One of my pet peeves is how annoyingly the AMS’s math subject classification is for people working in quantum algebra and quantum topology. The MSC has 97 different major subjects and my field is not one of them, and instead appears many times a subheading. In the new 2009 classification there’s at least the following: 16T, 17B37, 18D10, 20G42, 33D80, 57R56, 58B32, 81R50, and 81T45. Here I’m only counting things that are obviously quantum algebra and quantum topology (for example I didn’t list subfactors, quantum computation, knot invariants, etc.) By way of contrast, on the ArXiv there are only 32 categories, yet one of them (math.QA) contains the vast majority of work in my field (of course, many of those are cross-posted).
This mini-rant of mine came up at dinner at an AMS meeting in Waco (more on the excellent “fusion categories” special session later). Someone pointed out an interesting side-effect of this issue that I hadn’t thought of. One of the awesome things about mathjobs is that rather than simply having a large paper stack of applications, the people on hiring committees can instead sort the applications automatically in many different ways. It makes a lot of sense that mathjobs has this feature, but none of us who were on the applying side of things had ever considered it. Here are a few examples of things you might want to search for: look at people applying from a specific school, find everyone who has a recommendation letter from Prof. X, and (relevant to this post) sort by AMS subject classification.
This means that choosing the right AMS subject classifications is actually somewhat important. If you choose poorly then someone who might be interested in hiring you might never actually find your application among the hundreds they’re looking through. So if you’re in a situation like mine it’s worth asking a professor or two which AMS subject classifications they’d be most likely to look through.
Since then I’ve been wondering whether it might be a useful for mathjobs that the data they ask for also include which arxiv classifications applicants have posted preprints under, as that’s the search that I would want to use if I were on a hiring committee. What do people think? Mathjobs is very responsive to requests, so if people think this makes sense I may send them an email.
Rereading Noah’s graduate school advice post, I realized I’d forgotten to stir up trouble at the time about his comments on REUs. In part, one should understand this post as an attempt to goad him into explaining.
First, a little personal history. I’m basically the poster-child for REUs; doing an REU in the year between my junior and senior years was the only organized math outside of school I participated in before grad school, and was the only experience with research I had before grad school, essentially. I had an excellent relationship with my advisor from the REU, met several people I liked a lot, did good enough research to turn it into a solo paper (admittedly, several years later), and generally had a really excellent experience. I’ve always recommended REUs to students, especially if they were considering grad school.
This has always seemed like a no brainer to me. If nothing else, since an REU is essentially the only real chance that an undergrad has to test drive grad school before committing years of their life to it. So, I’ll admit, I was a little surprised to find out that “REU-hater” is a category of person that exists. And now I’m curious; are there any more of you out there?
Masochist that I am, I’m one of the few individuals in the universe who voluntarily use all three of Windows, Mac OSX and Linux on a basically daily basis (I have Mac and Windows laptops, and use a Linux desktop in my office). Now, on Mac and Linux installations, there is no question as to which editor I will use; I confess to being an Emacs evangelist (especially to Mac users who haven’t tried Aquamacs). I recognize a lot of people have trouble with the learning curve on Emacs, but once you’re through it, every other editor just seems annoying.
Unfortunately, I’ve never found a good version of Emacs for Windows. In my day, I’ve used Winedt, and LEd (actually, I wrote much of undergrad thesis in Notepad, but I was young and foolish then), both of which I found basically fine, but I’ve always kind of felt like there must be a better program out there. Does anyone have other suggestions?
Let me start out by apologizing for two things, first the horrible pun in the title, and second my absence from the blog for the summer. Between moving twice (once cross-country), graduating, getting set up at a new job, buying furniture, trying to finish some papers, and being academic coordinator at Mathcamp I was pretty swamped. As a result I missed out on some developments in the math blogging.
Frequent commenter Danny Calegari started a blog in May. It pays to occasionally click on the links in comments here as sometimes you’ll find brand new blogs. My mathcamp friend, Matt Kahle, who is a postdoc at Stanford also started a blog. It has a fun mix of some elementary stuff (like the Rubik’s cube) and some of his research (which as an interesting mix of topology, combinatorics, and statistical mechanics, it definitely involves a lot of sending n to infinity in ways that would make my advisor happy). I’ve been meaning to link to both of those since sometime in June but just haven’t gotten around to it (though I did manage to add them both to the blogroll). It’s been that sort of summer, just ask me about my passport. Also, low dimensional topology has become a group blog. I find group blogging a great model both as a reader and blogger because it promotes conversations and allows one to maintain a reasonably updated blog even when someone disappears a whole summer.
Finally, over the summer there was a great conversation about what mathematicians need to know about blogging. Here’s my two cents. One thing incredibly valuable thing about blogging is the opportunity to have discussions and get advice about how to be a mathematician. It’s often hard in real life to have a discussion involving people at many different places in their careers about professional questions. In that spirit, here’s a question I’ve been wrestling with lately. How do you balance your research time between the following three activities: working on problems you basically know how to solve, working on problems you don’t know how to solve but are important problems, and learning new tools. When I was in graduate school I felt like it was pretty easy to balance things because any time I had any idea that was at all worthwhile I just worked on it and when I didn’t, I learned new things. I had few enough research-worthy ideas that it was feasible to think about all of them. Now that I know more I can’t keep doing that because I simply don’t have time to work on all the easy problems that I could solve. So the need comes to prioritize. I was wondering how other people strike this balance.
Timothy Burke, a professor of History at Swarthmore, writes
[L]et’s just say that you’re a prospective undergraduate who wants to study one subject more than any other… [H]ere’s how I think a prospective who self-identifies as highly interested in one topic or subject ought to work through the questions involved.
First, are you sure that you’re really that interested in a single topic or issue, so sure that you want to make that a primary axis of your decision about where to go to college? Why are you that sure? Do you just like the topic or are you thinking already of a profession narrowly based on it? Are you sure based on an understanding of what a likely undergraduate-level curriculum around that topic looks like, or based on what you know about it from your high school experience? Are you making that choice with a wider awareness of the subjects that even a small college will offer to you that virtually no high school curriculum can focus on?
Second, are you SURE? Really? Then you’re a really unusual applicant. Most of what prospectives think they’re interested in is not the same as what those subjects turn out to be, and most of their interests are based on a very incomplete understanding of the range of academic subjects even within a particular discipline.
Third, if you’re really that kind of unusual person, absolutely certain that your first, second and last priority is to comprehensively study a single subject area while you’re an undergraduate and that this priority is unlikely to change, then: a) don’t apply to any small undergraduate institution; b) pick a place with as few general education requirements as possible; c) find a program in your preferred subject at a large institution that is stuffed to the gills with faculty and courses and make sure undergraduates with a dedicated interest get access to the most prestigious or high-powered faculty in your area of subject interest. The relative difference between one small college and the next doesn’t really matter to you if you’re that driven, because in either case, they’re going to have a relative paucity of resources in comparison to a large institution. You don’t really care about any of the other resources at an institution if you’re that focused: just your area of study and whatever direct supporting skill areas you need (say, language or quantitative training). An undergraduate applicant who is this specifically focused is really more like a proto-graduate student, and should use selection rules much closer to what a graduate student might employ.
This sort of student may be extremely unusual in history, but I would say that they are only somewhat unusual in mathematics. By time I got to Harvard, I knew I wanted to be a mathematician and was struggling to learn as much as I could, as fast as I could. I was not at all the most sophisticated student in my year, and I think that the top undergraduates and high school students are noticeably better now then we were then.
So, I thought it might be interesting to see which of our readers identify with Burke’s hypothetical student, and what they think of his advice.
Early in my graduate student career, I was told by several people that I should go to conferences and talk to professors. If you work in mathematics, you’ve probably heard this piece of advice before, and it’s hard to see how you could damage your career by following it (given reasonable assumptions on your behavior). I encountered two problems:
- What sort of talking am I supposed to do with a professor if I don’t know anything?
- How do I make my way into one of those small circles of people that inevitably form between talks?
I’ve heard that some advisors actually go to conferences with their students and introduce them to colleagues, and this pretty much solves both problems, but I’d like to focus on the case that this doesn’t happen, since I imagine it will be the norm for a while. This isn’t meant to be a definitive guide, and I’d really appreciate further suggestions and anecdotes.
Combining a couple of previous topics, I was wondering: is there a good platform for writing a math paper on a wiki? This seems like a desirable goal, both for small groups of collaborators and for any MMORPG’s (massively multiplayer online research project groups), and I’ve never seen such a thing, but I’ll hold off on crankily complaining about its absence until the blog readership has had a chance to tell me whether it’s out there.
Here’s what such a thing would have to include:
- The ability to take in proper TeX code, including packages, bibtex, anything else people use in arXiv papers, and produce some kind of reasonable preview. Obviously, it wouldn’t have to be precisely what LaTeX would produce, but it would have to be readable. Clearly this is somewhat possible, since WordPress and Wikipedia do a decent job with it.
- The ability to sync with a local copy quickly and easily (hopefully with something roughly approximating svn).
- All the usual wiki features (user control, full history, etc.)
I feel like this is not a lot to ask, since all aspects of it seem to be in wide use in different programs, but I’ve never seen the whole package brought together. Am I just missing out?
Of course, this process could go on endlessly, but I think there was an important point that Noah didn’t emphasize enough: talk to people.
There are a few categories of talking that deserve special attention.
- You should make a point of going to conferences whenever possible (it can be extremely easy to get travel money for conferences as a grad student), even if they’re not exactly your field. If you have something to speak about, and can get a speaking spot, even better. If you’re wondering how one goes to conferences, there’s a simple algorithm.
- read the AMS math calendar
- request funding for any ones that sound interesting
- rinse and repeat.
- You should do whatever you can, non-annoyingly, to cultivate relationships with mathematicians, especially ones who are older. They can give you valuable advice, serve as good references, and can be good collaborators.
I feel like it can’t be emphasized enough: mathematics is a social activity. You’ll never learn it properly from books and papers, and you can’t rely on your advisor to tell you all the things you need to know. Rather, you have to talk to the people around you, and make sure you have people around you to talk to.
Of course, different levels of talking are good for different people. I’m a pretty sociable guy, and that shows in my mathematical work (it’s been almost 3 years since I’ve written a solo paper and don’t have any on the horizon), but even if you don’t want to collaborate with people, you really do need to talk to them about math.
The past week or two while my thesis was out waiting for comments put me in somewhat of a retrospective mood. So I thought while things were fresh in my mind I’d try to pull together my advice for graduate students. I’m going to try to give advice which it is possible to disagree with, which will hopefully spark some discussion. (That way I can learn something too!) Necessarily all of this is going to be best suited for people in a similar situation to me and most of my friends (at a top school, planning to continue in research, etc.).
I’ll organize my thoughts around the following ideas.
- Prioritize reading readable sources
- Build narratives
- Study other mathematician’s taste
- Do one early side project
- Find a clump of other graduate students
- Cast a wide net when looking for an advisor
- Don’t just work on one thing
- Don’t graduate until you have to
EDIT: Just so people don’t get the wrong idea, I’ll mention that I’m not suggesting this because of some personally traumatic experience I’ve had with job searching; in fact, the last difficult career decision I made was when I was 18. I just think it’s an idea worth considering, and one worth hearing other people’s input on. END EDIT.
As I’ve read more about the medical resident match, I’ve recently become a lot more convinced that a match for mathematics jobs makes a lot of sense. Fundamentally, the point of a match world be that schools and candidates wouldn’t ever have to play mind games with each other. Everyone would just make a list, and the computer would make sense of them.
I feel the benefits of such a scheme are obvious. What about the objections?