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After completing a PhD in Particle Physics I left academia and have been working in industry for a few years now. However, during that time I've become more and more interested in Pure Math, to the point that I am considering trying to go back to academia and pursue my interest in full.

However, since the topic is so different from my PhD, I realise this would involve doing another PhD, if not a MSci before that. The grades that got me into my first PhD (an MSci equivalent degree) were not bad, but perhaps not enough to get me into a top MSci/PhD program now. My PhD dissertation, on the other hand, was awarded the maximum grade.

My question is: is it possible to use a previous PhD as an entrance degree to a second MSci/PhD? Would this be regarded positively by a top-level admissions committee?

As background, my first MSci and PhD were in Spain, and I am considering studying either in the UK (my current residence) or Germany.

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  • Why don't you try some coursera courses, instead? It will allow you to learn advanced mathematics courses, and continue working at the same time.
    – dalloliogm
    Jun 26, 2014 at 14:24
  • I am studying a few topics on my own, but at some point I would like to spend some time devoted 100% to it. Working full time limits the amount you can do as well as the depth to which you can do it :)
    – finitud
    Jun 26, 2014 at 14:30
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    I'm not using Coursera in particular because I haven't found the courses I'm interested in listed there, but do use online video lectures when available, as well as books, notes, and Math.SE/Mathoverflow.
    – finitud
    Jun 26, 2014 at 14:31
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    You might want to search this site for "second phd" to find a number of related questions. In particular, some institutions have a policy of not accepting students studying for a second PhD. Jun 26, 2014 at 15:41
  • @NateEldredge: in those cases, what would someone in my situation be able to do? MSci followed by applying to postdocs? :)
    – finitud
    Jun 26, 2014 at 15:44

2 Answers 2

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If you got the maximum grade on a dissertation in another PhD program, that would be viewed positively. The admissions committee would be hoping that you will do the same in their program.

The basis for concern is that your pre-dissertation work will "average down" the value of your application. It's not something to be ignored, but most admissions committees will give the greatest weight to 1) the highest level of work that you have achieved and/or 2) the most recent level you have achieved. in both cases, your PhD dissertation grade is a big help.

I might refrain from taking math courses until getting into a program, even at the expense of being less prepared. Because if you take those courses and do badly, that becomes the new "most recent."

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With a PhD in particle physics, you'll get on most MSc programs in maths, and if you show expertise in a certain area of pure maths, lots of PhD advisors would be interested.

One thing I would say is that to convert from physics to pure maths really requires going from the beginning of undergraduate (at least via private study, which you'll find very enjoyable given your experience), so 4 years, then 4 more years or so for the PhD.

One fast track idea is Part III (MMath/MASt) at Cambridge (or something similar), but actually look at those exams. Eventually, you trace it all back to first year undergraduate courses you/I didn't do, like group theory or number theory. There is a lot of abstract algebra for example. There is no shortcut. The sort of maths you learn on a physics degree is of little value in pure maths (I converted to mathematical physics/applied maths career from a physics and philosophy degree). Pure maths is a world in its own, there is almost no crossover. Not so true the other way, but still very true.

You can skip straight to the PhD and avoid the previous degrees themselves, but you need to study this stuff, its amazingly different from physics. Once you know a certain area e.g. algebraic geometry to a graduate level (which requires 4 years of about part-time work even with a physics PhD, including more or less every course you see on a maths degree as a preliminary), you can definitely get on a PhD in that area. I suppose any attempt to fast track it will just make you passable but ultimately not particularly good at what can be an almost impossible research world to take part in even with 1st class honours etc in a maths degree. But not impossible, just need the desire and commitment.

Just teach yourself maths (i.e. all the usual courses, see e.g. here), then maybe do some research and publish it (you have experience in this). Then apply to do a PhD in that area, given you've already published in the field. That will probably be faster, easier and cheaper than the degrees, and you can select the courses directly that back up what you want to do. Getting a publication in a pure maths area should be a good sign you are very ready to do the PhD, as you know from your own experience in particle physics.

Could also be good to just apply now to some PhDs and see what happens. A crossover between pure mathematics and particle physics might be a good idea as you can sort of do all this on the job. If you self-fund it will be much easier, as the funding from what I understand is potentially reserved for first time PhD candidates. Much depends on the specific university/grant, though as I say they tend to bias funding for first time PhDs.

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  • Nice answer! I am about to begin my PhD in quantum information later this year. I'm currently in my master's course and had a first taste of string theory. I'm very interested in this field but feel like I'm pretty behind with math, and it really takes some times for me to catch up. I'm thinking about pursuing a second PhD in string theory after my first one. Is this generally feasible? I'm a bit worried the universities or potential advisors don't want to recruit a student who has already obtained a degree. (there are no professors at the university I'm going to studying string theory.)
    – IGY
    May 23, 2023 at 0:02
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    I suppose it depends on what sort of string theory. With the mathematical physics side, its probably ok to just do the one PhD, then work to develop a research profile in string theory. Might help to start around now reading up on it. String theory is more mathematical physics than pure maths, so your QIT PhD will be enough academic background, definitely. See there notes, you can follow these simply by digging into some mechanics (e.g. Lagrangian), and a first course on quantum field theory. QFT is definitely a good idea first.
    – apg
    May 23, 2023 at 0:14
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    @IGY, don't do a second PhD in string theory if you already have one in QIT, the fields are similar enough. Instead take a look at the overlap between AdS/CFT and quantum information, that was a big thing several years ago starting with Brian Swingle's MERA AdS/CFT conjecture and it-from-qubit followed this thread a bit (though I feel its lost a bit of steam in recent years). Reformulating aspects of string theory in the language of quantum information is probably more valuable than inserting yourself into the over-saturated field. May 23, 2023 at 7:43
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    Will probably result in easier/different maths, thus a better understanding. The perimeter scholars international program (PSI) from the perimeter institute has a lot of good lectures for learning mathematical aspects of physics if you want a broad overview. And you can watch them for free online while doing your PhD. May 23, 2023 at 7:43
  • @N A McMahon Thanks so much!!
    – IGY
    May 23, 2023 at 10:16

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