Pure math field for PhD when planning to go into industry

Question

I'm a mathematics student just starting my third year. Since entering grad school, I have become rather firmly convinced that academia is not the place for me. The intellectual work is great, but the life side sucks. I hate the administrative bloat, the grad student/post-doc slavery system, being constantly surrounded by people with no social skills, the whole toxic self-sacrifice culture. I think I want to just go into industry, find myself some niche, or work my way up a corporate ladder. Probably in tech or finance since that's who needs mathematicians.

Problem: my research area is real pure, pretty much no direct applications at all. So, since deciding to go into industry, I've started to look at another field which I have taken a class on and is interesting to me, but I don't really know very much about yet. It's a relatively new discipline which has seen recent applications in data. There's a couple of people in my department who do related work so I might ask one of them to be my advisor. (I don't have one yet- the first two years here are very coursework heavy and this is the semester to choose.)

The trouble is, I feel like I'm starting back at square one. I fell in love with my original field during undergrad and have been going hard on it ever since. I was research-level before entering grad school, published a paper in top journal, had a bunch of ongoing side projects, and have read enough that I can easily hold conversations with professors about most topics. I know 100% I could bang out a thesis in the next three years if it was in this field. I even have an original topic based on a generalization of my earlier paper, and have made some progress on it on my own.

In my new field, I feel like a beginner. If my peers in the new field have the same level of expertise as I did in my original field, then I'm way behind. I might take longer to graduate, or have a crappy thesis. Or maybe I'll discover I just have no talent in it, that my brain is only built for original field. I don't know.

I am very confident in my original field, but from an applied perspective it is useless. Is it worth anything to get a PhD in a pure field if you know 100% you're going into industry? Would it be worthwhile for me to attempt to change to something more relevant in which I am a beginner?

Answer 1

It's hard to say much without more concrete info about which fields you are talking about.

I switched from geometric analysis as academic to quantitative finance in industry pretty easily. But it was probably easier at the time in that they didn't expect you to know much, just be smart.

Being an analyst meant that the distance to applications was much shorter than from many fields. However, the PhD badge does help whatever your original field; I have helped people with topology PhDs make the switch.

My general advice to people planning to switch is to do something related to probability or statistics. There are plenty of pure problems but it leaves you well placed for applications.

(see my guide on www.markjoshi.com for more discussion.)

Answer 2

A pseudo-answer: It is my impression that academic "applied" mathematicians who style themselves "applied", and the topics they pursue, are not at all reliable perceived as knowing or doing anything relevant to actual industrial, tech, business pursuits. This is explained by inertia, by the cachet (such as it may be) of hijacking "applied" as a modified for one's enterprise, etc.

Then there's the issue of passion... Indeed, it's hard to excel at something one doesn't really care about, and if that thing is not what one thinks it is anyway, it is doubly a waste of one's life.

I've had about 2/3 of my PhD students decide to go outside academia for various reasons. Usually insurance, phone companies, banking. Yes, necessarily, mostly this was 10-20 years ago, so things may be tighter now. But all the reports back were that having a PhD in math (of any serious kind) from a good university is at worst a certification of one's brains, perseverance, and analytical talents.

The traditional notions of "applied-or-not" are largely ignored by anyone outside academe... in case there were any doubt. If anything, perhaps having "applications" pretense without genuine knowledge of current practice is more discrediting than a more honest "here's what I have done and know about".

(After all, it still seems to be essentially that PDE and/or numerical solution schemes for PDE have claimed exclusive rights to "applied math". That is, "applied math" doesn't mean (in many peoples' minds) math that's applied... Crypto still doesn't count, nor error-correcting codes? Ignorance, yes, but inertia and pop-culture trump facts always.)

Answer 3

You are not going to use very much of your specific pure math PhD thesis knowledge anywhere in industry (or even applied math for that matter). Most employers will not care about your specific thesis topic. You will use your soft skills more than any (pure math) domain-specific knowledge, and you will be better off getting into industry as soon as possible. There is no substitute for learning on the job, and PhDs tend to be rather good at learning. Trying to go into a new field (that you guess is more relevant) without knowing exactly what it is you want to do is not worth the lost couple of years of industry experience. The opportunity cost of losing real world industry experience in order to hopefully make yourself more marketable does not pan out.

Switching fields or focus requires you to rely on your soft skills more than your intimate knowledge of how to run an R simulation of some uber-specific blah blah monte-carlo sampling nonsense. Here are some of the soft skills that you will use, regardless of your specific thesis work:

• You will know how to chip away at a big problems and make incremental progress.

• You will most likely be pretty self-directed, and so do not need much supervision. You will be able to make estimates, organize your own schedule, and set deadlines on the month/year/multi-year time scale (compared to the day/week timescale).

• You will most likely be rather tenacious. Getting a PhD is hard work that is often extremely unrewarding. People with the perseverance to push through and get to the finish line are sought in all industries, especially tech.

• Most importantly, you will know how to think: Logical thinking, "big picture" thinking, and identifying implicit assumptions are skills that people value.

Of course, you will need to cut the mustard with your "hard" skills as well, but for an industry job those hard skills will almost certainly be much more generic than your thesis research (those pesky google-style algorithms-and-data-structures type questions come to mind).

If you are sure that academia is not for you, I would certainly recommend you take or sit in on some programming/stats/"applied" courses while you are still enrolled as a full time student (or whatever courses you see fit). Take advantage of the opportunities you have as a student. Good luck!

Answer 4

You're in a great position to try the side path, because you have a pretty solid contingency plan (go back to the original area and topic).

But, um, if you like coding, it sounds like applied math could be a fun direction for you to go in. And it would give you an easier transition to industry, I would think.