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My friend loves mathematics and wants to continue research as a mathematics PhD student, but this doesn't seem possible!

She did a prestigious but inadequate bachelors program (almost no math) and because of this she is having a very hard time getting good grades for her master courses. Thus she feels she has inadequate knowledge for a PhD position; which is probably right.

Her thesis adviser told her that she cannot continue a career in research mathematics: no university would consider her given the situation now nor if she took an extra year or two to study more.

  • Question: Is this true? Does it really stop here?
  • I'm interested in similar experiences, opinions and suggestions (from experienced professionals).
  • I'm particularly not looking for a rosy picture!

In my opinion she is very talented, motivated, original and quick! She would flourish given more time to take specific foundational bachelor and deepening masters courses. Until now she performed extremely well (near perfect score) and this is confirmed by for example two scholarships she won (BA and MA).

PS. I tried to keep it terse but please ask for further details if needed.

Thanks a lot!

Update: Thank you all very much for the responses and useful comments.

It turns out that there is much more "staff rotation" in applied PhD programs and it seems plausible that she can find a nice position there; from which to continue her studies.

Thanks again.

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    $\begingroup$ She needs to consult someone who is realistic but more supportive than her advisor. It is not true that taking an extra year or two (or three) to study will reduce her chances. In fact, if she can afford the cost, I would encourage her to take as much time as she needs before applying to and entering a Ph.D. program to develop her mathematical knowledge and skills as much as possible before starting the Ph.D. program. To me the time matters far less than her strength when she does enter the Ph.D. program. $\endgroup$
    – Deane Yang
    Commented Feb 23, 2011 at 23:46
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    $\begingroup$ You left out an important detail, which is geography: where is this taking place? How far would she be willing to move to do a PhD (including another continent)? etc. All these are huge factors. $\endgroup$
    – Thierry Zell
    Commented Feb 24, 2011 at 1:05
  • $\begingroup$ I understood that she was in almost no math BA program. By indication that she ahas a hard time in getting good grades in MA program I suppose the MA program is closer to math. But what is really her MA program about, this is not clear to me from the description, and it seems relevant. $\endgroup$
    – Zoran Skoda
    Commented Feb 24, 2011 at 14:49
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    $\begingroup$ I would suggest a PhD degree in applied math and/or biosimulation. The following career history will be familiar to many. Undergraduate major in history, minor in linguistics: did not pursue further. Worked as a political operative for a losing campaign. Grad school in economics: dropped out. Grad school in applied math: dropped major. Grad school in physics: received PhD, found tenure-track job following two post-docs, but ultimately was denied tenure eleven years post-PhD. That student's name: Edward Witten. $\endgroup$
    – John Sidles
    Commented Feb 25, 2011 at 16:36
  • $\begingroup$ Ha :-) Great comments everyone... thanks! $\endgroup$
    – wires
    Commented Mar 15, 2011 at 1:48

7 Answers 7

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To supplement Kevin Lin's point about the Berkeley pre-PhD program, Smith College (in the U.S.) runs an analogous post-baccalaureate program that has been successful in placing students in various graduate programs. It seems a good fit for the situation and aspirations of the person described:

"This program is open to all women with a serious interest in pursuing a higher degree in the mathematical sciences."

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I'm not sure if we do it anymore, but Berkeley has (used to have?) a "pre-PhD" program. See page 25 of this. Probably some other schools have similar programs as well.

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  • $\begingroup$ Berkeley is the only school I've heard about with such a program, so it may be unique. It would be nice to introduce more, but I guess one problem is how to fund them. $\endgroup$
    – Peter Shor
    Commented Feb 24, 2011 at 18:14
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    $\begingroup$ Peter- Berkeley may be the only such school to have a separate program, but at Oregon, the default first year of graduate school is roughly comparable to the pre-Ph.D. program at Berkeley, in that one is taking essentially advanced undergrad courses (see this webpage: math.uoregon.edu/graduate/courses.php; the 500-level courses are also cross-listed as senior-level undergrad courses). I assume things are in practice similar at other comparable schools (but of course, I don't know them as well). $\endgroup$
    – Ben Webster ♦
    Commented Feb 24, 2011 at 20:56
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Her thesis advisor's opinion of her chances may weigh heavily in any PhD application packets, since the advisor would normally be expected to write a recommendation letter. Usually, if you are advising a very strong Master's candidate, you would not be dismissive of her chances, especially if she has offered to study for an extra two years to make up any gaps in her knowledge. I'm sorry that this isn't rosier.

But perhaps there is more to understand... There seems to be a contradiction in your question when you say she is having trouble getting good grades, but has at the same time won two scholarships and has near perfect scores.

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  • $\begingroup$ Thanks a lot for you comments; the bachelor she took was not in mathematics, but a ``University College''. There were little mathematics courses; Groups, Algorithms, linear optimization and I think that was it. She was admitted to a pure maths masters with single semester preparation where she took at least number theory and topology. All-in-all way less that what a regular bachelor student does; she does pass the masters courses, but obviously has a very hard time getting along. I hope this clears it up a bit. Again, thanks a lot; highly appreciated. $\endgroup$
    – wires
    Commented Feb 23, 2011 at 23:40
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I don't know whether this is true today, but 30 years ago I had the impression that there were Math Ph. D. programs in the United States that would accept anybody with a pulse, just so they would have warm bodies to put in front of their Calculus classes. Naturally, we're not talking about Princeton here, but there were (and are) a lot of Ph. D. programs in the US, and they couldn't all be real choozy. Where there's a will, there's a way.

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    $\begingroup$ Teaching Calculus classes - they needed warm bodies to serve as Teaching Assistants. $\endgroup$
    – Gerry Myerson
    Commented Feb 23, 2011 at 23:53
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    $\begingroup$ @unknown: Gerry is probably talking about the students having TA positions to teach the undergrad calculus classes. $\endgroup$
    – Josh
    Commented Feb 23, 2011 at 23:55
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    $\begingroup$ @unknowngoogle: Math departments use grad students to teach calculus, not take it. $\endgroup$
    – Jim Conant
    Commented Feb 23, 2011 at 23:59
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    $\begingroup$ @Ben, 30 years ago a foreign student asked me to write letters for her. I told her I would write that she was the 16th best student in a class of 23, and that I didn't think such a letter would help her much. She said that was perfect - she knew she wasn't cut out for graduate work, but her country required her to apply to grad school as a condition of paying her college bills, so she wanted a letter that would get her rejected. So I wrote the letters as requested - and a couple of places accepted her! I'll grant you that "pulse" and "warm body" were overstatements, but not by a whole lot.... $\endgroup$
    – Gerry Myerson
    Commented Feb 24, 2011 at 11:31
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    $\begingroup$ Gerry- I'm not disputing your experience. (Though you definitely should have said "a pulse and a BA.") But I still think it makes your answer less helpful and less convincing. Someone with a master's degree in math, even if they are a bit underprepared, can get into a much better graduate program than that, and that's a point worth emphasizing. $\endgroup$
    – Ben Webster ♦
    Commented Feb 24, 2011 at 19:10
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Here is a wild and crazy idea: answers to similar MathOverflow questions suggested going for a Master's degree en route to a Ph.D. Perhaps she (after finishing her current Masters) can enter another Master's program at the university in which she wants to do Ph.D. research. She can at least ask at that university what her chances are for trying such. (It may be possible to do cross discipline; for example a Masters in statistics or computer science might be acceptable before trying for a Ph.D. in mathematics.)

Gerhard "Thinking Outside The Normal Framework" Paseman, 2011.02.23

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Does she really need to become PhD Student in Mathematics? Why doesn't she try with something different?

I mean, a mathematician is, in my experience, not just a person who studies abstract mathematics. There are plenty of other occupations that involve the same skills and duties as pure mathematics. There is a lot of mathematics needed into other similar subjects, like computer science. Moreover, the interdisciplinarity of computer science should help her in getting such a position. Finally, original thinking and ability to formalize and being a hardworker are skills really needed and rewarded in this field!

To say my experience, I graduated in Mathematics (in the field of arithmetic geometry) but now I'm a PhD Student in computer science... and despite my lack of knowledge in specific topics, like programming, I feel I'm really helpful here!

Moreover, in some areas of Mathematics the research borders are quite far, so starting "late" could imply facing with difficulties in the future... or at least, I feel that this is what the most mathematicians think about this, and probably is the reason why she's having hard times in finding a PhD position in Maths...

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Getting top grades in GRE will probably help her a long way to get into a PhD program. Trying past and practice GRE exams will probably give her a good idea whether she is ready to face a graduate program in mathematics.

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    $\begingroup$ -1: Sorry. But I really think the GRE is a terrible indicator of whether or not someone should be working towards a PHD in Mathematics for the next 4-5 years. There are an enormous number of things that will help you much more than studying for the GRE. $\endgroup$
    – Eric Naslund
    Commented Feb 24, 2011 at 0:32
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    $\begingroup$ An exceptional score in the subject GRE might help, but even then I'm not sure and it would be hard to get. The general GRE would not help at all. $\endgroup$
    – Thierry Zell
    Commented Feb 24, 2011 at 0:59
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    $\begingroup$ I'm ambiguous about this advice, but I'm not sure I vote against it -- I think a lot of top programs essentially ignore GRE scores as they count as a low-level indicator compared to someone who's already written a research paper, or has a really wide basis of knowledge in the field, but outside of this handful of places a stellar GRE score might grab someone's attention. I also slightly disagree with Thierry in that I think a stellar score on the general GRE with an unusual background would interest me more than a high score on the subject test (which is pretty mundane as a mathematics test). $\endgroup$
    – Kevin McGerty
    Commented Feb 24, 2011 at 3:34
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    $\begingroup$ In my experience with graduate admissions (Harvard, University of Washington) the math subject GRE score is important---certainly much more so than other comments above suggest. For example, the Berkeley math grad application page says "Experience has shown that the score on the Mathematics Subject GRE is a partial indicator of preparation for Berkeley's PhD program. A score below the 80th percentile suggests inadequate preparation and must be balanced by other evidence if a favorable admission decision is to be reached." See math.berkeley.edu/graduate_phd.html $\endgroup$
    – William Stein
    Commented Feb 24, 2011 at 19:20
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    $\begingroup$ I'm going to second the impression that this probably deoends on the program. I was once asked if I wanted to read some graduate applications at a top program. Once we sat down with these big files full of scores and statements and what-not, I asked what to do and was told "just read the letters" $\endgroup$
    – Ramsey
    Commented Feb 24, 2011 at 20:28

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