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I've posted a few questions here in the past couple of days regarding grad school decisions; apologies for asking so many! It's a big decision and I want to do it right, but I don't want to bombard this forum with too many nitpicky questions. This should be the last one! The previous two are here and here, if you want additional context for this.

The gist of it is: I did my undergrad major in math and linguistics, and I'm looking to pursue research at the intersection of the two fields. For various reasons, it seems the optimal path is to come at this largely from the math side rather than the linguistics side. So I applied to grad programs in both fields, hoping to get into a math PhD. Instead, I got in to a few math Masters programs (at respectable, though not top-ranked, schools) and a linguistics PhD program at a top school. The PhD program also seems like it will offer me the chance to take some math classes along the way, and to pursue some generally math-heavy research topics. This, along with the fact that the degree is fully funded, made it very attractive, and I ended up selecting this school on the April 15 deadline.

However, now I am having some regrets. I feel like choose a math program would have given me much greater flexibility, and perhaps afforded me the chance to research other math topics that I really like (e.g. knot theory) that don't have much to do with linguistics. I am fearful that, by choosing this linguistics degree, I may have locked myself out of ever touching certain areas of math, whereas choosing a math school would given me the option to work on applied problems in linguistics and pure math problems, eventually in my career. I also heard something to this effect directly from a former professor of mine, and with this in mind I am having some serious regrets.

However, I see one option (though I'm not sure I really want to take it, but I at least want to consider it): perhaps, since it is still the weekend, I can contact one of the math programs whose offer I declined and let them know I have changed my mind, and see if they still have a spot for me. I am not sure if this would be the right decision, and even if it was it feels like a long-shot, but perhaps it's the right gamble to take. Apparently, others here have considered similar questions before, but their situation seems different enough from mine that I think posting my own question is probably warranted.

My main concern is that, because I've already accepted the offer to the linguistics program, contacting one of the math programs in this way would be against the rules (I am not totally sure?) and could get me rejected from both for some kind of ethics violation. I would really not want this to happen, so I want to double- and triple-check before I even consider this. It is worth noting that both of these programs are part of the same state university system (this is in the U.S.), and so I fear that contacting one would quickly get back to the other and possible hurt my reputation there.

Does anyone have any advice on what to do?

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    "For various reasons, it seems the optimal path is to come at this largely from the math side rather than the linguistics side." There is no "optimal path". It's impossible to meaningfully predict your career based on vague generalities about it being easier to move from math to linguistics. The specifics of the two programs are much more relevant. What you're doing is imo the very definition of letting the perfect be the enemy of the good. Rejecting a fully funded Ph.D. at a top school, after you accepted it, for a Master's based on vague generalities and speculation is imo not a good idea. Commented Apr 18, 2022 at 11:57
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    Beware of the lure of the road not taken (greener grass, etc). Whenever you have to make a choice that closes other avenues, it's easy to panic at the loss of opportunity - that does not mean that you've made the wrong choice, only that you've made a choice. Any choice you take will cancel others, and that loss can be painful. Learning to accept this is the only way to avoid living paralysed by indecision. For what it's worth, I think you've made the right choice. Good luck.
    – Ottie
    Commented Apr 18, 2022 at 18:16
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    You should never, ever, ever do an unfunded master's degree that won't immediately lead to a well-paying or at least secure job, unless you're already independently wealthy. All the less given that you actually have a good option available. Commented Apr 18, 2022 at 22:05

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[this] would be against the rules (I am not totally sure?) and could get me rejected from both for some kind of ethics violation.

The current version of the "rules" only require you to inform your linguistics department if you decide to renege on your promise to attend. You don't even need their permission.

see if they still have a spot for me...I fear that contacting one would quickly get back to the other and possible hurt my reputation there.

You should only do this if you have definitely decided to change your mind. Telling the math department that you want your offer back, only to reject it again, would be sub-optimal. And telling them that you may want your offer back does not make much sense.

But if you have actually changed your mind and definitely would accept an offer from the math department, then all the advice from the question you linked applies -- namely, the decision could go either way, probably depending on how many students accepted their offers before the deadline, relative to their target number. If your math department knows about your commitment to the linguistics department, it does not seem impossible that they would seek an OK from your linguistics department before extending you another offer - all the more reason to be sure before you ask for your offer to be reinstated.

As for your reputation: it's true that wishy-washiness and reneging on commitments may hurt your reputation, but it's also very understandable this early in your career. I seriously doubt it will do any real damage.

Does anyone have any advice on what to do?

I'm neither a mathematician nor a linguist, but for what it's worth...I think you made the right decision already. Accepting an unfunded offer is usually a mistake. The linguistics program will probably be happy to let you pursue as much math as you want (whereas the math program may limit your time devoted to linguistics). The thought that "once you know the math, the application domain is trivial" is not always true (relevant XKCD). You may find that working with math, linguistics, and computers will give more career options post-PhD than pure math. And finally, the fact that you've already made this decision and chose the linguistics program is an important data point...it's a good rule of thumb to never reverse a done decision unless you have a really solid understanding why that decision was incorrect.

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    +1 for: "it's a good rule of thumb to never reverse a done decision unless you have a really solid understanding why that decision was incorrect." Commented Apr 18, 2022 at 12:01
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I think your best option is to stay put

Adding to cag51's excellent answer - I think your best bet is to stay put. It sounds like you're a good fit for your current program. I think what you're experience is somewhat common, and normal - just don't act on it. There is a good chance your fears will calm themselves.

You've just been through months of extra studying for the GRE, getting great letters of recommendations, and crafting great applications to the schools you choose. You spent hours or days researching the schools, weighing where you'd be happy to spend the next several years of your life there.

You've spent months with what-if scenarios and day-dreams about what life would be like at each school. Since you accepted the offer, all those vague what-ifs are being replaced by concrete things. Some of which are not as good as the fantasy that came before. That's normal.

The reality is you will never have enough time to pursue every interest you have. The good news - you found a program that lets you focus on 2 very different fields.

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(Disclaimer - I did not do my PhD in the US, so maybe there is something that makes my suggestion harder in the US, but here goes:)

I think that you cannot fully know if a PhD program is right for you before you have actually tried it -- in either direction. Since you have obtained and accepted this very good place with funding, why not give it a go and see how you like it? As a student, it first feels like a catastrophe if it turns out that you didn't make the right choice for your PhD (speaking from experience), but that can happen to anyone, regardless of how certain they are beforehand, and it does not have to be a final choice.

If, next year, you find that the linguistics degree is not what you want to do, why not re-apply for maths PhDs then and see if you can get a good funded place at that point?

It sounds like there's a good chance that you'll love this program and will never think about changing, but if you do want to change later, you can still do it at that point.

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    This is probably good advice, thank you for the answer. Since I'm doing my PhD in the US, is there anyone familiar with the US system that can attest to any difficulties with this?
    – Max
    Commented Apr 20, 2022 at 6:55

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