Can research breadth be a downside when applying for doctoral positions?

Question

I'm going to apply for a doctorate position in mathematics soon, and I'm wondering if my breadth can be of any disadvantage. I have two MSc degrees, in mathematics and engineering respectively. The past years I've coauthored papers in different field on the side, all of which had novel content. My work has ranged from pure math, nanotechnology, to high performance computing and numerical analysis.

I'm wondering if this can be held against me when applying for a more "pure" math doctorate. As a side note, in my country a doctorate is the latter part of an American PhD, after you're done with the coursework and you mainly do research. So, the main focus will, of course, be on my research aptitude. I have demonstrated this through my work, and also by participating in competitions/conferences.

By the time they decide I will also have had some applied/industrial math experience, working for a research institute, and I have teaching experience with undergraduate courses.

Would I seem a much less interesting applicant than someone who has only focused on pure math, but doesn't have the same research experience (which is often the case)?

Answer 1

You could say something like:

"I've done a pretty wide range of different things, trying to find out where my true passion lies. Getting multiple masters degrees shows that I'm not a dilettante, I get stuff done. And it's been an enriching experience, letting me see the connections between different fields. But after long consideration I've decided pure math is what I want to settle down on."

And it has the virtue of being true (from what I read in your question).

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Consider what a professor might think, while reviewing two candidates, one pure math straight up, and you who's tried several different things and finished them.

• The pure math student might have a lead on you in pure math.
• You've demonstrated persistence and an ability to get things done. Likely, you will also get a PhD done.
• You've shown that you're mentally flexible enough to master multiple different subject fields.
• The math student might at some point decide he's not seen enough of the rest of the world and worry if staying cocooned in pure math is really what he wants. You on the other hand have tasted the various forbidden fruits and decided this is really the one you want.

Just on the surface like that, you look like a candidate worth interviewing.

Answer 2

As long as you have the required background and the commitment to study deeply in a field you should do fine. I doubt that anyone would hold other experiences against you. But you will need to be clear in your SoP for study in mathematics that you are serious about mathematics and have the desire to go deep into some relatively small area to do the required research for a dissertation. If you say you want to study all of these things equally in the future you might not be taken seriously.

But the only way to know for sure is to make application and show that you are a good candidate for success. In Europe (I assume UK or EU) you might need to convince an advisor of your seriousness to achieve admission. You seem to understand that doctoral study is narrow and deep, so I'd guess you can make it work.