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I am a junior mathematician, currently on the job market. I have been involved in a number of projects spread over several very different topics of mathematics, some being very mathematical projects that appeared in computer science theory forums (I do not consider TCS my specialty).

I had thought that breadth would make me an appealing job candidate (if I work in two areas, I can apply to jobs listed in both!). However, it was recently mentioned to me that this might be viewed negatively as 'lack of focus' and even hurt my job prospects. Another criticism I have heard is that a research group in area X might be reluctant to hire me out of fear that I'm really more interested in area Y. I have been most troubled by recently witnessing a member of the hiring committee at my current university demonstrated a complete ignorance of TCS forums (i.e. not knowing what FOCS is). I assume this means that this individual would value such publications negligibly at best (in contrast, I'd expect/hope that he would be able to identify the a top journal in an area of math outside his expertise).

Can any mathoverflowers either confirm or dispel these concerns? How do committees evaluate candidates with work in multiple areas (and/or reaching into other fields)? I am also interested in hearing how others have marketed themselves in similar situations.

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I'd view it positively but I can well imagine some people viewing it negatively. It will vary from person to person and your question has no answer. At the very least, you should make it community wiki. –  Felipe Voloch Jan 3 '11 at 2:20
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"People who build bridges get pushed off them" -- Bert Kostant –  Allen Knutson Jan 3 '11 at 4:29
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By the way, as meta-advice, once you have submitted all your job applications (and assuming your advisor/mentors agree that you have applied to enough places), I highly recommend trying not to think about it until you have to. I know this is easier said than done, but you can make yourself miserable wondering and worrying about things you can't change. If you can find a good distraction, the waiting process becomes much easier. –  Henry Cohn Jan 3 '11 at 4:58
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9 Answers

For all I can tell (and I've been on a hiring committee for the last 2 years), to have extra areas of expertise is always a plus, and to have areas of expertise that can connect you to other departments is a great plus. The caveat is that you still have to do something really good in at least one area. Having just mediocre record in many areas won't work.

Now, if somebody really doesn't want you to be hired, he can claim that you have "lack of focus" but you can be 100% sure that if you were working in just one area, he would claim that you are a "too narrow specialist", if you were married, he would claim that "you are too busy with family to do good research and won't come anyway because of a two-body problem", if you were single, he would claim that "you don't have any ties and will leave as soon as you find a girlfriend somewhere", etc. I'm exaggerating a bit, but the point is that one first decides whom he wants and whom he doesn't in some often fairly mysterious way and then puts forward logical arguments to convince other people. If that one is as ridiculous as I was in my last two examples, it is obvious to everybody but if he is seemingly (but only seemingly) less ridiculous like in my first two examples, that may fly and if a job candidate hears of such stories, it may make his head spin.

Just make sure you have a good research record and a fair teaching one and let all other things sort out by themselves. In many places the hiring process is more "political" than "scientific", so you can easily get or not get hired because last year group A quarreled with group B and now group C uses this feud to dominate the hiring. What arguments will be aired during the discussion in such case won't matter in the slightest.

Don't assume that when somebody says something, he really means it, and rely on your common sense more than on various rumors. You do not mind if the plumber you called to fix your sink is also a well-known singer in the local choir as long as the sink is fixed right, do you? Moreover, if you sing yourself and he has time for a chat, you may have a good conversation with him in addition to the service. But, of course, if you don't care about singing, you'll just check that the sink is OK in the end of his visit.

Similarly, working in area Y won't diminish your credentials in area X but you shouldn't expect the "X-only" people to appreciate or even to care about your "Y-achievements" without an external prompt. If there is someone in the department who understands Y, he'll attract their attention to it. But if there is none, just consider your Y-knowledge as an ability to speak Chinese in addition to English when visiting some rural Southern area. Nobody will admire it but nobody will consider it a drawback either unless you start to demonstrate it to everyone and insist that they appreciate your language skills.

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When my department (mathematics) tries to hire or promote someone with publications in selective computer science conferences (like FOCS), we explicitly point out in the file (which goes first to our own faculty and then to the higher administration) that acceptance of a paper in such a conference is equivalent to acceptance in a high-quality journal. The equivalence is, by now, fairly well-known, but we don't want to take the risk that someone who doesn't know it will cause trouble.

Turning to your more general question, I think breadth is generally viewed positively. What would, of course, be a problem is if people in area X say "well, he's not all that great in X, but we're impressed that he also does Y" while the people in area Y say "well, he's not that great in Y, but we're impressed that he also does X." Once these people talk to each other, "not so great" will win and "impressed" will disappear.

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I'd split this into several issues:

(1) Does demonstrating breadth actively hurt your application, by creating the impression of a lack of focus? For example, might you do better on the job market with only a proper subset of your papers listed on your CV?

In general, I think the answer is no. Of course, it depends on the circumstances; for example, adding low-quality papers to your CV could actually hurt your chances, so it's not simply monotonic. However, I don't think I've seen any cases in which I thought a candidate was hurt by having good papers in several research areas.

(2) If two people have written the same number of papers of comparable quality, but one works in a single area and the other in several areas, which person will do better on the job market?

This is a trickier question. There are definitely cases in which each would have an advantage. Sometimes having many papers in one area can excite a research group in that area, and sometimes having great breadth can build broad support within a department for making a hire. Overall, you need to show enough depth in at least one area that you don't come across as a dilettante, and that you attract the interest of someone in the department, but otherwise it's not clear which approach is best. [I should say that for most beginners, it is better to focus. If you have only a few papers, then you very likely will look like a dilettante if they are all in different areas, and they would have to be awfully good to make up for that. However, it sounds like that is not an issue here.]

I wouldn't worry about this too much. I think it's largely a matter of personality: some people love to focus and get distracted if they are trying to juggle too many projects, while others feel terribly constrained if they are doing just one thing. If one approach lets you do your best work, and the other doesn't, then you should go with the one that fits you best.

(3) Is it better to write one great paper, or two very good papers in different areas?

This one really depends on who is evaluating the application, and on their judgement of the quality difference. However, the central issue here is quality vs. quantity, and breadth is a secondary concern. (In many cases, the answer won't depend on whether the two papers are in the same area.)

As for theoretical computer science, you're right that many mathematicians have little idea how to evaluate the quality of CS conferences, and this can be a problem. However, I don't think it's a big problem in practice, because people who are interested in the topic certainly know about this, and they are generally able to explain it to the rest of the department or the administration. Letters of recommendation also play a big role here: if well-known recommenders praise your work, then that carries more weight than whether the conferences stand out as impressive on a CV.

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Just to reiterate what has been mentioned in some of the other answers: the standard way that complications in an application (e.g. explaining TCS work/publication criteria/other issues to a hiring committee/department/dean) are dealt with is via a carefully crafted letter explaining the situation.

So: if you are submitting an application in which you get to nominate your letter writers (which is likely the case, since you describe yourself as a junior mathematician, which suggests that you will be applying for tenure track jobs, for which typically you choose your letter writers), then, when you choose your TCS letter writer, be sure to choose someone who understands how to communicate TCS issues to mathematicians. In fact, hopefully you can choose a letter writer with whom you are sufficiently comfortable that you can raise this issue with them. (Not the issue of breadth being a weakness --- I don't think it is appropriate to raise concerns about weaknesses of your case with a letter write; those are for them to judge and comment on if they choose too --- but rather the concern that a math hiring committee may be unfamiliar with the TCS culture; I think this is a legitimate issue to raise with a potential letter writer, and if your chosen letter writer does their job properly, they will then include some explanations of TCS publishing culture and so on in their letter.)

More generally, I would think that generally speaking breadth would be regarded as a strength in a candidate, but not at the expense of quality and depth. But this is not something you can really control, since surely you are already trying to do the best work you can!

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Not only the cultures of math and TCS are different, but I doubt that the cultures are even uniform across a single discipline. –  Thierry Zell Jan 3 '11 at 4:09
    
Dear Thierry, No doubt. But nevertheless, a well-written letter by a recognized TCS expert (and one who will be recognized as such by a math dept. hiring committee) should be able to explain the relative ranking of the fora in which the candidate's research has appeared. Information of this nature is not only useful for the candidate; it will be welcomed by the committee. –  Emerton Jan 3 '11 at 5:52
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The majority of answers have suggested that breadth doesn't hurt you, but I have a more pessimistic view, based on my personal experience. I find that it is quite common for people to judge your research ability by what they consider to be your best piece of work. So if you're faced with the choice between

focusing on a single area, and publishing two papers in that area, one mediocre and one outstanding; versus

working in two different areas, and publishing one good paper in each area,

then my belief is that you will usually be perceived to be a better researcher in the former case. Now, it's true that the above dichotomy may be a false one. Perhaps your skills and temperament are such that if you choose to focus in just one area, you get bored and can't produce any good papers. But to the extent that you are faced with that choice, then I think choosing to focus on producing one really outstanding piece of work will generally be better for your reputation as a researcher.

Having said that, I don't necessarily advocate shunning breadth (again, assuming you actually have a choice). First of all, as others have pointed out, depending on what job you're after, your perceived status as a researcher may not be the most important factor. Secondly, in the long run you are almost certainly better off working on things you're interested in, rather than pursuing things that you think will impress other people. Of course, some compromise may be necessary since you do need to find employment somehow. But if your natural temperament inclines towards breadth, then ultimately I think you'll be more productive if you pursue your natural inclinations instead of forcing yourself to specialize in a way that you find distasteful. One advantage of breadth is that you have a good chance of finding connections between areas that specialists would never have seen. It may take you a longer time to produce that outstanding paper, but it could very well end up being even more outstanding than any paper you could have published quickly by specializing.

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As someone who actually is inclined towards breadth, and found this rather inconvenient when trying to "write papers to get jobs", I think this is sound advice. –  Yemon Choi Jan 3 '11 at 19:09
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Whether breadth is considered to be negative or positive will depend on the kind of job for which you are applying.

For example, consider a high-powered research department looking for someone in area X. If only half of your work is in area X, then you're at a disadvantage.

On the other hand, consider a department that values faculty research mainly for its ability to enhance the undergraduate experience, or bring in generic prestige, or whatever. Here you could be at advantage if you can sell yourself as a generalist. But beware: The problem of perceived "lack of focus" is very real. You want to show that you have a research program that could keep you occupied for many years. Perhaps you want to be seen as "not narrow", rather than "broad".

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I was going to say more or less the same thing: in particular, breadth can be a huge boost at a small liberal arts university. I imagine it must be a drawback at a Tier 1 research institution. –  Thierry Zell Jan 3 '11 at 3:15
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Breadth is a "drawback at a Tier 1 research institution"? It is a wonder that most of the active MO contributors are gainfully employed –  Igor Rivin Jan 3 '11 at 3:22
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Igor, I agree that breadth is not a drawback perse. There's nothing wrong with breadth, as long as you demonstrate significant strength and contributions in at least one important area of mathematics. –  Deane Yang Jan 3 '11 at 3:50
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I don't have any experience on committees making these kinds of decisions, so you should take my answer with a large grain of salt (or perhaps just ignore it). I would expect that the dominant factor in decisions is going to be how good your research is in your strongest specialty, but that to the extent that breadth is a factor it's a plus and not a minus. Much like with teaching, people have a tendency to make the leap from "X is good, but isn't important enough to make up for deficiency in Y" to "X is a minus and not a plus."

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I can only speak for my own experience in my department, but here I'm fairly certain breadth would not hurt you. Two ways (tenure track) applications tend to get looked at are

  • are the letters exceptionally strong, written by authorities with detailed knowledge of your work? This is independent I think of breadth, you just need to have to chose letter writers very wisely. For example, it might help to have letter writers who understand the different communities. eg I wouldn't know what FOCS is or know how to evaluate journals in specialties far from mine, but a letter writer would do well to mention the importance/selectivity etc of publications since letters are read by a broad range of people, and it might not hurt to mention this to letter writers!

  • do the interests of the candidate fit our department? this often means a combination of having some areas of significant joint interest with a significant segment of the faculty, while helping to broaden our faculty in new directions. Here breadth would certainly help!

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In the tradition of answering a question with a question: what is the point of the original poster's query? Your interests are either broad or they are not. Either way, you don't have to worry about what might have been. And, since the point of being a professional (academic) mathematician is to do whatever interests you at someone else's expense, it would seem unwise to tailor your interests to those of some (probably mythical) hiring committee.

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I think this is oversimplifying the poster's issue, and the reason why is addressed under (1) in Henry Cohn's answer: the poster might feasibly be asking, whether he would be better off suppressing different parts of his research in his different applications altogether and not to change his interests. –  Alex B. Jan 3 '11 at 3:35
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"the point of being a professional (academic) mathematician is to do whatever interests you at someone else's expense" - for some of us, this is more easily said than done; or rather, some of us are sufficiently mediocre that we have to do something more in our job application letters than say "I am good, and my work is good even if none of you care about it" –  Yemon Choi Jan 3 '11 at 3:42
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@Yemon: You might well need to say more in your application letter, but if you do not feel that "I am good, and my work is good even if none of you care about it" than you are probably in the wrong line of work. On the other hand, I completely agree with @Alex in that there is a difference between what you do and how you sell it. I absolutely $\emph{disagree}$ that suppressing the work you have done is ever the right thing. You must have found it interesting -- you just need to say why. –  Igor Rivin Jan 3 '11 at 3:57
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@Deane: If you mean that one paper in JAMS is better than three parts of that paper in lesser journals, I agree. Otherwise, I do not agree. Many good departments claim that they only care about the $L^\infty$ metric of someone's work. The truth is closer to $L^p,$ for some $p>0,$ where the value of $p$ is positively correlated with the strength of the department (lower-rank departments are worse at judging the quality of the work, but they can still count...). I have been on many (too many) search committees, and have never seen a signed measure. –  Igor Rivin Jan 3 '11 at 4:01
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I agree that the scientific value of a body of work is monotonic, so if there's any non-monotonicity, then it's a psychological effect. However, I think it's real. My impression is that when people evaluate a CV, they don't just sum the (perceived) values of the publications, perhaps normalized by time. Instead, they also take something like a weighted average, which helps determine how they think about the candidate by assigning an average quality level. If your weighted average goes way down, it can make a worse impression even if your sum is going up at the same time. –  Henry Cohn Jan 3 '11 at 4:31
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