Math in Business
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.
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.
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.
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!