Considering a second PhD, this time in statistics. Will any professors be interested in working with me? 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?
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.