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I am currently getting my M.A.T. in secondary mathematics. As a part of my degree, I take graduate level math courses. I am currently in a PhD level math class, and the instructor of this course has told me that if I want to get a PhD in mathematics he would want to work with me because he believes I have a "future" in his subject area.

My question is, what is the value of his offer? Is his kind of offer easy or hard to come by?

The mathematics department at this school is not renowned, but I respect this professor's work. Is his offer something I should definitely take advantage of, or should I shop around for different universities/offers?

I hope my query isn't too specific. I am feeling quite conflicted and would appreciate any and all input.

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The easiest way to get into a Ph.D. program is to have a professor who knows who you are and wants to have you as a student. In many other questions on this site, people talk about the difficulty of standing out from the crowd amongst the large number of applicants to any decent Ph.D. program. With this professor, at least, you have stood out, and that's quite significant... if you want to do a Ph.D. with them.

First a sine qua non: don't even consider it if the program doesn't guarantee some degree of funding. Every respectable university should be offering support for its STEM Ph.D. students through some mix of research and teaching assistantships. It should be the department and not the professor that guarantees funding (though if the professor has funding, they may be able to give you more time as a research assistant rather than a TA, if that is what you both want).

Beyond that, key things to ask yourself:

  1. Do you actually want a Ph.D.? Getting a Ph.D. is a terrible, soul-wrenching process and it renders you unfit for most employment. If you are truly drawn to research, however, it is the best and only course to take.
  2. Are you OK with not being at a famous institution? There are only a few famous institutions in any field, and getting into them is a gamble. Often, however, there are a great many solidly respectable institutions that can launch you on a totally reasonable career, especially since it is often possible to "upgrade" institutions through postdocs.
  3. Do you really want to work with this professor? You don't know what working with this professor will actually be like. One advantage of the high-profile institutions is that if you find things aren't working with your advisor, there are often many opportunities to switch to others. In a smaller and less renowned department, you will likely have less alternatives should things go wrong.

Ideally, if you answer yes to all of these questions, you should start doing some work together now, so that you can get a sense of whether there's a good working relationship. If so, embrace it and be grateful that you found a good match.

  • Unfortunately, no one can be told what the Matrix is. You have to see it for yourself. – Danny W. Nov 2 '14 at 15:34
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    I like the rest of the answer but: "Getting a Ph.D. is a terrible, soul-wrenching process." C'mon. That's a bit dramatic. Getting a PhD is not always easy but it's not necessarily terrible and soul-wrenching. I know it's not everybody's experience but I found getting a PhD to be wonderful, fun, challenging and exciting and with less frustrations that my previous work in industry. – Benjamin Mako Hill Nov 2 '14 at 19:57
  • "Getting a Ph.D. is a terrible, soul-wrenching process." This reminds me of the joke that doing a Ph.D. is much like trying to take the Ring to Mordor. See: danny.oz.au/danny/humour/phd_lotr.html. – Stuart Golodetz Dec 29 '15 at 14:36
  • Also that line from the first LOTR film that explains Ph.D. students: "They were elves once. Taken by the dark powers, tortured, mutilated. A ruined and terrible form of life." I guess that makes postdocs Uruk-Hai? :) – Stuart Golodetz Dec 29 '15 at 14:40
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Whenever you get an offer, always shop around. That is not academia-specific.

Generally professors who work in Ph.D. granting programs want to have Ph.D. students. It may even be necessary for them to get some Ph.D. students in order to keep their jobs. Therefore it can be easy to find a faculty member who will encourage potential Ph.D. students. I would not put much value on this sort of offer unless it includes and offer of RA or fellowship funding.

Never get a Ph.D. to please a professor; do it only for your own benefit.

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