Am I taking a wrong approach while looking for an academic position in applied areas - brutal criticisms appreciated! After a PhD in pure mathematic, I wanted to do work in applied areas where I could bring in my pure math expertise. So I did two postdocs in computational medical imaging where I could apply my pure math knowledge coupled with machine learning (which I also liked because of my pure math background). But the reason I wanted to do computational medical imaging were:
1) I felt the market for pure math would be hard, and it'd be difficult to obtain a permanent position. However, if I worked in imaging, then my CV would show that I was capable of doing both pure and applied stuff, hence would keep my options open to industry as well.
2) I looked through some papers in medical imaging, and what attracted me was the mathematical tools that they used in these papers, but I didn't pay much attention to the actual unsolved problems in medical imaging. It was definitely not like I didn't care about these problems in imaging, but they were not the main reason I got attracted to it. But I went ahead with the postdoc anyway, but worked mostly on problems that were of somewhat general nature (e.g. problems at the confluence of differential geometry and machine learning, of interest in imaging. I didn't really work with raw images, rather some heavily processed images that'd fit my differential geometric model).
After finishing these two postdocs, I tried to continue in medical imaging, but for reasons that were not under my control, I couldn't, and thereafter, I tried to switch to industry and worked unsuccessfully in several companies for short times, and currently I'm again looking to move back to academia.
The reason I ask this question here is that, I recently had a long talk with a friend of mine who's also a PhD and successfully transitioned into industrial R&amp;D from applied math/machine learning to autonomous driving. He told me that I took a wrong approach to working in applied areas. The reason to work in applied areas should be &quot;I want to solve this problem in this applied area (in my case medical imaging)&quot; as opposed to &quot;This applied area uses this and that tools, which I'm already familiar with and like using, hence I must like that applied area as well&quot;. The second one was my approach, and I'd like to know if I were wrong? Even to this day, what principally excites me in an applied area is the underlying math I can bring in to solve the problems there, hence in a project, I seek to stay on the theoretical side, rather than the practical one. For example, I'm definitely more at ease with pen and paper, but I can and do code for a problem that requires machine learning, but I'm no fan of e.g. keep tuning parameters to obtain the optimal model like they do in data scientist positions (I had some, didn't feel passionate about and was unsuccessful) - I rather like to write an algorithm, prove its convergence if needed, and test it on small and gradually bigger datasets. MY QUESTION: Am I being wrong in my approach? Please be brutally honest! Is there a middle ground that I can take, and how? Thanks in advance!!
If you are making a mistake, it may be in narrowing your focus, closing off opportunities. Especially if it is you who is giving a too-narrow definition of your capabilities.
A math PhD should be able to teach (nearly) any undergraduate math course and many MS level courses. Every college and university teaches math and so needs people to teach those courses. The market is enormous. But for, say, medical imaging, there are few places that are truly interested. While it is also true that your skills should, and do, enable you to work on a vast range of problems, if you exclude those from consideration, or seem to, then your opportunities also close.
In a lot of ways a mathematician is like a Swiss Army Knife, being able to attack many problems, pure and applied, since they have a facility with abstract thought and how things fit together synergistically. But be careful, in any application, that you define yourself in a way that is flexible enough that others can see your potential.