What to do in industry

I’m a mathematician looking at the long-term academic career path, and it’s terrible. It’s certainly a perfect career if everything works out, but there are very few jobs available and so many factors completely out of your control along the way. About fifty years ago, it was simple: You finished your PhD, your advisor made a few phone calls, and you wound up with a postdoc and eventual professorship somewhere. That’s certainly not the case anymore. Math research comes down to being lucky enough to have the right epiphany at the right time (after spending countless hours in preparation, of course), and even with the right CV you still have to have attend the right conferences and depend on the largesse of those above you in the chain.

As such, I’ve been thinking about industry. I certainly don’t want to go into industry, but I may not have any choice. Now, I know what I like about math and academia: solving deep, challenging, unsolved problems in a field (namely, pure math) I find endlessly fascinating. Is there anything like that in industry? I want to do something that genuinely matters, rather than helping some middle manager put some tech widget on the market, and I want to work on something intricate and nontrivial.

Whether it’s accurate or not, I had an industry recruiter tell me a while ago that he saw all issues in his field as optimization problems: it’s just a matter of throwing enough time and money and manpower at anything that comes up, and the goal is to minimize the amount you have to throw. That sort of environment has zero appeal to me. I also look at my friends who are software engineers, and the thought of spending my entire day, every day, in a cubicle writing code comes close to giving me a panic attack. They’re very smart and talented people who love their jobs, but I couldn’t stand something like that.

So: Is there anything that I would like in industry? I love the idea of thinking about very challenging and deep ideas— not even specific problems— and understanding them, and I like having the autonomy to work on projects I’m personally interested in without having supervisors or managers getting in the way. Can I find something like that, or at least close to it, outside of academia?

You’re pretty clear on what you want: a job that requires deep thinking, lots of math, more theory than practice, no piddlyshit little details you have to obsess over, with lots of autonomy and minimal oversight.

What do you think you can bring to the company that pays your salary?

Well, that’s the thing. My background is in math, with some physics and computer science on the side. Are there companies that like that sort of thing? There are certainly companies that want mathematicians, but usually not to do math. (Finance companies, for example, love applied physicists for their data analysis skills.) On the other hand, I have an acquaintance who worked for a private crypto company, as well as a friend who worked for a consulting firm doing various bits of mathematical data analysis.

I too have a friend with a maths modeling consultancy. They mostly do environmental impact statements and the like, and have an AMAZING maths communication staff, who make the results meaningful and accessible.

Can you do that? You said you weren’t into cubicle-dwelling, is that because you’re actually a people person who likes communicating? Or can you get some skills/experience/further training to become so?

Otherwise, there’s the coming up with the models and running calculations bit, which is honestly a pretty small skillset.

I’m definitely not a people-person, though I have (successful) experience in writing and communication in general (my posts on this board notwithstanding). I can’t say I’m thrilled about the idea of making math “meaningful and accessible.” It’s probably something that’s in high demand, but I really don’t get any warm fuzzies from explaining or simplifying, rather than actually doing, math. For that matter, I’ve never been particularly interested in teaching.

The cubicle thing is really more an issue of personal space. I like to have a door that closes and to be able to work without having other people constantly watching over or listening to me, and vice versa.

Yeah, that’s the frustrating part. It really doesn’t require that much of a skillset to make models and run through calculations, and I don’t want to leave all that math behind.

The skillset required to make a good model, validate it, and apply it to a real world problem is very different from that required to prove theorems about it. It’s certainly not a lesser problem.

If you “certainly don’t want to go into industry,” no manager will want to hire you.

Have you considered an actuarial career? Several of the actuaries where I work are maths PhDs with backgrounds in academia. And all of the major actuarial consulting firms in town employ maths post-grads.

Admittedly you wouldn’t have the total autonomy and freedom from managerial oversight that you’re seeking. I can’t really imagine how that would ever be possible in the commercial world. But you would be working on interesting problems and you’d have very good pay and job security.

Where are you in your training? You’re right that the road to tenured math prof is an extremely hard one, but if it works out you’ve got the best occupation on earth - so you’ve got to try, surely? OTOH, if you’re on your second postdoc already and it’s not happening then it’s probably time to look at the finance sector.

Worth noting that only a small minority of people have PI potential in any research group (I’m speaking from my own experience of leading a chemistry lab, although I realise that maths is sort of a unique subject), and it’s usually clear from quite an early stage. It’s important to know whether you’re in or out of that grouping as it will critially influence the latter stages of your PhD.

When you boil it all down, though, to get a PI position somewhere good you’ve got to have done something brilliant. You get two chances at this, your PhD and your postdoc. This is the thing to concentrate on - all the networking, career planning etc is important, but it’s extraneous to this core fact.

I’ve known several mathematicians who worked as programmers, analysts or consultants; generally the “programmer” phase was short, as they tend to be good at analysis and good analysts are much more difficult to find than decent programmers.

Making math “meaningful” doesn’t mean “simplifying”. I can’t remember his name, but it took a poster in these boards for me to understand set theory. All those years I’d been asking “but what IS a ring?” and none of my teachers had thought of telling me “a ring is 'any set of mathematical entities which has the properties we call ‘properties of a ring’ - the list of properties is the definition.” When the Dean of my HS asked one of my classmates whether the new math teacher was as bad as he’d heard, my classmate (the best student I’ve ever met) answered “all the math I learned in the two years I had her, I learned from Chemistry and Physics, not from Maths.” Maybe using integrals to calculate a distance is a simplification rather than a purpose, maybe “the definition of any type of set is its list of characteristics” is a simplification, but I suspect both have more to do with too many teachers not knowing what they’re having to “explain”, and thus being unable to explain it (reading the book <> explaining).

The hot career that we are seeing is Data Scientist. You just need to find an industry - Petrochemicals to Healthcare - that you have a personal interest in.

I’m curious: In the academic world, do they really speak of the non-academic/non-government world as “industry”? Or, itself, are you merely interested in those businesses involved with the making of things?

In today’s Big Data world, I would think that you would do well to go into analysis, IT, even marketing. For example, in that last, many businesses have customer loyalty cards and could definitely use somebody to do analysis on buying trends, the effectiveness of various promotions, etc.

In the business world, there are still plenty of fields, businesses, and entire industries that can be revolutionized with the application of higher-order mathematics. Even such “simple” things as trash pickup can be radically changed with proper route-optimization routines - much of which is still done by hands-on experience today with little mathematical guidance. Akin to that, traffic management and road design is something where math should be the guiding principle, but isn’t.

Hell, in Law… does anybody take a mathematical approach to law? Is it possible to calculate the probability and risk-reward of taking on one client over the other - do people currently do that, and if not, why not?

Anyway, gotta go… but I hope you get the idea. Find the need, the area where math isn’t used… and try to develop plans on using it.

I’m neither an actuary nor a mathematician, but FWIW I’ve read more than once that the actuarial profession consistently ranks high in job satisfaction, compensation, and employment opportunity.

I’ll second or third analytics as a good thing to get into. It is a hot topic and getting hotter.

But let me touch on your real issue. When you say that you don’t want supervisors getting in your way, I sense you think that you are smarter than they are, and they’ll just hold you back. Maybe. On the other hand, they might be just as smart as you and a lot more experienced, and instead of getting in your way can move you forward.
Is your PhD advisor getting in your way? Or did you actually learn something from him? Managers can have PhDs also - in fact they will in any place even resembling your ideal job.
You can get a job with autonomy. But you have to earn it. No one is going to give it to you right out of school - unless you go into academia. Show them that you understand their problems and can do something about them, and in ten years they may trust you to find your own. But if you hate for your work to have practical applications, industry is not the place for you.

35 years ago when I started Bell Labs had a math research group, but that was probably harder to get into than academia. We had an applied math group who had a lot of PhDs and who did optimization problems.

You could always try writing a web comic.

Granted most of the math is fairly well established as I understand it but the worlds of high end logistics/supply chain have tons of needs for mathematical modeling. Some supply chains are straightforward, some you have to pull WAAAY back to see the patterns.

One of my favorite examples: Scholastic Book Fairs

a few good pics here

In a nutshell, a selection of books is sent out to a school for kids to purchase from.

The challenge is in determining how much to pack of thousands of different items to optimize revenues while minimizing product floating out to fairs and returning unsold as well as minimizing orders having to be shipped out after the fact. I worked there for 7-8 years and was part of a prototype program putting folks with some math and spreadsheet skills to start trying to break down these types of problems and optimize the situation as best we could. We made a big difference early on and there were huge improvements in inventory utilization, but even then, the problem is a bit bigger than an average twentysomething who held his own in algebra 2

The academics in Australia whom I know (mostly in actuarial and finance faculties) all use the term “industry” in that way.

They call anything outside of academia “industry,” accompany it with a shudder, and use the term to taunt other mathematicians who can’t hack it, which they think is the only reason to leave their ivory tower.

I’m using ‘industry’ as simply the opposite of ‘academia’, but I’d prefer something like a government research lab to a tech company. (It’s a bit odd to consider, say, doctors or lawyers as ‘industry’, but there you are.)

It’s certainly a field where there are many jobs and where there’s some application for mathematical modeling, but I can’t excited about analyzing the effectiveness of business’ marketing approaches. I’d certainly rather than do it than starve, but it’s really not something I have any interest in.

This is a bit of a tangent, but one thing I’ve noticed that really annoys some mathematicians, scientists, and engineers it that law isn’t at all mathematical. Rather, they expect it to be entirely algorithmic, with laws essentially equivalent to computer programs: you pop in the relevant facts as parameters, check to see whether your ‘function’ returns true of false, and take corrective action accordingly. It doesn’t quite work that way in real life.

Anyway, gotta go… but I hope you get the idea. Find the need, the area where math isn’t used… and try to develop plans on using it.
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That’s quite a bit of an assumption to sense. Back when I was in getting my PhD, I would meet about once a week with my advisor (and this was math, so we weren’t meeting regularly in a lab or other setting), plus email for specific questions. I actually have worked in industry before, and there the expectation (despite having a very smart manager who also thought I was very smart) was regular status updates, individual meetings, team meetings, and so on— about half a day’s worth of meetings per week. It’s unreasonable to generalize from that particular experience, but it does agree with anecdotal reports of my friends in similar jobs.

Well, no, it isn’t the place for me: I don’t care about practical applications, I don’t have any interest in the sorts of problems industry solves, and I don’t want to spend another N years after N’ years of academic positions to get the same level of autonomy. Ideally, I’ll stay in academia. But if that doesn’t work out, what’s the best alternative?

It is harder, unfortunately. Private, industry research labs aren’t really a thing anymore; there’s Microsoft Research, Bell Lab, something with Google…and that’s about it. There are tech company positions that involve research and publication, even if they aren’t specifically research-oriented.