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I am 19 years old. I was average in high school in Mathematics. I never participated in IMO or related competitions. As a result I didn't join a prestigious undergraduate school. However during 2nd year in abstract algebra courses I developed an obsession for the subject. My advisor told me to look over some graduate level abstract algebra textbooks which I certainly will.

My school can offer me some grad level courses in my fourth year like Class Field Theory and Modular Forms. Nonetheless, not being able to attend a prestigious undergraduate still haunts me. I know it will certainly affect my graduate school admissions.

In the long term, do late bloomers in Mathematics have a chance to pursue good research careers in Mathematics?

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    Forget "prestigious." I came from a relatively new school to one of Texas' best schools. If you can do it, nobody can stop you. – Sean Roberson May 10 '18 at 21:51
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    Late bloomer? You are 19, not 90. Anyway, passion, drive and ability matter far more than age (and the percieved prestige of your current university). – astronat May 10 '18 at 21:53
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    You don’t need to be “amazing” to have a good research career, I think. Maybe if you wanted an amazing career. :) – Obie 2.0 May 10 '18 at 22:08
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    I find that most people don't really know what mathematics "is", at least what it is at a research level, until they've taken some courses like abstract algebra, etc., requiring theorem proving. If you're appreciating it at that level more than you did the more basic levels, this bodes well. – Jair Taylor May 11 '18 at 1:35
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    I was a late bloomer and now I'm a f***ing rockstar. Don't worry. – Glen Pierce May 11 '18 at 5:55
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It is somewhat common to find highly intelligent, promising students that find it difficult to apply themselves in topics they are not interested in. Upon finding that one topic, these people excel quickly because it consumes them. I actually know scientists at top universities that previously flunked out of college for just that reason. So the fact that you’re experiencing this now is not surprising; in fact you’re fortunate that you’re still so young - plenty of time to dive in.

On your less-than-reputable undergrad institution, this may hurt you a bit as names do matter, sadly. Fortunately, if you mean to go academic in life, this is less a problem for undergraduate institution than graduate. So, you should set your sights on a good graduate school and start working on it. The best way to do this is to gain the respect of a professor you know to secure a strong letter and also start reaching out to specific people you’d like to work with. Take a very impassioned, personal approach, and you’ll be given a bit more consideration than the nameless others that apply.

Good luck, future mathematician!

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    "Less than reputable" is stronger than what OP said. Maybe it was an issue with English? – aparente001 May 11 '18 at 3:05
  • @aparente001 fair point. OP merely notes undergrad wasn’t ‘prestigious’. Yet, I stand by my comments irrespective. – HEITZ May 11 '18 at 3:51
  • I'm just recommending that you edit that bit. The answer is otherwise helpful, I think. – aparente001 May 11 '18 at 19:35
  • +1 For LOR. A letter from a respected PI can go a long way. – magu_ Nov 5 '19 at 14:07
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It might be easier to advance well in a more scintillating, rigorous department. But there's a lot to be said for being a big fish in a little pond, for example you might find more personal attention in the little pond. And it's easier to stand out (make a big splash!).

If you want to transfer, in principle, after the sophomore isn't a bad time to do it. But check deadlines carefully.

Will you run out of courses to take at your current college? In some locations, one can take a couple of courses from a nearby more rigorous department or a larger department in the senior year. You might not be able to transfer those credits in; but that might not cause problems if you've collected enough credits at your home institution (without adding in the transfer credits) in order to graduate. If you know that the transfer credits won't be accepted, you might want to save some money by auditing when you register for the summer class(s).

It might be worthwhile to check if your college has a foreign exchange program.

Let's say you finish out the degree where you are, but don't get into the level of program you would like in the first round. In this case, it can be helpful to take some additional classes somewhere with a strong teaching record, as a non-matriculated student, to build up your knowledge and experience.

I can't swear to this in the context of a pure math programs, but in my experience with applying to a top-notch computer science department, the undergraduate institution's name didn't matter. They were looking at the transcript, essay and recommendations. I think for math, the GRE would be on that list as well. If you can get some undergraduate research experience (possibly this coming summer).

Would the delay (compared to your peers) hold you back? Not necessarily. Many people think the undergraduate degree is some kind of race. It isn't.

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I'm training a 19 year old undergraduate at this time. He seems a bit insecure and hesitant because he has an average background, but he keeps up with my assignments, which are quite hard, and has learned a lot of stuff over the few months since we work together. He actually is better at what he does than many graduate students. He has the motivation and the drive and is very curious -- I'd say he's scientist material.

He has to learn one thing: how to tackle complex problems. Once you learn that thing yourself you're out there with the big boys. It's not easy, because complex problems need lots of time, but with proper advise, persistence and motivation you'll get there.

Solving complex research problems involves learning how to simplify them (e.g. divide them in subproblems), how to search for the resources necessary to find solutions to subproblems, how to ask the relevant questions, ignore irrelevant information, be organized, etc. Once you have found your own way to approach such problems, your output and originality will only be limited by how good is your approach and what resources in terms of people, time and money you can access.

Oh, and I'm at a truly disreputable institution and my previous student is now at a very strong school in EU.

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    Nice story -- inspiring. "Disreputable" -- funny! (It has another meaning that you might not have realized. Or maybe you did!) – aparente001 May 11 '18 at 19:37
  • The part about "better at what he does than many graduate students" is the sort of thing I like to see in applications to graduate school. – Andreas Blass May 11 '18 at 23:38
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Not at all. I was just an enthusiast before but am now studying highgrade mathematics. Not to mention it only happened in two years span. I am now 21.

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