Fast Food Research?

I recently got a new job — to coordinate math students at RSI (Research Science Institute). RSI provides a one-month research experience based at MIT for high school juniors. The program is highly competitive and kids from all over the world apply for it.

Before the program started, I asked around among mathematicians for advice on how to do a great job with these talented kids. I was surprised by the conflicting opinions on the value of the program. I thought you’d be interested in hearing those opinions, although I confess that I do not remember who said what, or anyone’s exact words. I will just repeat the gist of it.

Former participants:

  • I went there, it was awesome.
  • I went there, it was underwhelming.
  • Canada/USA math camp is more fun for sure.
  • RSI is an absolutely fantastic experience for students, and I think the adults who take part enjoy it very much as well.

Potential participants:

  • Cool, if I get there I’ll try to prove the Riemann Hypothesis.
  • Last year Eric Larsen won $100,000 as a result of this program. If twenty math students participate, then the expected return is $5,000 per one month of work — not bad for a high-schooler.
  • MIT is my dream school; just to be there will be inspiring.
  • I will prove the Riemann Hypothesis.
  • Yeah, I can become famous.
  • Cool, I want to be a mathematician — I should try this.
  • I love Canada/USA math camp and I’d rather go there.

Grad students, former and potential mentors:

  • My professor doesn’t have a good problem for me. If he gives a nice problem to a high school student, that will be unfair.
  • It’s just a job.
  • What if I solve the problem first, do I keep silent? — That doesn’t make any sense.
  • What if this high school student is better than me? That would be a bummer.
  • This job was a lot of fun; I enjoyed it.
  • I used to participate in RSI myself, and that was great. Now I would like to be on the giving side.
  • RSI teaches students how to get versed in impressing people. For the Meet-Your-Mentor Night the students showed up in suits. How many real mathematicians do you know that own a suit?

Professors on the program in general:

  • Usually students study mathematics for many years. RSI allows them to actually do mathematics.
  • I studied for many years before I could start to do research. This RSI experiment is degrading to mathematics and disrespectful to mathematicians.
  • Most students are wired towards problem solving, and very often they need only one basic idea and 15 minutes to solve a problem. Research has a completely different pace; it is important that kids try it.
  • Some students go to this program because they want to win competitions and get to good colleges. These goals should be secondary. We should accept students because they want to try research.
  • One month for research? Is this a joke? Do you like fast food?
  • These are the best students from around the country. It feels nice when a potential future Fields medalist looks up to you.
  • These students might be better than average undergraduate students at MIT. It might be fun to work with them.
  • I think that the number of students who might be a good fit for such a program is very small; the number of professors who might be a good fit is very small too. If this program grows it might become completely useless.
  • High school students are being mentored by grad students, who themselves have just started their own research. Grad students do not have enough experience to really guide people through research.
  • It is such a great opportunity to get a taste of research while you are in high school.
  • People usually choose projects for their research. These kids are given projects: this is not research — it’s slave labor.
  • One month is not enough for interesting research. It would be good if students use this month to jump-start some research and then continue it after the program.
  • It’s a waste of time to learn mathematics for many years and then discover that you do not like research. This program gives an opportunity for students to decide whether they are interested in research very early in their lives. This is tremendously useful.

I asked some math professors to suggest problems for these students:

  • I have some problems I can give, but they require deep knowledge of topology. The students would need to take some courses to understand the second paragraph of the paper I would give them, which they can’t succeed in doing in a month. Can we replace this program with my course?
  • It wouldn’t be nice to give them a problem that is too difficult. If the problem is easy, then I usually have an idea how to solve it. Instead of wasting two hours describing an easy problem to students, I can use this time to solve it myself.
  • Ask Ira Gessel or Pavel Etingof. I have heard that they generate problems faster than their graduate students solve them.
  • I have some leftover problems I can give away. However my concern is this: what if they solve it or mostly solve it, but then go back to school without writing their paper. What do I do? Giving the same problem to someone else or writing a paper myself without mentioning the student would not be kosher. Writing a joint paper for them is a burden. I need to think about a leftover problem I do not care about.
  • If I have a good project, I will give it to my graduate students. Why would I invest in a high school student who is here for a month and probably is not ready for this anyway?
  • That’s great, the online database of integer sequences contains tons of conjectures. They even have an index pointing towards “Conjectured sequences” and towards “Unsolved problems”. Besides, you can search the database for the words “conjecture”, “apparently” or “appears”. There is also an article by Ralf Stephan describing 100 conjectures from the OEIS.
  • I have some things I need to calculate, but I do not know programming. If someone can do this for me that would be good.
  • They usually want to submit papers for competitions, which means they do not want me to be a coauthor. I do not have problems I just want to throw away.
  • Richard Stanley keeps a list of unsolved problems, ask him.
  • There is a list of unsolved problems on wiki, but they are too difficult.
  • They can always try to find a different proof for something.

The 2009 RSI has just begun. We have awesome students, great mentors and quite interesting problems to solve. I am positive we’ll prove the negativists wrong.

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10 Comments

  1. misha:

    Interesting…, btw, generator should be generate.

  2. Tanya Khovanova:

    Misha,

    Thank you, I fixed it.

  3. Maria Roginskaya:

    If you want it to be a fair imitation of research you might ask them to come up with their own questions, and then try to modify it so that the project be of a proper size and then redirect them to the mentor who is in the close area. I had a similar course (for our curtailed program for school teachers, who also don’t know any advanced mathematics), and this can give a good result if you can “think on your feet” which must be exactly your style. (You also have to be aware about the qualifications of your pool of supervisors and stir out from the blank areas.)

    Unfortunately those programs often are organized in the way that students are invited to choose a project from the list, so that the projects have to be formulated in advance. The disadvantage is that then the participants have to be explained the project afterwards and it is often not what they thought it was when they have choosen it (and it alway take more time to start on the project which is handed to them).

  4. Maria Roginskaya:

    Just as a reflection on the mentor who was worrying to solve the problem before students: One should just forget the own solution (and don’t try to hint to it, as the students may find a different one).

    As we all do Mathematics on different levels it may well happen that you encount a collegue whos cherished research question you can solve on a glance. My own policy is that if I think the person be in my “weight” as a researcher I suggest a collaboration, if not (which by default is the case between a supervisor and a student) I leave them alone and don’t say anything. I assume most of the collegues which can solve on a glance my problems have the same courtesy.

    I don’t think of it as a luck of respect, as people may not seeing the short way because they pursue a different route, which may have own advantages (even if one learn a lot of facts which doesn’t relate to the problem one still becomes an expert of something and can contribute to the mathematical community as such).

    It is also somewhat self-serving policy, as when one claims a fact as proven, one gets a certain obligation to write it down (because we never know what may be of use for other people, and nobody writes down facts proven by other people). Now, if you will write down everything which you can prove in five minutes, you will finish spending 99 percent of you time (which you can spend on research) in the tedious writing. Even if one leaves aside the matter of having fun, isn’t it better to write one paper which will impress people insteed for a dozen of a weaker ones (which would leave the impression that you cann’t do better)?

  5. misha:

    Maria Roginskaya wrote:

    As we all do Mathematics on different levels it may well happen that you encount a colleague whose cherished research question you can solve at a glance. My own policy is that if I think the person be in my “weight” as a researcher I suggest a collaboration, if not (which by default is the case between a supervisor and a student), I leave them alone and don’t say anything.

    I find this attitude somewhat strange, don’t you want your students to learn something new every now and then?

    She continues:

    I assume most of the colleagues which can solve at a glance my problems have the same courtesy.

    This one is even stranger, don’t you want to learn something new from your colleagues every now and then?

  6. Boris:

    I participated in RSI and some of the other camps as a student, and I have been back to RSI as staff. I found these comments very interesting; thank you for collecting them.

  7. Maria Roginskaya:

    misha: I don’t mean just any problem – there is a lot of interesting things one can learn if one (often aimlessly) discusses Mathematics. What I have written is applicable to “pet problems”, i.e. something one works on closely (and is likely to make a progress on). I know, a lot of people will not anounce a result if they know that a graduate student have something similar in a pipe-line, so I don’t find it strange (just extending the same principle to everybody else).

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  9. Tanya Khovanova:

    I would like to clarify that I wasn’t hired by RSI, but rather by math department at MIT to do this job.

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