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.