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I have a PhD in applied mathematics from a top university. I didn't realise it at the time because I was so focussed on my research, but it seems my research area (numerical analysis of PDEs) is actually very niche in terms of real-world problems in industry.

All the job listings I see are looking for people with a probability/statistics/machine learning background. There are literally hundreds of listings for these types of jobs for every one job in my area. I am currently a postdoc but I plan to leave academia for industry (probably finance) in the near future.

As the need for people with statistical skills is so clear, I have started considering the possibility of doing a second PhD, this time in a statistical area.

It would have to be part-time as I will be working full-time in industry. However, I currently work 7 days a week and very long hours on research as a postdoc, it is my hobby as much as my job. So when I begin working in industry, which is a standard 40 hour Mon-Fri working week, from my perspective I will have a huge amount of free time, i.e. eveninings and weekends, that I could dedicate to statistical research.

So I have several motivating factors for considering doing a second PhD:

  • Statistical skills are very much in demand and are of far more use in real-world applications than my own niche skillset. I would like to work on important real-world problems and it would be ideal to have a qualification for this.
  • I absolutely love research and having a goal to work towards to motivate me to get really deep into a topic. I will have alot of free time when I move to industry soon, and I would like to dedicate that time to something constructive.
  • I am interested in probability and statistics from a theoretical perspective and I would like to make a contribution to this field. Originally I applied for PhDs in this area, along with applied math PhDs; I went with the math PhD as I was also very interested in that area and it was a great opportunity to work with an excellent supervisor and university.

So a second PhD in a statistical area seems to make alot of sense to me.

Questions:

  • Would any professor even be interested in working with me considering that I already a PhD and that I plan to work on the second PhD during evenings and weekends?
  • If you think there are professors that might be interested, how should I go about approaching them? I would not like to appear unprofessional.
  • I don't need any funding as I will be working full-time. Will this help me in finding a professor for a second PhD or is it largely irrelevant?
Wrzlprmft
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SecondPhD
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    Why do you want to do a second PhD? There is no advantage of obtaining a second PhD in a related field over simply switching your future research to that field. A second PhD is simply not an efficient use of your time and resources. The natural step, if you want to stay connected to academia, would be a post-doc. It's very common to switch to a slightly different field during one of your post-docs. –  Mar 11 '20 at 11:21
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    A PhD certifies you can do research. It is not an efficient way of certifying that you have knowledge of a particular field (that was usually a precondition before entering the program). So a second PhD is not going to help you. What you need is to fill the gaps in your knowledge and get some work experience. Probably the most efficient way to fill the knowledge gap is to join some MOOCs. – Maarten Buis Mar 11 '20 at 11:40
  • @Roland I already am a postdoc and when my contract ends I will be leaving for a job in industry. But I still want to perform research on the evenings/weekends as it's my hobby as much as my job and I love it. As I aim to move into the area of statistical analysis I would like a qualification in this area. I can't simply stay in academia and switch my research..nobody will hire me for a postdoc involving stats/probability, they will hire someone with much more expertise in that area. I also have financial commitments which mean I cannot afford to do another postdoc. – SecondPhD Mar 11 '20 at 11:40
  • @MaartenBuis It seems to me that a PhD does certify that you have deep knowledge of a particular field. Anyone I know who completed a PhD in mathematics is far more knowledgeable about their field at the end of the PhD than they were at the start. The precondition for entry in mathematics is that you have potential based on your prior academic achievements. – SecondPhD Mar 11 '20 at 11:49
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    Of course you know more about the subject of your thesis after writing it than before. That is not the point, because your research is in all likelihood way to narrow and specific to justify hiring you for a substantial amount of time. The real value of your diploma is that it shows you can do this again, and again, and again on different topics. – Maarten Buis Mar 11 '20 at 12:02
  • @MaartenBuis Yes and I would very much like to do it again in the area of statistical analysis. What else am I going to do in the evenings/weekends..watch TV/go drinking with friends/computer games? I want to continue my current lifestyle when I leave academia for industry..I want to perform research on the evenings/weekends, and publish papers. Longer term, I want a career in the area of statistical analysis and I would like to be highly qualified for this. My own area feels too niche and of little relevance to the real world. – SecondPhD Mar 11 '20 at 12:51
  • If I move into research in this area I will gain far more proficiency if it is as part of a structured cutting edge research project with clear goals and I am working with a professor who has years of experience. At the end of the process I will have a qualification that certifies my expertise in this area. I would be in a far better position than I currently am - there are countless jobs that I am very much interested in but I am not eligible for because they require probability or statistics PhDs. – SecondPhD Mar 11 '20 at 12:54
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    So, perform research on evenings and weekends. Nobody is saying you can't do that. All we are saying is that you don't need to do a second dissertation. It's quite unlikely that you'd find an advisor anyway, because they would also see it as a waste of their time. What you should look for is a cooperation. You should read the answer to this question. –  Mar 11 '20 at 13:14
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    @SecondPhD - you seem to be of the opinion that you need to go do another PhD if what you are working on isn't quite what you did your first PhD on. I would suggest that most PhDs are doing something fairly different within 5-10 years of their thesis, yet do not feel they need to get another PhD - they learned how to learn new stuff on the fly without courses in the first one. – Jon Custer Mar 11 '20 at 14:11
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    I agree with @MaartenBuis - the first PhD should have given you the skills needed to do independent research. You don't need to relearn that with a second PhD, and moreover, you should be able to do independent research in the field of your proposed second PhD without the need for a PhD advisor. You'll want to be in touch with some domain experts, but you should just focus on research rather than "learning to research," which is no small part of a PhD. – Nuclear Hoagie Mar 11 '20 at 19:11
  • "my research area (numerical analysis of PDEs) is actually very niche in terms of real-world problems in industry." Very strange. I know people in industry who have spent literally decades working on that topic. Maybe you aren't talking to the right companies. – alephzero Mar 11 '20 at 20:02
  • Relevant Meta: https://academia.meta.stackexchange.com/questions/4623/contesting-a-duplicate-question-non-standard-career-path-and-two-phds – Anonymous Physicist Mar 11 '20 at 22:11
  • @alephzero Yes there are some jobs in this area it is definitely a niche area these days compared to the amount of positions that look for a statistical skillset. Practically every decent sized company/institution is looking for a statistical skillset now. – SecondPhD Mar 12 '20 at 08:37
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    I have realised based on the answers I've received that my math PhD will be viewed as essentially equivalent to a stats/ML PhD in industry so I can see now that there is no need to do a second PhD in this area. – SecondPhD Mar 12 '20 at 08:45
  • Here, in Germany or at least at my former university, it is not possible to receive two PhDs. If one wants, they have to be done in different fields. Let's say someone earns a Phd in chemistry then you would get a "Dr. rer. nat." like everybody did in nature sciences (biology, chemistry, physics and also mathematics,.. etc.). So the 2nd would have to be done in.. Idk.. history or so..

    but btw, here you would have no problem to get a job in statistics/mal even when you're not from that field. Mathematics is sufficient. And I doubt a phd in statistics would help

     – Ben Mar 12 '20 at 10:21
  • as it is very specialized. My background is experimental particle physics and I'm working in a machine learning job now. Before that I worked with the statistics lecturer (a mathematician) and the skills needed in the industry are very different. You need much more software and programming than statistics/ml. At least on a daily basis. Nevertheless, I feel that there are a lot of statisticial questions during the week and they are so very applied that I think one can only answer them thanks to experience and/or as studying statistics (but not as a phd..). – Ben Mar 12 '20 at 10:23
  • If you want to do research in statistics, why not doing just that? You can publish without being part of a university and you can use your free time for actual research and not the things which are attached to being a PhD student. – WoJ Mar 12 '20 at 15:31
  • @Ben That's interesting. How did you mange to hired for a machine learning job ahead of statistics/ML people when your background is experimental particle physics? – SecondPhD Mar 13 '20 at 07:58
  • @SecondPhD Probably because of two aspects: Though I'm part of a relative large AI team (around 25 people) but finally I'm part of a small team embedded in an engineering department (here I benefit from my experience in particle physics, especially as my work included a lot of technical details and also data analysis of particle experiments) and, as I just mentioned, my work was related to a lot of statistical questions. I had no clue about machine learning but I'm, at least, familiar with statistics and programming. – Ben Mar 13 '20 at 09:30
  • Finally, I would say, statistics is a field of a lot of applied tasks - and I think, a phd would focus on "only" improving some optimization tasks behind some questions, so rather mathematically. So I guess, in a "typical" data science/ml job you wouldn't really benefit from that. On the other side, there are, for sure, jobs which are very suited for such tasks, where you would work on implementations and so on and less on "answering applied questions". The former would be very mathematically while the last would be more applied statistics, programming and so on. – Ben Mar 13 '20 at 09:35
  • However, my (small) team consists of: A mechatronic engineer, an electrical engineer, two mathematicians (one of them is my boss) and me. A company near to us is developing concepts and pipelines for other companies and they only hire mathematicians and physicists. They told me that, as a data scientist, you wouldn't almost need any programming as you pass your (mathematical) models on to (pure) programmers which convert the models into software later. I guess, e.g., this would be a perfect job for you - while I feel more comfortable around technical guys :) – Ben Mar 13 '20 at 09:38
  • Just a few things to consider: it might not always be that the hours you have to put in the job in finance industry are limited by 40h per week. Also, maybe you are the exception, but a lot of Phd students who think they work 7 days per week are actually surprised about the high pace of industry work. Your first priority should be to survive the first year on the job well. – lalala Mar 13 '20 at 09:49
  • I used to have a job as a quant in a top hedge fund and I only had a masters. I actually left it for a phd in machine learning. You definitely don't need a different phd. you're perfectly well qualified. Just pick up some books on machine learning/general finance (e.g. bishops book and grinold & kahn) and you''ll be fine. – user27182 Mar 13 '20 at 14:14

4 Answers4

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As most of the comments already say, doing a second PhD is probably not a good use of your time and not very helpful. From an industry perspective you have a math PhD, that means you are very smart and can learn anything, especially any maths very quickly. Learning some statistics or machine learning can be very helpful for an industry career but there is no need to get a formal degree in it. You can state in job applications that you have a math PhD and that you know statistics. Even if the statistics is entirely self taught in the real industry world this is equivalent to a PhD in statistics.

quarague
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    This. If I ever saw an applicant who returned to school for a second PhD, especially in such a closely related field, it would seriously devalue both degrees - because even after completing one, the person still seemed incapable of independently teaching themselves something new. That's not a good sign. Going back to training wheels is not a step forward. – J... Mar 11 '20 at 20:30
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    "Learning some statistics or machine learning can be very helpful for an industry career but there is no need to get a formal degree in it." As someone who reviews applicants for data scientists, I have to strongly disagree with this. There is plenty of work that someone without formal training in Stats/ML can do, but there's also some work that just can't be. There are plenty of stats related positions that are open if you don't have formal training, but some that are definitively closed. – Cliff AB Mar 11 '20 at 23:26
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    My Ph.D. was in discrete optimization, I was hired for an industry research position in statistics/time series analysis/forecasting, I have been working in this job for 14 years, and I endorse this message. +1. – Stephan Kolassa Mar 12 '20 at 07:21
  • Ok this puts my mind at rest. I thought I had no chance at these jobs compared to stats/ML people but if you say my PhD will be viewed as essentially equivalent in industry then I should be fine. I was concerned I had pigeonholed myself into a niche area. – SecondPhD Mar 12 '20 at 08:41
  • @CliffAB As someone who has transferred into data science from a physics background I disagree with the statement that some can't be done without formal training. I'm not saying its easy but there are plenty of resources out there to learn if you want to. The OP has shown they can learn independently in a related field, I wouldn't have reason to doubt they can do so without another degree/PhD. I believe the idea that anything is 'closed' without formal training is flawed. – Lio Elbammalf Mar 12 '20 at 14:20
  • @LioElbammalf: where I work, much of the role involves advising other non-stats PhDs on statistical methods. This requires a lot of breadth of knowledge. I've interviewed a lot of physics PhDs that understand a particular area of stats/ML well, but if you ask them something outside that area they have no idea. Hard to do statistical advising if that's your background. – Cliff AB Mar 12 '20 at 15:40
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From your question and comments it seems that there are two distinct issues:

  • Finding a good industry job with your profile: since you mention statistics I assume that you are looking at jobs in the area of data science. There is so much demand in this area that you don't even need a formal diploma, you could just teach yourself and acquire some experience with online material. In case you really want a diploma, what you need is a Master, not a PhD.
  • Keeping doing research because you enjoy it: you don't need to do another PhD in order to keep practicing research as a hobby. Most advisors would be reluctant to take you on anyway if you are not able to work full time on the PhD: they would often see you as a "flight risk", since you don't have any specific funding and no strong reason to finish a (second) PhD. However you could certainly collaborate on some research projects, many academics would appreciate a skilled collaborator that they don't have to pay.
Erwan
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  • Thanks for this advice, this sound like I a great idea. I will attempt to find an academic with experience in this area so I can collaborate while transitioning into this area. – SecondPhD Mar 12 '20 at 08:43
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I'm a retired Uni academic.

If you are determined to study more (and bravo for that), I would strongly recommend an MSc or an MMath in the subject. If you are short on skills, you will get far more from a good Masters. It will be cheaper, quicker and more intensive. Frankly, you will learn more as well. You've proved you can do research and that's the end of PhD for you. You would slow down your career too much by doing another.

Distance learning is appropriate if you are strapped for time.

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I also have a PhD in numerical analysis of PDEs (I would be interested to know in more detail what you studied).

During my studies I made good friends with a senior statistics professor at the university and I was pretty surprised by the amount of overlap some of the things we were looking at. In particular we had a good conversation about applications of the Proper Orthogonal Decomposition which had applications in my particular studies (reduced basis approximations of high dimensions PDEs) as well as in simplifying complex statistical models.

There is also an obvious huge overlap if you ever worked in the area of stochastic PDEs. I feel like I could have definitely continued a post doctorate with this statistics professor if he had anything available and I actually wanted to. I would suggest doing some background research into what some specific statistics professors have been working on and see if you can tie any of it back into your own studies. I think you'll be surprised.

On a side note, I didn't want to continue in academia and instead became a software developer. If you have some computational experience, which I assume you will having done numerical analysis, then I would also recommend looking into this because it is also in huge demand at the moment and it's really fun. ;)

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  • More properly, you did your PhD research on a certain topic. You were awarded your PhD in some larger field, like Math or Comp Sci. – Scott Seidman Mar 12 '20 at 11:20