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This is something that has been troubling me for a long while now. I am an undergraduate mathematics major (a sophomore), and I wish to apply to Ph.D. programs in pure mathematics in the future. I'm very passionate about research and academia.

On basis of what I've read on this website, graduate admission committees (mathematics) select candidates on basis of how capable they are of doing research in the future, and there are several indicators for this, of which grades are just one. Everyone knows that research in math and in general is a lengthy process. It is not like working on problem sets for courses or writing exam papers in 2-3 hours. It is a lengthy process in the sense that people take months, sometimes years to solve problems and publish papers (I hope that I'm right?)

That being said, to what extent are grades and potential for research (and in turn, graduate admissions) correlated?

While getting As does signify that one has probably mastered the material, is getting a few Bs really that bad? I'm sure this isn't something new that I've thought of, so how do graduate admissions committees deal with this problem - i.e. making sure capable and deserving candidates are not left just because of their grades (none less than B) in some courses?

P.S. We know that LoRs, and other things matter too - but I don't know how important each component is, and hence the question. This question specifically targets to ask how important grades are and how this obvious problem is addressed.

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    It is a lengthy process in the sense that people take months, sometimes years to solve problems and publish papers (I hope that I'm right?) Yes, e.g., en.wikipedia.org/wiki/Andrew_Wiles
    – user2768
    Mar 4 at 15:24
  • I'm under the impression that there are three different questions (explicitly or implicitly) present in the post: (1) To what extent are undergraduate grades correlated to personal potential for doing good research? (2) To what extent are undergraduate grades a good indicator that somebody will do good research? (3) How do admission committees select the candidates that get admission into a PhD program? These questions are, of course, related, but they are not identical. Could you please clarifiy which of the question you are interested in? Mar 4 at 17:25
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    My question is mostly about how admission committees use grades to judge whether or not a person deserves a place in the particular math PhD program. This is obviously related to the other questions, and it'd be nice if you could answer this in particular and/or throw some light on all three questions to some extent. Thank you so much! Mar 4 at 17:43
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    Do you want opinions or solid data on this?
    – user151413
    Mar 4 at 17:59
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    I don't think solid data is available - so opinions are all we've got. Though data is good to supplement any answer, in general - adds credibility! Mar 4 at 18:01
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Like most things, there is some correlation, but it's not perfect. In other words, good grades are an indicator of future success, but not proof.

This is why most places look at a wide variety of things, not just GPA or individual grades. In the US, letters of recommendation carry quite a lot of weight, for example.

No, a few B grades probably won't hurt (much), especially if they are in a topic that you don't intend to pursue further. Note that true insight into mathematics isn't uniform across sub fields. For example, I had great insight into real analysis and point-set topology, but very little in algebra or even in some other aspects of analysis. But I did fine, since I worked in an area where my insight was deep.

I'll note that when I took the GRE subject test in mathematics I was extremely discouraged when I left the test center. There were so many questions that I had no insight in to at all. But that was really because mathematics is so broad that no one (anymore) can understand all of it (not since the early 20th century, I think). I did well and got into good graduate programs.

However, don't neglect the fact that good programs are very competitive.

The key is to put together a complete application (including letters) through which a reader can have confidence in making a prediction of your future success. If you get to write a Statement of Purpose (SoP), make it forward looking, not just a recapitulation of what is in the CV. Goals, plans, ...

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  • "a few B grades probably won't hurt (much)" - Well, what are some ways in which one may be disadvantaged or hurt? Mar 4 at 15:29
  • "...don't neglect the fact that good programs are very competitive." - I agree, they are - but then how do they deal with the same issue? I mean, just because they are good programs it doesn't make sense to give more weightage to grades as opposed to other things? Mar 4 at 15:31
  • Indifferent letters of recommendation will probably hurt (US). Really good ones will overcome a few bad grades. But B's aren't really bad.
    – Buffy
    Mar 4 at 15:36
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    Absolutely. Primarily people who (a) know you well and (b) can confidently predict success. Note that what a professor writes about you reflects back on themselves as well, especially when they are writing to places where they know some faculty.
    – Buffy
    Mar 4 at 15:40
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    I would always suggest having someone in academia you trust read your SOP. A surprising number of otherwise good candidates get tripped up by writing an SOP they think looks sciency or mathy but is really just word salad. The admissions committee isn't a first-year TA who will give you a passing grade for that.
    – user133933
    Mar 4 at 16:07
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In good departments such as mine grades (GPA) are considered after other parameters: evidence of ability to do research, letters of recommendation, how good is the undergraduate University. We did admit a grad. student with undergraduate degree from Harvard and low GPA (she, unfortunately, did not finish her degree).

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  • And there might have been several reasons she didn't finish. It might have been unrelated to academics.
    – Buffy
    Mar 4 at 22:44
  • @Buffy: It was related to her grades in our courses. She failed my course, for example.
    – user135405
    Mar 4 at 22:47
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    Harvard is no guarantee of future success. Too many people think it is, sadly.
    – Buffy
    Mar 4 at 22:51
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    @Buffy: Everybody knows it but, nevertheless, a Harvard graduate has more chances to be admitted to our grad school than a graduate from North Dakota.
    – user135405
    Mar 4 at 23:42
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to what extent are grades and potential for research (and in turn, graduate admissions) correlated?

You need to be good enough: A broad understanding of your chosen research field is needed. That can be demonstrated by good grades. But good grades are neither sufficient nor necessary. (See Good Will Hunting for a dramatisation.) Grades have, however, become a heuristic for research potential. They're imperfect (and other factors are considered too), they're just better than other metrics. That's why you needn't have the best grades.

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    Hmmm, the movie mentioned twice in two days.
    – Buffy
    Mar 4 at 15:41
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    That movie is the most insultingly inaccurate depiction of mathematics research and of academia that I know of.
    – Alex B.
    Mar 5 at 9:42

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