Discussion section for MO question 16587

This post is up for anybody wanting to constructively discuss MO question 16587 (please read it first if you come from somewhere else).

Remember, we all love maths and science :-) the aim is only to discuss efficient ways to teach them…

To sum up:

I’ve made the assumption that the main reason that very few scientifically-enclined people of age 16-20 do research is not that they are “less intelligent” than at say age 25, it is that simply they didn’t have the time to learn all the background.

So the question: could it be that with a bit more focuss on a topic, i.e.  basically an earlier start than today just for that topic, we could see more youngsters doing real research at age 20?

Of course the key point in this proposal is to organize at the beginning a one-week or two-week panorama of science and maths, with lots of interactive presentations of scientists in the classroom and labs.   That would give the youngsters a basic but wide scientific world-view, and offer them a real choice.

And of course they would still follow other courses to learn other topics, just as today, but they would learn them a bit slower.

But all this is open to discussion…

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9 Responses to “Discussion section for MO question 16587”

  1. Akhil Mathew Says:

    I think the RSI program (which I mentioned in the thread) fits pretty much everything you just mentioned! PROMYS, Ross, Mathcamp, etc. do to a slightly lesser extent, I think (though this is not to disparage them, since they have different aims). Also, REUs are an example, no?

    • Thomas Sauvaget Says:

      Yeah, thanks for the reply, I gave you reps for your answer. By the way, just had a quick look at your blog, it’s great especially as a high-schooler. I guess you’re a good example of what I’m suggesting, that it’s possible to focus to get farther a bit earlier than usual at that age. Keep it up!

  2. Akhil Mathew Says:

    Thanks! Your blog looks interesting too.

  3. Qiaochu Yuan Says:

    I don’t think that students should have to choose what to specialize in so early. My own mathematical interests have been constantly shifting for the last several years as I’ve acquired more background. Not that it’s a bad idea to enrich the standard experience – as I mentioned in the question I’ve had the privilege of enjoying several such enrichment experiences which have strongly influenced my mathematical development. But students should always have the freedom to do something else.

    I also have to challenge one of your assumptions. It seems to me that an important component of mathematical research is having the emotional maturity and patience to not be frustrated when you don’t make immediate progress. The human brain does not fully mature until age 25 or so, and I think this is an important difference between a bright high-schooler and a grad student: in other words, I think that emotional maturity is just as important a component of research success as background or baseline intelligence. There are plenty of smart people who aren’t cut out for research, and it would be cruel to try to lead them down a path that will ultimately make them unhappy.

    • Thomas Sauvaget Says:

      Qiaochu, thanks for commenting. Yes, of course interests evolve, but that in fact is true all life long… So to actually do some research one has to take the decision to stop and become a specialist on a narrow subject just for a while, before again moving on. And indeed, most researchers switch fields during their career at least once, some quite often. But of course freedom is essential, if the student loses interest on the topic then fair enough, I wouldn’t force them to stick with it for 4 years!

      About maturity, you’re right that one is wiser at 25 than at 17, but those are the two extremes. In the curriculum I had imagined, students would get to a nowadays-grad-student level of maturity at around 20, not at 17 when the topic is first started.

  4. Is early specialization good? « Delta Epsilons Says:

    [...] on MO on whether specializing early is a good thing.  It got into an interesting discussion, which continues on his blog.  I have placed some of my own thoughts there, so I won’t ramble [...]

  5. srivatsan Says:

    As someone in grad school in the US, i honestly believe that specialization is too early even for beginning graduates. Infact, i also think undergraduation is too early to choose a major. I would advocate especially at undergrad to take courses from as many different sciences as possible. If in the process, you happen to encounter a problem for which you potentially see a solution for further research, well and good; but i dont think its wise going out to find a problem to research/to specialize because you think you need to do it. Wasnt it Robert heinlein who said ‘ specialization is for insects’!!

  6. Woett Says:

    As a 20-year old who already knows for a few years what he wants (doing research in elementary number theory) but is kind of frustrated that he isn’t able to do so, because there is no such thing as early specialization, I can only agree. I know that a lot of students have no clue what they want after grad school, so the way it’s arranged nowadays isn’t necessarily bad, but it would be cool to have some options.

  7. What about a Galois Prize for young European mathematicians ? « episodic thoughts Says:

    [...] have noticed, and also have been told, that there are, in the USA, several great programs designed to mentor students interested by doing [...]

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