Pure math field for PhD when planning to go into industry 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?
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.)