The mathematical internet is a great opportunity to promote yourself, but be polite!

I just posted this over on a discussion thread at meta.MO, and I thought it might deserve more visibility.

We’ve had some questions on meta.MO about how undergraduates applying to graduate school should view a presence on Mathoverflow, math.SE or in the math blogosphere. I was on the graduate admissions committee for the University of Michigan last year so, for what it is worth, here is my take:

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What are the downsides of the arXiv?

The title above was a recent (somewhat contentious) MathOverflow question by Igor Pak. While I still think this is a slightly problematic framing, it’s a discussion people seem to truly want to have, so I thought I might as well create a space for it.

Let me start discussion with the biggest concern (I don’t know if it is a downside) I have about the arXiv:
What is the arXiv’s policy on what can be posted and what can’t? I ask this as an honest question (with some trepidation about getting flaming from both sides). On MO we have an FAQ that tries to lay out as clearly as we can what sort of material should be put on MO and what should not. I cannot find an analogous statement from the arXiv about what they will accept and who they will accept it from. I doubt I disagree very much with what they do in practice, but the lack of an easily located statement of what that practice is actually disturbs me a bit. I apologize if such a document is publicly available somewhere on the arXiv website, but I maintain I shouldn’t have to hunt for it.

EDIT:
After reading the discussion below, I’m even more convinced that the idea of “downsides” is so tied up in one’s values and personal experiences that its impossible to come up with a list that makes sense to everyone. For example: one serious worry seems to be that if you put your papers on the arXiv, people will write follow-ups to them before you’ve had a chance to fully process your ideas. I’ve had this (sort-of) happen to me, though from a talk, not the arXiv; I gave a talk about my research program, and about 6 months later got an email from a graduate student saying he and a collaborator had solved one the problems in my talk. And you know what, it was great. He’d found a reference I hadn’t that made it possible to do lots of other stuff he hadn’t thought of, and I got to farm out that part of the research program to his paper. It really was a problem I wish I had a lot more often.

On MathOverflow career advice questions

Since this blog has already spawned one rant about career advice on MO, I thought I would make a play for first post written for PlanetMO by commenting a little more on such questions. I’m of a very split opinion of such posts. On one hand, I think most of them are a bad fit for MO and it’s very hard to get good advice from them, given how little MO commenters know of the author. I’m moving more and more to a policy of writing this as a reply to essentially all such questions.

On the other hand, I feel tremendous empathy for the questioners, and really want to help them (seriously, I am announcing here, if you want to write an MO question asking for career advice, email me instead with actual details, and I will answer). Good advice is incredibly hard to get in general. The writer of this question has a genuine quandry, and I’m sure could benefit from discussing the matter with a more senior and experienced person, and I understand the temptation to use MO as a substitute for such a discussion.

Even worse, there’s some part of my psychology that makes it hard not to answer these questions (for example, I couldn’t help answering this question after it moved to math.SE). And there’s no compelling suggestion I have for where to go instead; it’s easy to say that you should discuss these things with a trusted older colleague (especially since its true), but not everybody has such people in their lives. Even though I certainly do, it hasn’t always been trivial to get good advice.

So, maybe the point I’m getting to at the end of this is, is there somewhere to send people? I really wish I had a place to send people like, say, the author of this post, since I think MO is not really filling her/his needs. If s/he doesn’t have someone to ask such basic questions of instead of MO, it’s hard to imagine s/he has someone to talk to about the more serious matters involved in switching jobs.