions (i.e., "I don't understand this particular 'obvious' implication", not "I don't see the forest for the trees")? – darij grinberg Apr 17 '16 at 0:30
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    @darijgrinberg Well, if mathematicians would have to explain all "obvious implications", they would be busy a looong time. My experience is that "obvious" implications can vary from "correct, but you figure it out how I got to that and if you don't, you do not deserve to understand", via "correct, but I am too lazy to write/think out the details" or "I thought it's correct, but, ok, add required uncritical technical assumptions to make it work" to "Oops. I thought it would work, but actually it doesn't. Hmm.". – Captain Emacs Apr 17 '16 at 11:03
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    That's why I said "particular". Not "I don't understand any single sentence in the paper.". – darij grinberg Apr 17 '16 at 11:15
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With a little bit of poking around the Internet, you can find videos of lectures given by prominent mathematicians freely available online. For example, here is a video of Manjul Bhargava giving his Fields Medal lecture, where he gave an explanation of his work to a general mathematical audience. As another example, the Arizona Winter School is an instructional conference for graduate students, and they have posted videos of all their lectures for a long time. Most of them are quite good.

If you just want to get an idea of what leading researchers are working on, I think that watching videos might be more enlightening (and more entertaining) than trying to read papers.

In general, please don't send unsolicited e-mails to professors -- especially if you are choosing the recipients because they (or their universities) are famous. If you develop a particular interest in, and some understanding of, a subject area in contemporary research, then it may become okay to send unsolicited e-mails in certain circumstances. Also, if you want to seek a research mentor from a local university, then e-mails might get a positive response, especially if this university is not famous, and/or if you have a math teacher who is willing to write first and say you are exceptionally talented.

One famous mathematician told me that he gets a huge number of e-mails such as yours. He feels bad ignoring them, but he gets so many that if he tried to answer all of them it would leave him no time for research.

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As a suggestion, when it comes to math, I would highly advise looking up other resources. A few things I could recommend:

  1. Slide decks: How they communicate their work to peers. Or, even better, the slide decks that they use to present their work to grant sponsors who aren't necessarily experts in their field.
  2. Websites: These should summarize their goals and general field of work, and should also be more accessible.
  3. MS Student Theses: Masters' theses from their students will often be more accessible, since they often cover a lot of background that established experts take for granted and don't bother covering in much detail. Or, in other words, they're worse papers, but the redundant/useless information could be useful to you.
  4. Wikis: Honestly, lots of commonly-used advanced math (at least for stats and machine learning) is on the web. While it won't show you the novel aspects that a given professor is working on, it will help fill in the baseline information. Otherwise, it would be like asking a professor who designs steering wheels what he does, but without even knowing about the existence of cars.
  5. MOOCs: Try out EdX or other free online courses that are for introductions to advanced math that are interesting. Some of these are geared very much toward people in your position.

These are often vastly more accessible than the published papers, which tend to be for a narrow audience. For example, during grad school I once leafed through an optimization algorithm paper off and on for a few days to grasp the novelty of the approach. After a bit, I finally figured out from the math and supporting papers that the prior approach used a shrinking n-dimensional ellipse, while the new one was a shrinking rectangle. Which was not stated outright in the text anywhere in the ~15 page manuscript. A single slide with 2D or 3D depiction of each approach would have made the concept very clear.

Finally, it seems like you would be much better off looking into high-school research experiences where you'd visit a lab for a few weeks. This would give you a much better idea about what to pay attention to. MOOCs are also an option for this.

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    Regarding #1: mathematicians almost never give slide presentations to grant sponsors. – Tom Church Apr 18 '16 at 22:55
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    Regarding #4: Wikipedia is a surprisingly good resource for math, from undergraduate material through graduate topics and beyond. I regularly use it to learn new mathematics. (I'm a math professor.) – Tom Church Apr 18 '16 at 22:58
  • @TomChurch Then how do your sponsors ever communicate their findings to anyone above them? ;) Which is a non-trivial question, because other than organizations like the NSF which have very rigid and reliable funding structures, (most?) other funding sources (defense, congressional, state, corporate) often involve different research topics competing for a shared pool of funding. So successful or particularly interesting research is often briefed up the chain, to ensure that whole topics of research are grown or maintained each year. – Namey Apr 30 '16 at 22:35
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  1. Have a look at the chair's web site. The textual content is often outdated, but the list of publications is usually very up-to-date. You can also use academic search engines, such as citeseer or Google Scholar, to search for that professor's name. The abstracts and introductions of papers usually detail the field of research.

  2. If available, you can also read the list of supervised student theses. These are frequently about current research topics at that chair.

  3. Look at lecture material, slides and scripts, if they put it online. Lectures are often about the fundamentals of the research field of that chair. This way it is easier to judge whether you have the necessary foundation to understand the research topics.

  4. If you can visit that university without too much hassle and have the time, you could also just visit a lecture by that professor. This makes it way easier to get in contact in person.

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