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One of the contradictions of being a math professor is that a big part of your job is to train people to do things which are quite different from what you do yourself professionally; this is especially true for undergrads, but to some measure also with grad students.

This is not particularly helpful when it comes to convincing students that they should major in mathematics; most mathematicians I know, myself included, are quite ignorant of what people will actually do if they get BAs in mathematics, and don't go to graduate school, or otherwise enter education, which is obviously something students will be very concerned about in these tough economic times.

Obviously, the correct response is to educate one's self on what the job opportunities are for people with BAs in math. I'm mostly interested in the US context, but would be happy to hear about other countries as well.

The best resource I know is the AMS Early Career Profiles page. This is a lot of links (some broken) to profiles of BA graduates in math that individual departments have put together. There some other reasonable links on this website. Is there anywhere else I should be looking?

Ben Webster
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    This is a problem for professors in most subjects, not just math professors. (But I think this is a good question.) – Michael Lugo May 05 '10 at 02:07
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    Ben, you're at a department with some talented undergrad math majors. Find out from the dept. admin. if they have records of what undergrads have done who haven't gone to graduate school. Also find out what master's degree students in your dept. have done if they didn't continue towards a doctorate, since they may have chosen careers where math skills are needed but a Ph.D. is not. There was a talk in the math club in my department this semester by someone who has a career in industry using math. Do a google search on "math grad in the real world: a job in remote sensing" – KConrad May 05 '10 at 03:49
  • Are we restricting to jobs where a Mathematics degree is a genuine advantage (otherwise, why would it be relevant to MO)? What about jobs where Mathematics is a disadvantage?! – Zen Harper Aug 01 '10 at 00:10
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    @Zen: Are there jobs where a degree in Mathematics is a disadvantage? I can certainly see where it could be neutral. Do you have an example in mind where it actually hurts? – Jeremy West Oct 27 '10 at 00:35

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My experience, based on years in and out of academia, is that both students and professors vastly overestimate the connection between a major and a career. If you speak with successful professionals 20 years after their college graduation, you find that their majors are really kind of random. Among the people I talked with today, for instance, were a super-talented programmer who majored in English, a tech entrepreneur who majored in graphic design, and marketing executive who majored in philosophy.

I think the best advice for a student is to major in a subject that they'd enjoy studying for four years. That way they'll have a good time and find it easy to work hard! Note also that "enjoy studying" means the whole process, taking into account which subjects have inspiring professors and interesting fellow students.

could-not-log-in
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    You are correct. However, a properly trained math major should have stronger analytic and logical reasoning skills, as well as some useful knowledge of mathematics (especially, say, probability) that can give her or him an advantage over others in certain types of work. – Deane Yang May 05 '10 at 02:21
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    I'd certainly agree that a math background is helpful for certain specialized positions, like actuarial work. But I've seen no evidence at all in my non-academic professional life that math majors have any advantage in general logical reasoning or critical thinking skills. (And really, why should they? Just imagine what your colleagues in, say, the history or philosophy departments would say to that suggestion...) – could-not-log-in May 05 '10 at 02:34
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    @could-not-log-in: Frequently, they say "math professor? That was my worst subject" and get all defensive, in my experience. (Not always, by any means.) – Allen Knutson May 05 '10 at 15:05
  • btw, @could-not-log-in, if you're interested in logging in drop me an email scott@tqft.net and I'll help out. – Scott Morrison May 09 '10 at 03:37
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    Could-not-log-in: I like your answer, but I'm not sure about the negative assessment of a math major's skill at logical reasoning, which I've heard in several other contexts as well. Obviously, I wouldn't expect the average math major to have outstanding analytical skills, even from the best universities. But a meaningful comparison might be made not to the outstanding student of, say, literature, but just the average achiever from a random discipline. I believe I do have anecdotal evidence that the math major fares better on the whole. This is the way education works, on the average. – Minhyong Kim May 09 '10 at 16:39
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    The situation here is somewhat reminiscent of the discussion surrounding a mathematician's aptitude for adding up the bill. Mathematicians themselves are fond of claiming incompetence, often as a result of a mission to dispell the image of mathematician-as-calculator. But if the comparison is again made to the average person, it's obvious that this self-deprecation is in reality nonsense. – Minhyong Kim May 09 '10 at 16:44
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    @could-not-log-in: I think there is actually a reason why math majors should be better than the average graduate in logical reasoning (maybe not drastically better, but at least a little better). At some point in their undergraduate studies they should have had to learn about proofs: how to write a proof, what are common logical fallacies, how to prove something by proving the contrapositive. These skills are mostly presented in a mathematical context, but I think they do transfer over some to non-mathematical reasoning. – Jon Peterson Oct 27 '10 at 14:41
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As one of the previous posts reply pointed out, the B.A. in mathematics can lead to anything: from M.D. to M.B.A, to some kind of engineering or actuarial degree. The really difficult question is how do you encourage your students that Ph.D. in mathematics might still be a good idea, even if they might not like teaching or unsure about their research skills. Essentially, you have to tell them there is plenty of demand for mathematicians in the industry or the government (think NSA, CCR). This is also suggested by this ranking, btw. Unfortunately, in the past few years there has plenty of drum against going to grad school (see here, here, here, and somewhat less applicable but still strongly worded followup here). So how do you respond?

My answer is trivial: start early. While in graduate school, take advanced classes in CS, applied or numerical math, finance, or economics. It is often easy to cross register at the business school, but very few people ever do this. But you don't even have to do that - the lecturer might allow you to just audit the class. If things work out, you succeed in mathematics and become a professor, you will know what to say. But if things don't work out, you will know what to do...

Igor Pak
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    Wow. The articles you've linked to are depressing. I wonder if they come from some parallel universe, because I (here in the UK) simply do not recognise the pictures they paint, or perhaps (more likely) I should get out more... – José Figueroa-O'Farrill May 05 '10 at 07:44
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    Except for the "women in science" article, those are mainly about graduate school in the humanities, which (I have been told) really is considerably less likely to lead to a tenure track job than math or science. I also have problems with the methodology behind that job ranking. – Michael Benfield May 05 '10 at 13:06
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    Even if they refer to humanities, I wish someone had told me such things before I went to graduate school. Not that I regret, but the perspective before and after you take your PhD changes radically; usually research is much more idealized by undergraduates. Almost every graduate student I talked to has thought to leave maths altogether at a certain point. From what I read, this is true of Atyiah and Serre as well. This certainly denotes a serious lack of communication at least. – Andrea Ferretti May 05 '10 at 13:54
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    I'm not sure about Serre, but I've heard Atiyah mention that he did think about leaving academia during his PhD in Cambridge. If I remember correctly, his doubts evanesced once he started getting results. – José Figueroa-O'Farrill May 05 '10 at 14:15
  • @Igor: thanks for the links. Excuse me while I revise my career plans... – Qiaochu Yuan May 05 '10 at 17:10
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    @qiaochu- I hope you took Igor's point that these sites are somewhat misleading and need to be balanced with a little reality. I mostly agree with Penelope Trunk's article, but you'll notice the worst she says about math is that it pays poorly relative to other careers people successful in it could have taken. And she's right that you'd be much better off just getting a job rather than going to law school. The other ones don't seem all that applicable to mathematics, though they may be more accurate for other fields. – Ben Webster May 05 '10 at 20:01
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    I definitely think it's true that grad school in math is something you should only do if you enjoy it on its own terms. At least (unlike, say law school) people don't tend to come out of it horribly in debt. – Ben Webster May 05 '10 at 20:03
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    Sorry everyone if you find links to be depressing. The point is that the are out there and people start paying attention. We as a community should figure out how to respond and maybe even change curriculum somewhat to address the issue. Also, remember, university faculty were mostly in humanities only 53 years ago, in the era before Sputnik http://en.wikipedia.org/wiki/Sputnik Big changes are starting to happen with the internet education and all. This belief that math will always be protected is unfounded, I think. – Igor Pak May 05 '10 at 21:13
  • Hi Igor,

    Your second paragraph is fantastic advice---I do wish I had done more outside mathematics while in grad school.

    But I actually don't think that the links you posted are particularly relevant for mathematics (with the exception of the first, which is quite positive). Luckily, mathematics is either (depending on one's viewpoint) an experimental science where the experiments are cheap (and therefore the pressure is off), or an art that's really applicable (and so math PhDs have plenty of options outside academia).

    Best, Stephen

     –  May 06 '10 at 13:55
  • Finally, Greenspun's article makes me really curious: what percentage of those PhDs who go on to postdocs (at say, US universities) have tenure within (say) 10 years of completing their degree? –  May 06 '10 at 13:55
  • Hi Steve! While I find some of these comments very relevant, like the "pyramid scheme" idea which suggests that many grad students think they can get a job at a similarly ranked university. A low salary per level of education is also kind of true but the argument is based on wrong assumptions (grad school is more like an apprenticeship than an investment). But the "denied tenure" part is rather irrelevant to math, I think. I happen to know a few people who were denied tenure (in itself a relatively rare event, mostly for the complete lack of publications), but landed an ok job a year later. – Igor Pak May 06 '10 at 17:47
  • I agree that the pyramid scheme hits pretty close to home.

    But for mathematics, at least, the dystopian picture that Greenspun paints seems far from reality---check some of the statistics in the answers to my question "How hard is it to get tenure in mathematics".

     –  May 07 '10 at 13:13
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I agree with could-not-log-in: From my experience outside of academia, if you apply for a job it is most important what you did the last five years. This means that if you manage to get a job and be successful for at least five years, the subject that you majored in becomes unimportant.

As for getting your first job: It will be very rare that there is any opportunity to apply anything you learned in academia in your job. You learned some probablitity and statistics? Well, try to get a job at an insurance company where you can apply this - but chances are that you will end up somewhere else where it's of no use. This applies to other professions as well, of course, not only to mathematicians. There are just too few jobs out there that need some specific mathematical knowledge. Don't tell your students that they should take classes in applied mathematics etc. It's far more important to work some hours a week outside of academia to gain experience about the workplace, the people and what's important to them.

So you should not look for jobs where some specific mathematical knowledge has to be applied, but for jobs where the secondary virtues and skills that mathematicians have are important:

  • analysing complex technical problems,

  • finding convincing solutions, being very critical until a maximum of clarity is achieved,

  • high frustration tolerance,

  • being able to explain the results to the uninitiated,

  • being able to learn complicated new stuff quickly on your own.

There are two areas that come to my mind that offer excellent job opportunities to mathematicians:

  • all kinds of consulting,

  • all kinds of engineering that need abstract thinking, the prototype being of course the software industry.

Example problem solving: Some engineers I know, when confronted with a problem, are used to sit down for a while until they come up with a solution. A mathematician will know that this does not always work, but that it will take time to brood, getting distracted, brooding again, until someday you get it. This is a crucial experience that gives mathematicians a head start. But it's the experience and knowledge how to tackle complicated problems, it's not the knowledge of specific topics in mathematics.

Tim van Beek
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When I was helping set up my department's web site, I wanted to create a web page providing similar information. It was rather frustrating how little information is provided by the professional mathematical organizations such as the American Mathematical Society. Here is the page: Careers in Mathematics

ADDED: I would add that I recommend strongly that a math department try to stay in touch with its alumni (both undergraduate and graduate). You can't do better than learning from them what kinds of careers they are able to pursue with their degree in mathematics.

MORE: Another suggestion I have, if you're up for it, is to take advantage of your right to earn money doing something else one day a week and try to work as a consultant for a company. Not many companies look for mathematicians, but if you talk to lots of people (parents of your kids' classmates are a great way to meet non-academics), you might stumble onto something. What I've learned from working in the "real world" has been of immeasurable benefit to virtually every aspect of my life as an academic mathematician. The least is the ability to give convincing advice to students on what kind of careers they can pursue and what they need to know to succeed.

Deane Yang
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As an undergrad who has recently been looking for jobs I would make the following suggestions...

1) Learn to program! MOST of the jobs I've run into that require mathematicians/statisticians will eventually require learning one or more of Perl/Python/R/C++/SAS. I'm in the process of writing a book on the subject (programming for mathematicians, specifically in python)

2) Learn probability and statistics! I didn't do that directly and wish I had because I run into problems all the time for which probability and statistics knowledge would be useful.

3) Kind of coupled with 1, but learn Algorithms and Data Structures. If you never program than this isn't worth doing, but algorithms is math heavy and most companies that want to hire people to do algorithms expect a base knowledge, and basic knowledge of data structures is a MUST in that scenario)

4) Try applied classes! Other departments will not eat you! I promise... unless it's the department of cannibalism...

5) FINISH projects! Make sure whenever you get involved with a project that you push as hard as you can to get something finished and a "product" to show off.

6) Talk to professors outside of the department if they do something you think looks interesting. I don't mean to stress coding so much, but coding is something that everyone outside of CS departments (since coders are a dime a dozen there) needs, at least in the hard sciences and engineering.

7) For someone who doesn't plan on going into academia... internship >> summer classes. Search far and wide for these, they're extremely valuable and show that you can handle a work environment in addition to being able to handle an academic environment.

These are most relevant to undergrads, I haven't a clue what a grad student should do b/c I haven't gotten there yet!!

Michael Hoffman
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In terms of educating both professors and their students about what opportunities are available with a degree in mathematics, I think our department has done an outstanding job.

First, we have the website When Will I Use Math which discusses a number of career opportunities, salary potentials, and gives other useful information. We have made it freely available to everyone; so you might take a look, or direct your students there.

Second, we have a bi-weekly seminar, in which we invite speakers from different industries to explain their careers. One week we might have a financial analyst, another week we'll have a cryptographer, and the next week we'll have someone who researches the effects of nuclear stockpiles. I'm surprised at some of the applications people find for their experience in mathematics.

Third, we are a bit more proactive, when mentoring undergraduates, in finding them jobs. To aid us in knowing what is available, our department creates a list of companies looking for internships, etc...

I hope this helps.

Pace Nielsen
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One thing that I think might be helpful is for professors to post information about their ex-graduate students' whereabouts on their web pages. Often you will see that Student X is now an assistant professor at University Y, but I think it would also be interesting to know that Student X is now a jazz musician. I do agree with could-not-log-in that there is not a strong correlation between majors and careers. Nevertheless it would be interesting to know what PhD graduates in algebraic number theory end up doing, and it would be convenient to access that information by visiting websites of algebraic number theory professors.

Tony Huynh
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    "Nevertheless it would be interesting to know what PhD graduates in algebraic number theory end up doing". Here's what one of mine ended up doing: 'http://en.wikipedia.org/wiki/Caribou_(musician)' – Kevin Buzzard May 05 '10 at 20:15
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    From which, by a couple of links, I learn that you scored a 42 at the IMO! Chapeau! – Andrea Ferretti May 05 '10 at 23:39
  • Iain Gordon tries to do this (although he's not in ANT): http://www.maths.ed.ac.uk/~igordon/phdstudents.html – Geordie Williamson May 07 '10 at 10:09
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Is it the job of an academic mathematician to be aware of all existing career possibilities?...

I think the following is more important: putting undergraduate (and graduate) students in contact with alumni who have recently graduated, and who are now pursuing a career outside academia. What P. Nielsen describes (a bi-weekly seminar with speakers explaining their successful careers) looks great. But it could be even more useful for the students to get to talk to people who graduated just a few years ago.

In the high-school in which I work, I've seen how they do it:
Once a year, they invite some of their alumni pupils to tell the other kids about their experience in the study that they chose... It should be possible to implement something similar at university.

The advantage is that alumni might be able to give a better guidance to the students, and answer questions such as:
• How do I go about applying for jobs?
• What are the concrete problems that I could encounter in my first 2-3 years after graduating?
• How can I deal with them?
That's what the students need to know.

Ed Dean
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André Henriques
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    Nice! Bringing in alums sounds like it would be useful. Though I think every university finds that they can't quite keep in touch with alums as much as they'd want to. – Thierry Zell Oct 13 '10 at 11:11
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Use a recruiter. An academic is unlikely to have the insight into the job market and connections that a professional recruiter will have.

If you want to go into software development, realize that a math degree by itself gives you zero credibility as a programmer. In fact, it may give you negative credibility. When I moved from academia to industry, some potential employers assumed I was a bad programmer because I had a PhD.

An advanced degree in math may persuade employers that you are smart. But are you impractical and distracted by interesting tangents, or do you use your ability to solve practical problems? You're probably not a mediocre programmer; you're more likely to be really bad or really good. Realize that's what people are thinking and do what you can to show you're in the latter group.

If employers think you will be a good programmer, they may be concerned about how long it will take you to come up to speed. Do what you can to show that you've learned on your own. Professional certification such as MCP may help. (On the other hand, don't over-estimate the value of certification. Most employers don't value certification nearly as much as experience, but if you have no experience, it's better than nothing.)

You might want to contribute to an open source project so you can point to real software you've written.

John D. Cook
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I majored in Math as an undergrad. My first job out of college was as a financial analyst performing multiple regression analysis of historical pricing and technical data with 5 other Math B.S. recipients. I eventually got a Masters in Systems Science & Mathematics and I ended up in Engineering. I now work with a Math Ph.D, an Engineering Ph.D., a Physics M.S. a Computer Science M.S., and several computer science B.S. people doing computer programming. I've known other Math B.S. people to end up as Statisticians and Actuaries.

Thus I'd say, in my limited exposure, this is an example of at least a handful of jobs a Math person could end up in with or without a graduate degree - engineering, programming, IT, statistics, actuary, or financial analysis.

And to answer the question directly, all an academic mathematician has to do to educate him/herself about job opportunities outside academia is to post to a site like mathoverflow.net and get personal testimonies. QED

DLP
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This answer is not so much about teaching others about carreer opportunities, but many universities offer coaching or training programs for this purpose. They are usually aimed (at least here) at PhD students or staff members though. Although they are not aimed specifically at mathematicians, I found such a program quite helpful (I recently followed a 2 day training). For one, it is important to find out your own qualities (and be able to convince others of this!). The interesting part is when you can get feedback from other participants, that come from a completely different field, to get useful suggestions for jobs that you might not have thought of. As mentioned by other people here already, it is not so much about the mathematics you learn, but more about the skills that you acquire that can be useful outside academia (an analytic mind, being able to see patterns emerge, etc.).

Pieter Naaijkens
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Rather than look at lists someone else has compiled of "what can you do with a degree in X?", I would suggest that it's more useful to go directly to the source: search job boards and company websites for the work people do outside education.

A few places I think make sense to start:

  • Principal business activity codes A list of business categories. As far as understanding work and career goes, I think it makes more sense to think in terms of industrial categories rather than academic departments.
  • Large public companies – Large-cap public companies are not the only places to work but they do have big hiring budgets. Becoming familiar with what they want done is certainly good, if only partial, information about business.
  • Job search – Pretend you are one of your students and ask yourself how you would go about finding a job. You may start searching with terms like "quantitative" skills and come to find a lot of unfamiliar terms representing what .
  • relative composition of your country – Wikipedia has nice pictures for many countries of the relative size of imports and exports, which is related to but not the same as how many people are employed doing various things.
  • View from the top – a set of interviews with CEO's

In my opinion the barrier to overcome is dividing the world according to academic department labels. (eg, thinking that $\textrm{management} = \textrm{psychology} \oplus \textrm{business}$) It takes time, but in principle it's not hard to apply a functor that repositions the topology (and adds new objects) according to the goals and methods of commercial businesses, whether that's Altria, TimeWarner, VeriSign, Tesoro, Cargill, or Airbus.

isomorphismes
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You can use any job searching site and subscribe to vacancies which contain words "mathematics" "math" of whatever.

In Russia I am subscribed on www.hh.ru - I am getting about 10-20 vacancies everyday, it is for free, absolutely most of them are not really related to math, but sometimes something related appears. But I guess in USA you will get much more vacancies where mathematicians are required or at least welcome. I think http://www.monster.com/ is Okay for USA.

I am sorry if this rather trivial answer already has been posted - I looked answers and did not see one. Any way I think your question is very good.

Alexander Chervov
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