Math in Business

October 22, 2011

Here’s an annotated version of my talk at M.I.T. a few days ago. There was a pretty good turnout, with lots of grad students, professors, and I believe some undergraduates.

What are the options?

First let’s talk about the different things you can do with a math degree.

Working as an academic mathematician

You all know about this, since you’re here. In fact most of your role models are probably professors. More on this.

Working at a government institution

I don’t have personal experience, but there are plenty of people I know who are perfectly happy working for the spooks or NASA.

Working as a quant in finance

This means trying to predict the market in one way or another, or modeling how the market works for the sake of measuring risk.

Working as a data scientist

This is my current job, and it is kind of vague, but it generally means dealing with huge data sets to locate, measure, visualize, and forecast patterns. Quants in finance are examples of data scientists, and they work in the most, or one of the most, developed subfield of data science.

Cultural Differences

I care a lot about the culture of my job, as I think women in general tend to. For that reason I’m going to try to give a quick and exaggerated description of the cultures of these various options and how they differ from each other.

Feedback is slow in academics

I’m still waiting for my last number theory paper to get published, and I left the field in 2007. That hurts. But in general it’s a place for people who have internal feedback mechanisms and don’t rely on external ones. If you’re a person who knows that you’re thinking about the most important question in the world and you don’t need anyone to confirm that, then academics may be a good cultural fit. If, on the other hand, you are wondering half the time why you’re working on this particular problem, and whether the answer really matters or ever will matter to someone, then academics will be a tough place for you to live.

Institutions are painfully bureaucratic

As I said before, I don’t have lots of personal experience here, but I’ve heard that good evidence that working at a government institution is sometimes painful in terms of waiting for things that should obviously happen actually happen. On the other hand I’ve also head lots of women say they like working for institutions and that they are encouraged to become managers and grow groups. We will talk more about this idea of being encouraged to be organized.

Finance firms are cut-throat

Again, exaggerating for effect, but there’s a side effect of being in a place whose success is determined along one metric (money), and that is that people are typically incredibly competitive with each other for their perceived value with respect to that metric. Kind of like a bunch of gerbils in a case with not quite enough food. On the other hand, if you love that food yourself, you might like that kind of struggle.

Startups are unstable

If you don’t mind wondering if your job is going to exist in 1 or 2 months, then you’ll love working at a startup. It’s an intense and exciting journey with a bunch of people you’d better trust or you’ll end up really hating them.

Outside academics, mathematicians have superpowers

One general note that you, being inside academics right now, may not be aware of: being really fucking good at math is considered a superpower by the people outside. This is because you can do stuff with your math that they actually don’t know how to do, no matter how much time they spend trying. This power is good and bad, but in any case it’s very different than you may be used to.

Going back to your role models: you see your professors, they’re obviously really smart, and you naturally may want to become just like them when you grow up. But looking around you, you notice there are lots of good math students here at M.I.T. (or wherever you are) and very few professor jobs. So there is this pyramid, where lots of people a the bottom are all trying to get these fancy jobs called math professorships.

Outside of math, though, it’s an inverted world. There are all of these huge data sets, needing analysis, and there are just very few places where people are getting trained to do stuff like that. So M.I.T. is this tiny place inside the world, which cannot possibly produce enough mathematicians to satisfy the demand.

Another way of saying this is that, as a student in math, you should absolutely be aware that it’s easier to get a really good job outside the realm of academics.

Outside academics, you get rewarded for organizational skills (punished within)

One other big cultural difference I want to mention is that inside academics, you tend to get rewarded for avoiding organizational responsibilities, with some exceptions perhaps if you organize conferences or have lots of grad students. Outside of academics, though, if you are good at organizing, you generally get rewarded and promoted and given more responsibility for managing a group of nerds. This is another personality thing- some math nerds love the escape from organizing, or just plain suck at it, and maybe love academics for that reason, whereas some math nerds are actually quite nurturing and don’t mind thinking about how systems should be set up and maintained, and if those people are in academics they tend to be given all of the “housekeeping” in the department, which is almost always bad for their career.

Mathematical Differences

Let’s discuss how the actual work you would do in these industries is different. Exaggeration for effect as usual.

Academic freedom is awesome but can come with insularity 

If you really care about having the freedom to choose what math you do, then you absolutely need to stay in academics. There is simply no other place where you will have that freedom. I am someone who actually does have taste, but can get nerdy and interested in anything that is super technical and hard. My taste, in fact, is measured in part by how much I think the answer actually matters, defined in various ways: how many people care about the answer and how much of an impact would knowing the answer make? These properties are actually more likely to be present in a business setting. But some people are totally devoted to their specific field of mathematics.

The flip side of academic freedom is insularity; since each field of mathematics gets to find its way, there tend to be various people doing things that almost nobody understands and maybe nobody will ever care about. This is more or less frustrating to you depending on your personality. And it doesn’t happen in business: every question you seriously work on is important, or at least potentially important, for one reason or another to the business. 

You don’t decide what to work on in business but the questions can be really interesting

Modeling with data is just plain fascinating, and moreover it’s an experimental science. Every new data set requires new approaches and techniques, and you feel like a mad scientist in a lab with various tools that you’ve developed hanging on the walls around you.   

You can’t share proprietary information with the outside world when you work in business or for the government

The truth is, the actual models you create are often the crux of the profit in that business, and giving away the secrets is giving away the edge. 

On the other hand, sometimes you can and it might make a difference

The techniques you develop are something you generally can share with the outside world. This emerging field of data science can potentially be put to concrete and good use (more on that later).

In business, more emphasis on shallower, short term results

It’s all about the deadlines, the clients, and what works.

On the other hand, you get much more feedback

It’s kind of nice that people care about solving urgent problems when… you’ve just solved an urgent problem.

Which jobs are good for women?

Part of what I wanted to relay today is those parts of these jobs that I think are particularly suitable for women, since I get lots of questions from young women in math wondering what to do with themselves.

Women tend to care about feedback

And they tend to be more sensitive to it. My favorite anecdote about this is that, when I taught I’d often (not always) see a huge gender difference right after the first midterm. I’d see a young woman coming to office hours fretting about an A- and I’d have to flag down a young man who got a C, and he’d say something like, “Oh, I’m not worried, I’ll just study and ace the final.” There’s a fundamental assumption going on here, and women tend to like more and more consistent feedback (especially positive feedback).

One of my most firm convictions about why there are not more women math professors out there is that there is virtually no feedback loop after graduating with a Ph.D., except for some lucky people (usually men) who have super involved and pushy advisors. Those people tend to be propelled by the will of their advisor to success, and lots of other people just stay in place in a kind of vacuum. I’ve seen lots of women lose faith in themselves and the concept of academics at this moment. I’m not sure how to solve this problem except by telling them that there’s more feedback in business. I do think that if people want to actually address the issue they need to figure this out.

Women tend to be better communicators

This is absolutely rewarded in business. The ability to hold meetings, understand people’s frustrations and confusions and explain in new terms so that they understand, and to pick up on priorities and pecking orders is absolutely essential to being successful, and women are good at these things because they require a certain amount of empathy. 

In all of these fields, you need to be self-promoting

I mention this because, besides needing feedback and being good communicators, women tend to not be as self-promoting as men, and this is something that they should train themselves out of. Small things like not apologizing help, as does being very aware of taking credit for accomplishments. Where men tend to say, “then I did this…”, women tend to say, “then my group did this…”. I’m not advocating being a jerk, but I am advocating being hyper aware of language (including body language) and making sure you don’t single yourself out for not being a stand-out.  

The tenure schedule sucks for women

I don’t think I need to add anything to this. 

No “summers off” outside academics… but maybe that’s a good thing

Academics don’t actually take their summers off anyway. And typically the women are the ones who end up dealing more with the kids over the summer, which could be awesome if that’s what they want but also tends to add a bias in terms of who gets papers written.

How do I get a job like that?

Lots of people have written to me asking how to prepare themselves for a job in data science (I include finance in this category, but not the governmental institutions. I have no idea how to get a job at NASA or the NSA).

Get a Ph.D. (establish your ability to create)

I’m using “Ph.D.” as a placeholder here for something that proves you can do original creative building. But it’s a pretty good placeholder; if you don’t have a Ph.D. but you are a hacker and you’ve made something that works and does something new and clever, that may be sufficient too. But if you’ve just followed your nose, and done well in your courses then it will be difficult to convince someone to hire you. Doing the job well requires being able to create ad hoc methodology on the spot, because the assumptions in developed theory never actually happen with real data.

Know your way around a computer

Get to the point where you can make things work on your computer. Great if you know how unix and stuff like cronjobs (love that word) work, but at the very least know to google everything instead of bothering people.

Learn python or R, maybe java or C++

Python and R are the very basic tools of a data scientist, and they allow quick and dirty data cleaning, modeling, measuring, and forecasting. You absolutely need to know one of them, or at the very least matlab or SAS or STATA. The good news is that none of these are hard, they just take some time to get used to.

Acquire some data visualization skills

I would guess that half my time is spent visualizing my results in order to explain them to non-quants. A crucial skill (both the pictures and the explanations).

Learn basic statistics

And I mean basic. But on the other hand I mean really, really, learn it. So that when you come across something non-standard (and you will), you can rewrite the field to apply to your situation. So you need to have a strong handle on all the basic stuff.

Read up on machine learning

There are lots of machine learners out there, and they have a vocabulary all their own. Take the Stanford Machine Learning classor something to learn this language.

Emphasize your communication skills and follow-through

Most of the people you’ll be working with aren’t trained mathematicians, and they absolutely need to know that you will be able to explain your models to them. At the same time, it’s amazing how convincing it is when you tell someone, “I’m a really good communicator.” They believe you. This also goes back to my “do not be afraid to self-promote” theme.

Practice explaining what a confidence interval is

You’d be surprised how often this comes up, and you should be prepared, even in an interview. It’s a great way to prep for an interview: find someone who’s really smart, but isn’t a mathematician, and ask them to be skeptical. Then explain what a confidence interval is, while they complain that it makes no sense. Do this a bunch of times. 

Other stuff

I wanted to throw in a few words about other related matters.

Data modeling is everywhere (good data modelers aren’t)

There’s an asston of data out there waiting to be analyzed. There are very few people that really know how to do this well.

The authority of the inscrutable

There’s also a lot of fraud out there, related to the fact that people generally are mathematically illiterate or are in any case afraid of or intimidated by math. When people want to sound smart they throw up an integral, and it’s a conversation stopper. It is a pretty evil manipulation, and it’s my opinion that mathematicians should be aware of this and try to stop it from happening. One thing you can do: explain that notation (like integrals) is a way of writing something in shorthand, the meaning of which you’ve already agreed on. Therefore, by definition, if someone uses notation without that prior agreement, it is utterly meaningless and adds rather than removes confusion.

Another aspect of the “authority of the inscrutable” is the overall way that people claimed to be measuring the risk of the mortgage-backed securities back before and during the credit crisis. The approach was, “hey you wouldn’t understand this, it’s math. But trust us, we have some wicked smart math Ph.D.’s back there who are thinking about this stuff.” This happens all the time in business and it’s the evil side of the superpower that is mathematics. It’s also easy to let this happen to you as a mathematician in business, because above all it’s flattering. 

Open source data, open source modeling 

I’m a huge proponent of having more visibility into the way that modeling affects us all in our daily lives (and if you don’t know that this is happening then I’ve got news for you). A particularly strong example is the Value-added modeling movement currently going on in this country which evaluates public teachers and schools. The models and training data (and any performance measurements) are proprietary. They should not be. If there’s an issue of anonymity, then go ahead and assign people randomly.

Not only should the data that’s being used to train the model be open source, but the model itself should be too, with the parameters and hyper-parameters in open-source code on a website that anyone can download and tweak. This would be a huge view into the robustness of the models, because almost any model has sub-modeling going on that dramatically affects the end result but that most modelers ignore completely as a source of error. Instead of asking them about that, just test it for yourself.


The closest thing to academics lectures in data science is called “Meetups”. They are very cool. I wrote about them previously here. The point of them is to create a community where we can share our techniques (without giving away IP) and learn about new software packages. A huge plus for the mathematician in business, and also a great way to meet other nerds.

Data Without Borders

I also wanted to mention that, once you have a community of nerds such as is gathered at Meetups, it’s also nice to get them together with their diverse skills and interests and do something cool and valuable for the world, without it always being just about money. Data Without Borders is an organization I’ve become involved with that does just that, and there are many others as well.

Please feel free to comment or ask me more questions about any of this stuff. Hope it is helpful!

  1. Gary
    October 22, 2011 at 12:28 pm

    As Mathbabe has written elsewhere, “quant in finance” has three parts, sell-side, buy-side and startups / hedge funds. The buy-side is a great place for someone like me that probably was a better instructor than researcher. Communication skills are even more important. The math is rarely original in an academic sense, but may well be new and exciting to your colleagues. Feedback is nice and Finance is alot simpler than number theory!

    The buy-side is also more flexible. Career paths that start quant don’t have to end up quant. It exists all over the country, so lots of different lifestyle possibilities, which can be a help if you have to solve the Two Job Problem or just don’t want the work/life intensity of NYC.


  2. Anonymous
    October 22, 2011 at 12:53 pm

    There’s been a lot of news about the big banks closing their proprietary trading units. The stories I’ve seen chalk this up to (1) the impending Dodd-Frank reforms, and (2) the fact that these units were getting less profitable anyway.

    My question (from the perspective of a graduating PhD student considering the finance route), does this translate into a large contraction in the math-finance job market? Are the independent funds having a bonanza these days with their competitors closing up show?


    • October 23, 2011 at 8:34 pm

      Yes and no. Yes because in the short term, what with Bank of America firing 30,000 people, it’s definitely not the best time to go into finance. But no because hedge funds aren’t going away and real math talent is rare. So I’m sure there will still be people hiring quants in finance for the years to come- I expect it to pick up gradually.

      One more note: if the government finally gets some balls and really puts into place a powerful Volcker rule, that will just mean the real cowboys of finance stay in hedge funds. The end results will be not-too-big-to-fail risk takers with their crazy models, and (hopefully in my opinion) higher tax rates.


  3. Allen K.
    October 22, 2011 at 7:22 pm

    Very smooth writing, and very nice idea to say “if you’re like this you’re [not] going to like this”. It was reassuring to say “Hmm, check, nope, nope, check, yes indeed I’m in the right place.”

    No verb in “Great if you know how unix and stuff like cronjobs (love that word),”.


  4. October 22, 2011 at 11:08 pm

    Cathy, not a quant here, but was wondering about something you mentioned regarding Shaw that isn’t uber-prominent here. You said Shaw had traditional work hours, but they weren’t demanding about putting in a lot of time. Was that your experience in other private sector jobs and did you mention that because I’m sure many women who fret about the family issues care about hours.

    One obvious difference between academia and finance is the lifestyle and $$$. Did that come up in the questions much?


    • October 23, 2011 at 6:03 am

      Thanks for bringing this up.

      The time commitment working at Shaw was not extreme at all by finance standards, although one week out of every three months I was “on ops”, which meant 24 hours a day on call for a week, which was time-consuming and very stressful.

      In terms of money, it was much more lucrative than my professorship, but on the other hand since I entered at the moment the crisis hit, my salary never became astronomical. Which was a good thing in that I never became accustomed to lots of money (of course that statement is completely relative- it is lots of money compared to many people), so when I left it didn’t hurt. One reason many of my friends are still in finance is that they don’t want to earn half as much if they leave.


  5. October 23, 2011 at 2:51 am

    I’ll bet it was a great talk.

    I was a little disappointed you didn’t mention what I did: become a software engineer/ There’s lots of fun to be had and it can be a complementary skill to data science 🙂 (I was a transport planner, too, for a while)

    I worry about data scientists who are inexperienced and don’t understand that when gets sufficiently big the chance of apparently non-random patterns arising randomly becomes large. So inevitably some false models get thrown up.

    Finally, from my experience, while open source software is here now, open source data is often merely an aspiration. Certainly in transportation planning, I found many times when essential data was only available on a propriety basis, or worse still, required data collection to be directly commissioned.


    • October 23, 2011 at 6:05 am


      Sorry I didn’t mention that, because absolutely it is a great alternative, and should be widely known.

      And agreed that data scientists who are not sufficiently skeptical often thing they see signal. It’s hard not to see something you’re looking for.

      I do aspire quite a bit on the open data front. But that’s the only way to make things happen, I believe.



  6. October 23, 2011 at 3:20 pm

    Really interesting blog post. I’m taking a math in (pure) math at the moment, and honestly have problems seeing any other career options than high school teacher or applying for professorship somewhere.

    Do you think pure mathematicians have a chance in business? (as long as they, for example, learn Python/R or something similar, maybe)

    Again, great post!


  7. Anonymous
    October 23, 2011 at 8:13 pm

    Posting anonymously because lots of friends read your blog…

    I’m currently in one of those highly-desired but hard to get professorships. With a tenure decision looming, I’m starting to think about Plan B’s that doesn’t include moving to whatever academic job will have me. I really like a lot of what you say about data science, and it gets me excited. But serious question: I already have the PhD, good communication skills, lots of cases of original thinking, and I know Python a bit (can get better, certainly). How do I find these jobs?

    Ideally, I would move to where I want to live… the Pacific Northwest, say… rather than doing a massive job hunt and moving for the job. Then what? Should I be terrified that I’ll end up destitute if I don’t have a job first? Just moving to the city you want to live in would be C.R.A.Z.Y. for an academic. Is that a possibility for someone thinking about a switch to data science.

    And seriously… where do you find these jobs? They’re not posted on mathjobs. Are they on Or what?


    • October 23, 2011 at 8:36 pm

      I found my current job by cross-searching “New York City” and “quantitative” on LinkedIn and filtering out all the finance jobs.


  8. October 24, 2011 at 7:12 am

    Often overlooked is being a high school (or middle school, or even elementary school) math teacher. After working for six years helping prepare teachers for their first years of teaching, I see a huge opportunity here for mathematicians. But, like everything on your list, there is a certain work culture, and it’s not for everyone.

    You’d be a good fit if you like explaining mathematics, especially to kids. You must genuinely care that your students learn, and be able to keep yourself and your students on a strict learning schedule. You must also be very patient, encouraging, and have the ability to seek out partial understandings and potential in all of your students.

    There are many high schools that are eager to hire mathematicians who are great teachers. Some typical examples (in NYC) are specialty schools like Brooklyn Technical High School, private schools like Saint Ann’s School, early colleges like Bard High School Early College, and gifted and talented schools like Hunter College High School. But don’t forget about other less extreme schools – often they’d jump at the chance to hire someone who is really good at math.

    In terms of pay and benefits, most teaching jobs have published salary scales. They’re competitive with other academic salaries, it’s easier to get tenure, and summers are nominally off. There are also teaching jobs everywhere, so the two-body problem is almost unheard of.


    • Michelle
      October 24, 2011 at 4:21 pm

      You must also not mind being generally disparaged by the public and the media, being paid crap wages, constantly hearing about how bad you (collectively, but still) are at your job, and (way too often) working for people with less training and experience than you have.

      It’s actually really hard to move with a teaching job once you’re established somewhere. (So, for example, if you teach for three years while spouse does a postdoc, then spouse gets a great job across the country, that three years counts for precisely nothing… no seniority, no pay bump, no tenure.)

      I taught for several years before going back to grad school in math. I make more than double what I did as a teacher, and I’m an asst. prof. at a state school. I’m not raking it in by any means. I have my summers off here just as nominally as I did as a teacher (meaning: not at all, really). And (shhhh) I worked way, way longer hours and way, way harder as a teacher than I do right now. Yep.

      Sorry, but until teaching ceases to be a crap job with low pay and no respect (from your boss, from the public)… I can’t in good conscience encourage folks to go into it as a profession. They’ll be miserable for 3-5 years, and then they’ll leave. (Of the people I taught with: precisely one is still a classroom teacher. We are doctors, lawyers, programmers, and professors. Know who’s still there? The fucking administrators.)


  9. October 24, 2011 at 2:38 pm

    Cathy, is there freelance work available as a data scientist or is it primarily an in-house kind of job?


  10. October 27, 2011 at 11:59 am

    Two things here.

    > The tenure schedule sucks for women

    The tenure schedule exists as such in North America only.

    > Feedback

    I like that you have chosen the neutral word “feedback” here, rather than “usefulness”. The only thing feedback tells you is what other people (more precisely, the people on top) want. If it has any relation to “usefulness”, it is in terms of what is conducive to your company’s generating a profit; you have given good examples elsewhere in your blog as to how quant work can go clearly, directly and shamelessly against every sort of societal interest.

    This is the dark side of other-directedness, really. I’d like to think there’s no inherently feminine inclination towards this – but then I’m skeptical that there’s an inherently feminine anything.


    • October 28, 2011 at 8:55 am

      Good points! And something I want to pick up on soon actually. Thanks!


  11. Bobo the Payaso
    October 28, 2011 at 3:36 am

    No mention of the moral aspect.

    1. Working for the NSA you work for an organization intimately involved in the worst abuses committed by the US government.

    2. Working in finance you work for the pirates who are destroying are society and culture.

    At least have your eyes open about what you are doing, and for whom.


    • October 28, 2011 at 8:49 am

      Absolutely agreed, and each of those topics could have been another talk. I certainly don’t consider myself a person who avoids talking about the implicit morality in a career choice. But I was, in this situation, separating the issues and making it purely informative.

      I’m interested in hearing more of your views on the morality of each job (especially the NSA since I don’t know much about it). Feel free to comment further.


  1. October 26, 2011 at 3:57 pm
  2. October 27, 2011 at 9:28 am
  3. January 28, 2012 at 10:09 am
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