I started off this recent threat about advice to graduate students with this contribution (also see here). Peter Klein was kind enough to contribute with these insights.

Superficially, Peter’s contribution might be seen as conflicting with mine, but I see it as more of a complement to what I said than a substitute for it. I advised students to put the blinders on, and do nothing apart from studying for their courses, for their comprehensive or oral exams, and writing their dissertations. Don’t teach, don’t be a research assistant, don’t do anything else except get that phd degree. Peter, in seeming direct contradiction to this mentioned the benefits of working with mentors, teaching a bit so as to be more competitive in the job market, etc. Peter, I think, was implicitly advising graduate students who were doing very well in their course work; I, on the other hand, had in mind students who were doing poorly, were on the verge of failing out. This might possibly reflect the different experiences Peter and I had in graduate school (I failed my first comprehensive exam, I almost failed to defend my dissertation — I think Peter did far better than me in this experience), and also the different experiences students of ours have had in graduate school. Although some of my undergraduate students were wildly successful — both in grad school and afterward (I would mention Andy Young, Ed Stringham and Dan D’Amico in this regard), all too many of my other equally excellent undergraduate students did not obtain the phd degree (Every time that happened I felt I was kicked in the teeth). Also, perhaps, I am more impressed than Peter with the fact than many excellent students leave grad school with an ABD (all but dissertation); that is, fail to obtain the phd. I think Peter and I might well agree that in the first year or so, before a student knows whether or not he is flying high, he should stick strictly to bidness (as we say in the south). Only afterward, if the student is earning excellent marks should he follows Peter’s advice; if not, I imagine, Peter would support my own suggestions, for marginal students.

I also want to thank Butler Shaffer for chiming in with another excellent contribution to this thread. Butler raises the issue of whether the grad student should try to get into the most prestigious school that will accept him (implicitly, other things being equal, such as amount of work required, scholarships, student loans). The usual procedure is to apply to two or three “reach” schools, two or three universities at which you think you have a reasonable chance of being accepted, and two or three “insurance” places you are sure to be accepted by. (This applies to applications for both graduate and undergraduates). I earned my degree at Columbia University, certainly a prestige institution of higher learning. I am glad I did. I think this helped me in my many job searches. So I agree with Butler on this. The only reservation I have is that some prestige universities accept many more students than they expect to award phd degrees, and flunk them out in the first year or so. Unless you are an exceptionally strong student, I suggest you would be better off at a more moderately prestigious place that did not follow this policy.

The Best of Walter E. Block