Is it possible to be an undergraduate researcher in mathematics?

is it possible to be an undergraduate researcher in mathematics?

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There are three types of students who do research in undergrad

>1. Prodigies who excelled in pretty much every math contest available, maybe completed a bachelor's early, manage to do original research in a field while schools like Harvard, UC Berkeley etc. fight over them. Extremely rare and noteworthy; these students are Fields medal material

>2. Talented students who probably started analysis in high school, attended a great undergrad program and have a very good chance of admission to a top 10 program. Relatively rare when considering the population of mathematicians as a whole, but disproportionately represented in the top ranks of academia. Many will find TT-positions relatively soon after graduation

>3. Reasonably motivated, hard-working undergrads who find a relatively easy problem in an obscure field that requires little background, e.g. combinatorics or group theory. These students tend to do well if they don't burn out in grad school, but finding positions in academia is a crapshoot

For the rest of us, the whole point of a PhD program is to prepare you to do research. Just about any problem that's worth the effort will require a huge amount of background material in a narrow field as well as basic skills across a large swath of mathematics.

I have talked to several math professors at my old school (top 20) who are skeptical about undergad research: unless it's poor research it doesn't hurt, but it's not a necessity to get into a good school like most students think it is.

Anyone can post in Vixra, so if you find an interesting problem that does not appear when you google it then congratulations, you are on your way to becoming a researcher.

Pro tip: In Vixra you can post under a fake name as long as it is not trying to impersonate someone else.

I just want to know what pathway exists for me to pursue research as a career. Im not fond of just putting it as a hobby because of the dedication needed but im afraid of not bejng credible.

The pathway to research is grad school. That is currently your goal. Therefore, do anything you deem necessary to get into grad school and try your best to get into a good school. (Though just getting into any school should be your goal, but optimization is never bad).

So go ask your professors about what is necessary. Remember, all of your professors are PhDs. They lived grad school. They literally know everything. Heck, if you have a professor from a good school ask for his recommendation to that same school.

I hope you have good relations with your professors.

Eh, I would say the quality of undergrad research also heavily depends on the prof/grad students you work under, if they aren't good at mentoring you (don't give you a guide to the research or help you at all with the background material, maybe they'll relegate you to doing bitch work like typing up the latex or making the code to run a minor numerical example, either way at the personal/research level they aren't doing much to help you become a proper researcher), can't find problems that are difficult yet tractable for you skill level/knowledge (this is especially important since by solving problems mostly by yourself you grow immensely as a researcher), don't have the time to properly chat with you so you can develop your own ideas and bounce them off the prof/grad student (I think it's pretty important for undergrads to try having their own ideas for research projects, sure most of the time it's crap but that's not the point, it helps them develop an intuition about what sort of questions are interesting yet solvable and to carve out a path for research), and so on. Even a prodigious student can have their growth stunted and become a relatively mediocre researcher (when an undergrad) if their mentor is shit. Likewise an average yet motivated student can become a great researcher in a heavy field given a mentor who knows what they are doing. At least these are the sorts of things I garnered from my experience, personally I fall somewhere between these two examples, in your criterion I'd likely be somewhere in the second category in terms of talent (maybe on the lower end), but because I have a fantastic mentor that I work with I have my name on a quite a number of papers in good to great journals (I've either been considered a co-author, first author, or second author) with more in prep and several mini projects that'll also likely lead to papers, so I do think talent is only half of what determines the quality of an undergrad researcher.

This is mostly right, but it is possible and there are many examples.

Yes, but I've been told it doesn't matter if the research isn't published or if published, if it isn't published in a top journal.

If you do research and then decide to switch fields, it's as good as not doing research since you have 0 experience in your chosen field.

Only good thing out of research is LoR. Unless you publish in a top journal.

If you want to build a resumé, then yes, you need to be in a journal with a good google scholar rating and get lots of citations.

If you genuinely have something that's an interesting discovery, you could post it almost anywhere and you would be recognized. An open journal is fine too.

Some fields need tons of refereed publications for tenure track. Some need just one to get you started. It really depends.

The proof of the Poincaré conjecture was posted on arXiv.

If you have something of that magnitude, post it on Facebook and you're good.

(((Perelman)))

>it doesn't matter if the research isn't published or if published, if it isn't published in a top journal
This patently false, very few undergrad are publishing the annals or AJM. There are such things are undergrad journals for that very reason, though many undergrad have publications in proper journals as well. An example of undergrads doing good work and publishing in good journals can be found here d.umn.edu/~jgallian/progbib.html (most of these people were admitted into top schools btw). So good (not top) journals are more than enough. I also think you're downplaying the merit of a good honor's thesis.
>get lots of citations
Also wrong, mathematics journals take several months, sometimes over a year to referee a paper, before that time it's likely not getting much attention, even afterwards when people start looking at it it'll usually take a year or two before it gets any citations. Also I think it's wrong to state that
>If you genuinely have something that's an interesting discovery, you could post it almost anywhere and you would be recognized
A lot of times mathematicians will simply ignore you, if you don't already have an established track record then it's very likely whatever you're doing is bs, this is why you work with a prof and get it published or continue in grad school and develop it further. I don't get what you mean by "interesting discovery" though, do you mean something you could base a thesis on? Something that could end up being one or two papers? Something like Tate's thesis that basically revolutionizes a whole field? It's extremely unlikely for an undergrad to come up with option 3 on their own, likely it's 2 or 1 (even then it's rare).

What if I have something on that magnitude and I make a thread here and type out the paper in Latex post by post. Then after I finish I take a screenshot of the thread to submit to 9gag, then I take a screenshot of the 9gag page and then post it in the comments of a Daily Stormer article.

Lets say we are talking about Riemann Hypothesis material here.

>A lot of times mathematicians will simply ignore you
I mean something like Perlman's proof of the Poincare conjecture. He posted it on arxiv. Nobody cares that it wasn't in a top journal.

>Also wrong, mathematics journals take several months, sometimes over a year to referee a paper, before that time it's likely not getting much attention, even afterwards when people start looking at it it'll usually take a year or two before it gets any citations

If you genuinely think that scholars don't obsess over how many times their papers get cited—and worse, if you don't think tenure review boards and grant committees and college administrators don't also—then you are going to have a bad time, mmmkay.

Every journal takes months (at least) to referee and publish papers. That literally doesn't change anything. A never-cited article in a decent journal is almost as bad as never publishing and not as good as 1,000 citations in a second-rate journal.

>I mean something like Perlman's proof of the Poincare conjecture. He posted it on arxiv. Nobody cares that it wasn't in a top journal.
Except it contained a proof of one of the biggest open conjectures by someone who already had a strong tract record (thurston's conjecture wasn't the first open problem he solved). I already stated this, but again, if you don't already have a strong record but decide to post on arxiv it's far less likely anyone will care (do you know how many "proofs" of the riemann hypothesis are on arxiv?) Also whatever you're going to publish is likely not nearly as good as what Perelman did, so I don't think it's fair to say that you could just post your result anywhere.

>If you genuinely think that scholars don't obsess over how many times their papers get cited—and worse, if you don't think tenure review boards and grant committees and college administrators don't also—then you are going to have a bad time, mmmkay.
>That literally doesn't change anything. A never-cited article in a decent journal is almost as bad as never publishing and not as good as 1,000 citations in a second-rate journal.

I was referring to citations with regards to undergrad reearch, which by the time you apply for grad schools will likely have very few, if any of them due to the time it takes for peer review. I am well aware that committees place a great importance on citations but these things don't happen overnight and expecting someone who only has 2-3 years of research to have citations in the double digits is absurd. This is especially true in pure math where it can take up to 2 years to publish a result making the time till you get any citations to be quite long, further you can get tenure without a lot of citation provided the work is strong, but new enough that people haven't published work on it, but plan too. I know this since a grad student who was offered a tenure at a mid tier based on their work (which didn't have a lot of citations)

If you're a math undergrad and you're not in a research group, you're doing it seriously wrong.

Where do I post my research if I'm alone and I don't study in a university?

If you're not affiliated with a university it's likely arxiv will not allow you to post your material there, vixra however will, but...it's vixra...

Yeah, anything else?

Research gate

There's nothing left to research in math. Try again, choose a different path.

what path will let me fuck your mother?