I want to start soon with a Ph.D. in mathematics, though I'm not sure, that long-term I want to stay in mathematics. But I know that I'm going to like doing mathematics full-time right now and invest the effort required for a Ph.D. so this unsureness will not deter me. Additionally, because I'm quite old, I want to do the Ph.D. fast(er that usual).
[This remark is bound to generate comments, I know - as "old" is relative, assume that I am compared to my colleagues and that I am bothered by the fact that I'm lagging behind compared to them; speeding up my Ph.D. is reasonable I believe, because 1) being "older" I've had more time to make sure I have all the mathematical prerequisits needed for the subfield I want to get my Ph.D. in (e.g. where some of my colleagues learned about Crandall-Rabinowitz only after being admitted to a Ph.D program, I know about it already now. "Bang. Just like that.") 2) I want to do the Ph.D in my home university (which is in Europe), where I already know all the relevant professors, have already taken seminars with them, know which Ph.D. programs exist, how I can get into them, how the system works etc. so I won't loose time by these non-mathematical things and I'm less hindered by formal criteria.]

Ok, this sound all nice and dandy, so where's the question. Here: Given the facts, that
a) I may not want to stay professionally in mathematics in the long-term, a Ph.D. degree from a very famous U.S. university, as they're world-wide the most well-known, could prove helpful for getting a job in the industry in a Western country later on (of course this doesn't apply to France, were you'd better have studied at ENS and not at Harvard, but I think I'm safe to chose a country were a degree from e.g. Harvard weighs) and that
b) I also like engineering applications of mathematics and I've read for myself books in a certain area of engineering and started taking occasional related, non-mathematical courses there and like to see research in this area,
I may like to apply, after having obtained by Ph.D. degree in mathematics, at a famous U.S. university for a second Ph.D. degree in engineering. (MIT comes to mind as prototypical example.)

What effect does a previous Ph.D. (in mathematics) has for me getting accepted at a highly ranked U.S. university ? (Good, bad, irrelevant ? It will show that I can to research, which is good, but not that good, since its research in mathematics and not engineering. If I have to do one of those pesky standarized tests, like GRE (do you know good programs, where this may be waived a Ph.D. ?), does this weigh more then the Ph.D. ?

Further reflections:

  • Besides the reputation of the university of the top U.S. universities, it seems that in the United States formal admission criteria for Ph.D. programs are less strict as in Europe (for an extreme example, take a look at the careers of these professors), so not having a bachelor in engineering may not knock me out from the start.)
  • For the nitpickers: Note that actually I'm not getting a Ph.D. in mathematics but a doctoral degree.
  • I also considered the possibility of directly applying for a Ph.D. in engineering in the U.S. But I doubt that I'll be able to do it as fast as the one in mathematics, since none of the reasons from 1) and 2) apply. Additionally I may have to exclude some programs, because my prerequisits aren't sufficient. So there only seem to be disadvantages to doing one directly.

closed as too broad by Alexandros, Cape Code, jakebeal, Peter Jansson, aeismail Apr 6 '15 at 21:07

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    I may not want to stay professionally in mathematics in the long-term then why on Earth do you want to do a PhD in mathematics? – Cape Code Apr 3 '15 at 15:49
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    You think you're smart enough to blast through a maths PhD at Harvard and do an engineering PhD at MIT but you think the GRE might be a stumbling block? This does not compute. – David Richerby Apr 3 '15 at 22:29
  • @CapeCode Because maybe I just love doing it, although loving something doesn't mean I want to do it forever on a professional level! There are more things to life than math and I want to explore those too! Sticking to math professionally won't allow me to do that because the publish-or-perish manner to climb the career ladder is too time consuming. To give an extreme example: If you know a bit about ODEs, you may have heard of N. Fenichel who is famous for his "Fenichel theory"; what is less known is that most of his theorems were published in his dissertation and afterwards he left math. – pink_pyjamas Apr 5 '15 at 10:08
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    [cont] And GREs aren't a stumbling block in terms of an intellectual challenge, but they waste my time for nothing, since I don't get any relevant knowledge for my PhD out of them. It's just another exam I have to prepare for, when I could be doing other more useful things that accelerate my progress. That's why I want to avoid them. – pink_pyjamas Apr 5 '15 at 11:02
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    You might find this useful : academia.stackexchange.com/questions/17232/… – Aru Ray Apr 6 '15 at 15:09

From what I know, it would hurt you. From the MIT ECE website (just as an example):

If I already have a PhD, can I apply for another PhD in EECS?

No, we will not admit an applicant who already holds a PhD degree (even if it is in a different area such as Physics or Math).

I'm sure it's like this at many of the top schools in the US. Here I'm assuming what you refer to as a "doctoral degree" will be treated the same way as the American/English "Ph.D."

  • This is a very useful information, although I'm not happy about it. Why do you think that other top schools also exclude directly from a PhD ? Is it custom for them to all have similar rules ? – pink_pyjamas Apr 5 '15 at 11:04
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    @pink_pyjamas I don't know for sure, but PhD programs put out a lot of money to fund their PhD candidates. I doubt they want to admit someone who is going to be a "professional student" so to speak. – JohnnyMo1 Apr 6 '15 at 15:40

I think the question that supersedes, "What effect does a previous Ph.D. (in mathematics) has for me getting accepted at a highly ranked U.S. university?", is the question of what effect your current plan will have on your overall career.

What I mean is this: Knowing, before you start a Ph.D. program, that you are going to switch fields immediately after your degree and get a different Ph.D. is just highly unusual. Having this as your plan from the get-go could potentially cause you problems for the rest of your career. Here are a few issues I see that haven't been already mentioned:

  1. If the admissions committee of your initial intended Ph.D. program knows that this is your plan, I imagine it will cause them to question why they should admit you. While nobody can predict what a student will do post-degree, I think that most professors will not want to spend years teaching and mentoring a student whom they know ahead of time has no longterm commitment to the field of study.

  2. Your attitude of thinking that you can just crank out your math Ph.D. quickly and then move on to your "real" subject is also likely to be negatively received by the math department from which you want your first Ph.D. In particular, it signals that you don't have a good grasp of hard work needed to obtain a Ph.D. in mathematics.

  3. For the rest of your career, you will likely be answering the question, "why do you have two Ph.D.s?" If you tell your story to anyone that has any connection to the academic world (including potential employers), they will almost invariably find it odd, and it may be perceived quite negatively (for reasons which I think have been addressed in similar questions on this site).

I think the third item addresses your question directly: If most academics will (in my opinion!) find your plan odd, then it will likely negatively affect your admissions to the second Ph.D. program.

You could always choose to keep your overall plan a secret at each intermediate stage of your career, but this I think carries its own obvious set of serious issues.

  • Thanks for your answer. I have to make some comments regarding 1.-3., at least for other readers, so that my question is better understod. Regarding 1. Because right know there are more open positions for PhD than students, so professors are happy if they get some students, because they are a) paid for tutoring b) it looks bad for their reputation if no one does a PhD with them (I'm curious, are you from the U.S. ? Because most comments strike me as being written from the perspective of people from the states, where academia seems to be rather different from Europe.) [...] – pink_pyjamas Apr 5 '15 at 11:14
  • [cont] Also notice that most PhDs done at not-top-schools (at least in Europe) end up leaving mathematics, so not having a longterm contribution rather is the rule than the exception. For 2: This is good to know, but probably varies very much from individual to individual, as some profs probably equate "crank out a PhD quickly" with "this student looks ambitious and promising, so I probably can rest assured by taking him on, that I won't abuse my offfice hours with his questions". – pink_pyjamas Apr 5 '15 at 11:29

This seems like a very weird plan to me. Even if you aren't explicitly excluded from applying for a PhD (e.g. as per @AlexMiller), you will likely be at a significant implicit disadvantage.

You also don't seem to have considered the implications for your post-PhD career. I was part of an early career workshop (applied mathematics) in which a post-doc with two PhDs asked how having two PhDs might affect her career. The general consensus was that, while it wasn't insurmountable, it did put her at a disadvantage and she would have to justify why she did two PhDs and why it was the best path for her (we weren't provided details, but it seemed as if there were extenuating circumstances that led to her doing another PhD - i.e. it wasn't her plan all along).

Assuming you don't have a master's degree (which you might), why don't you do a master's degree in maths and try to do a PhD in engineering from there? That way you get to spend some time pursuing your maths interest, without having to commit to it long term, but don't have the stigma of two PhDs. It also fits better with your 'older' time-line, as a master's degree takes far less time than a PhD. Furthermore, an applicant with a master's degree in math is going to be more attractive than an applicant that is immediately applying to do another PhD (how would you justify this in a cover letter? First thought would be that you became disillusioned during your first PhD - not exactly the ideal candidate unless you can spin a very good story.).

  • I already have a masters degree, but math really gets interesting only at PhD level, i.e. stopping now, when there are many interesting directions to pursue, would be annoying. – pink_pyjamas Apr 5 '15 at 11:32

Well, I know several math PhDs who work as faculty in engineering departments in fields like control, dynamical systems, optimization, signal processing etc. You can do your math PhD in such fields and work in engineering departments or some of the research labs. No need to do 2 PhDs.

Some representative departments/groups where math professors work in engineering are:

CSL at UIUC LIDS/CSAIL at MIT CDS at Caltech

There are several others.

The US academic system usually avoids students having multiple PHDs. There is some concern about students remaining perpetually in PhD programs without ever stepping up to obtain independent funding, as a faculty member.

The usual solution for a field switch or diversification is a post-PhD masters. In your case, you could get your Math PhD, then apply to MIT for an engineering masters. Or, since you have this plan up front, get a Math masters from your local college and apply directly for an engineering PhD.

So far as the GRE goes, don't sweat it. I got a perfect score with minimal studying. The math doesn't go above algebra, and the vocabulary, etc. are standard high-level English. If you're accustomed to speaking and writing technically in English, it shouldn't be an issue. Remember they use this same test with similar thresholds for entry into humanities graduate programs as well. It's very much lowest common denominator.

  • But you generally don't need to take the Math GRE for entrance into an Engineering program. That's for US Math graduate programs. – Byrel Mitchell Apr 6 '15 at 19:15
  • You're right, I misread. Sorry. – Nate Eldredge Apr 6 '15 at 19:56
  • Thanks, the idea with doing the master is GREAT, as a masters does give allow me to put a foot in the doorstep of engineering science and also takes less time then a full-blown PhD. And good to now about the GRE, I actually always assumed it was something like a European school-leaving exam, which, in some countries (e.g. where I'm from) are tough and time-intensive to prepare. – pink_pyjamas Apr 7 '15 at 7:54

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