Switching from physics to math PhD with NSF GRFP

Question

I will graduate this semester with a bachelor's degree in physics (in the US). I applied for PhD programs in physics, but have come to realize (rather late in the process) that I want to pursue a PhD in mathematics. However, I was accepted into two physics PhD programs and received the NSF GRFP. These two schools have respectable math departments.

As for my background in math, I have taken much of the undergraduate curriculum (linear algebra, algebra, complex variables, Lie groups, two differential geometry courses, algebraic topology); I have also taken around 10 graduate courses in physics, including quantum field theory. But I am missing core coursework in analysis. I am interested in studying low-dimensional topology, gauge theory, mathematical physics, and related topics in math grad school.

Technical details about the NSF fellowship (more here):

• It can be transferred between institutions (e.g., from master's at one school to PhD at another).
• Changes in the field of study can be proposed after the first year, and require approval by the NSF. My awarded field of study is condensed matter physics.
• It cannot be deferred; once accepted, I must enroll in a graduate program this fall. Or I can decline it and re-apply in the future.
• Once accepted, I can choose to use the funding for any 3 of the next 5 years.

Given these constraints, I am considering the following options:

1. Accept an offer at a physics PhD program. Re-apply to mathematics PhD programs after 1-2 years, leaving the physics program with a master's degree. Defer the NSF funding for two years, until beginning a math PhD program.
2. Apply to math master's programs still taking applicants. Use part of the NSF fellowship for the master's. Apply after 1-2 years of the master's program to math PhD programs.
3. Decline the NSF fellowship and take a gap year before applying to math master's or PhD programs.

Given my circumstances, do you think it is wise to pursue one of the options above for graduate study? Any other suggestions are welcome. (I am also not completely savvy with the NSF guidelines sketched above, so please correct any misconceptions.)

Answer 1

I do not think you should turn down the money unless you have a much higher-paying job lined up for your gap year. Looking at the rules, that implies you should enroll in a physics program in the fall. Switch to a math program as soon as the GRFP rules allow; that is after one year.

If you bring GRFP funding with you, most universities will let you do whatever you want so long as they get their share of the money. They won't mind that you do not know analysis. Clearly you are able to learn it.

You cannot enroll in a math masters the first year and keep the GRFP funding.

A master's in physics is virtually useless to a math PhD. I suppose you could use it to teach both physics and math at a college that is too small to support a physics professor.

Thanks to inflation, the GRFP has lost a large portion of its value.

Answer 2

Actually, the first thing I'd try is to talk to the math department at the places you were offered a physics slot, preferably in person. Ask them if there is any chance of giving you a math slot instead. I'd guess that the chances of this aren't very high, but it would be a shame not to ask.

Maybe cag51 will expand his comment into an answer, which would be the second thing I'd try.

It is likely that math and physics are in different departments, but there might be some coordination, especially among individual researchers.

Otherwise my own preference would be for your option 1, which seems far better (to me) than the other two. But that is my value system and yours may differ.

Answer 3

In addition to talking to math and physics professors at the University that admitted you, you really need to read the entire set of rules. Twenty-five pages is not long by NSF standards. In particular, you are considering a deferral for a reason other than a medical or military reason. You might qualify for reserve status, if you can fund the first year another way.

These awards are somewhat prestigious. For example, universities put out press releases sometimes when a current student gets awarded one. It is something worth listing on your CV for the first few years after graduation.

There may be a mathematically oriented program in the physics department. Something that is not a waste of time if you switch to math after one year. Something you might find interesting if you stay in physics.

Theoretical condensed matter physics today is dripping with modern math. Operator theory, C*-algebras and homotopy theory with a side-order of machine learning.