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Premise: I originally asked this on MathOverflow, but it was pointed out to me that it could be better fit for Academia Stack Exchange.

Note: I have received extremely varied advice on the following matter by various students slightly older than me, so I post the question here in the hope to get an objective 'technical take' from experienced researchers.

Assuming that there are several topics which are equally attractive to me and that the prospective advisors are all established researchers in their fields and "nice people", are there any objective circumstances that I should take into consideration when searching for a topic for an undergraduate research project (clearly, this question naturally generalize to the choice of Ph.D. dissertation topics and general research advice, about which, if you please, you are free to elaborate) to maximize my chances of making an "optimal choice" (e.g., in terms of mathematical results achieved, possibility of getting a good recommendation afterwards, personal growth, etc.)? Clearly, referring to research papers in mathematical education that partially support your remarks will be highly appreciated (although it is not necessary).


Side note: Just to clarify a little further: I've only said that the mathematical aspects and the advisors are equal to me, and what I'm asking is what else I should take into account when choosing a research area.

  • I understand the scare quotes around "objective circumstances", but why around "researcher" and "research topic"? – Trevor Wilson Feb 7 '15 at 0:01
  • As explained here, this site is meant for questions about graduate and post-graduate academia, not undergraduate. So it is actually more appropriate to ask about what you mention in your remark. Perhaps you want to edit your question. It would also be good if you elaborate on "optimal choice." What are your goals? Optimal for what? – Kimball Feb 7 '15 at 3:28
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    You cannot maximize your chance of making an optimal choice. Your chances of making an optimal choice are zero, because there is no optimal choice. – JeffE Feb 7 '15 at 3:43
  • How young is that researcher? Bachelors students, masters students, PhD students, Postdocs and assistant professors may all be young researchers. – Enthusiastic Engineer Feb 7 '15 at 7:43
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    I guess you got an idea of what I meant. — I understood exactly what you meant; my response stands. Every choice involves tradeoffs. – JeffE Feb 7 '15 at 17:40
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There is no "optimal coice". Getting "good" results, and recommendations does certainly not only depend on the choice of the topic, but more on yourself and your motivation. And that is the point. If all possibilities seem to be equal I would apply for the group in which I feel most welcome. It is so important to be in an environment in which you are allowed and encouraged to fail often (and early); where people leave titles at the door; where you can build on ideas of others and people dare to be wild and have fun !

Forget the results and, the recommendation afterwards. Do what you like to do, together with people you like and the results will be good automatically. You will find opportunities for future projects you never thought of yet. And to be honest, I do not think an undergraduate research project will change your life. Explore your style of work, your weak and strong sides and be open for ideas. I would not expect too much at this stage ("in terms of mathematical results achieved").

OK, that was a statement based on my personal opinion, but it is based on my personal experience as a PhD.

  • +1. I'd make a slightly stronger statement for the OP: pick the project working on which you'd enjoy most. – just-learning Feb 8 '15 at 10:21
  • Thank you for your suggestion. However, as I said, the people and the topics are equally interesting, so I was looking for some other points to take into account before making a decision. – user23758 Feb 8 '15 at 13:53
  • Use the numismatic determination principle (flip a coin) – Moritz Feb 8 '15 at 13:59
  • Funny. But really doesn't help. – user23758 Feb 9 '15 at 13:34
  • @Dal What do you expect? You're basically asking, "If I have X perfectly equally attractive options in all the dimensions that matter, which one should I pick?" – Roger Fan Feb 9 '15 at 16:15
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By far, the largest determinant of success is a person's personal interest and dedication in a subject. If there are several subjects that equally interest them, they are probably equally likely to succeed in any of them. Now, there are things that happen with "hot subjects" and "bubble bursts," and so on, but it's very hard to predict what will be going on in five to ten years from the beginning of a Ph.D. program. If you pick subject A over subject B for such a reason, then you are likely to be disappointed, and to have a lower chance of success because you haven't followed your heart.

Now, there is one major exception to this, and that is if you want to work outside of your home country and your field interacts with national strategic interests. For example, if you are an Iranian student in the United States and you want to study nuclear technology, then you are likely to come under close government scrutiny even as a graduate student and there will be many jobs that are simply unavailable to you unless you become a citizen. It is possible for this to go the other way as well: you may find yourself with some difficulty moving your work abroad from a country if it is considered sensitive. This can affect some unexpected areas: see, for example, the battles over cryptography in the 1990s.

So, in short: if you want to change nations, it's much easier if you stay away from anything that the military or intelligence communities care too much about. Other than that, follow your heart.

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