[pocp2]

Terry was probably like 17 years old when he took his qualifying exam? Interesting quote considering his later work:

"After this, they decided to pass me, though they said that my harmonic analysis was far from satisfactory."

[impendia]

I'm a math professor. I like to point students to this when they have a rough time with their quals :)

[eitally]

I have read his summary of his qual linked here before, and upon reading it this time I also read a few additional. My takeaway is that it seems like it would be a lot of fun for the profs to conduct these interviews (most of the time, with probably a few utterly disastrous one thrown in for good measure).

Unrelated: why was your post not repliable when I first saw it? I refreshed the page a few minutes later and the reply button was there. No idea why that happened?

[impendia]

> a lot of fun for the profs to conduct these interviews

They can be. But it can get boring if your colleague wants to see the details of some boring computation. And, more seriously, it can be painful if the candidate is doing poorly. Fortunately I have not yet had to fail anyone.

> why was your post not repliable when I first saw it?

I believe there is a delay, the length of which is a function of how deeply nested your comment is, to encourage more top-level comments. (In particular, it tends to defuse arguments if you have to wait a long time to reply...)

[graycat]

One way to help get through quals: The quals are, on the surface, in some common justifications, to be more sure the student can do the dissertation research. Okay.

Well, there's another way to be "more sure", really, more reliable than any quals can ever be: Have the student do the dissertation research independently before the quals. Now in this case, just what are the quals for?

Or, for an engineering Ph.D., a guy writes a good dissertation in applied probability with careful attention to the tricky subject of measurable selection, and want to hold him back due to some qual with some tricky issue about Feller I probability?

Or, there's a qual in optimization, in part on the details of the Kuhn-Tucker conditions, but the student has already done original, clearly publishable work, e.g., in JOTA, in optimization and, in particular, the Kuhn-Tucker conditions?

E.g., for problems in functional form, are the Zangwill and Kuhn-Tucker constraint qualifications independent? Along the way, given a closed subset of R^n (usual topology), is there a function f: R^n --> R positive on the closed set, 0 otherwise, and infinitely differentiable (not quite the same as the Whitney extension theorem)? Is the Mandelbrot set closed and, thus, an example? What about a sample path of Brownian motion? So an infinitely differentiable function can have a bizarre level set? What does this say about a question, without an answer, in the famous paper in mathematical economics by Arrow, Hurwicz, and Uzawa? And in this case, the qual in optimization serves just what purpose?

The quals might be to see if the student is prepared to take advanced grad courses, but he's already done that and used some of the best content in his Ph.D. research? Now what are the quals for?

The quals can start to obscure a basic point about the three things important in high end academics, research, research, and research, that is, the publishable kind. If a guy is doing well in research, want to hold him back because of what?

Can there be such students? Yup. I have an existence proof.

Besides, quals can be awash in politics.

The usual criteria for publication are that the work be "new, correct, and significant". At some good research universities, there is no coursework requirement for a Ph.D., and the dissertation is supposed to be "an original contribution to knowledge worthy of publication" or some such. So, for a student, do some research and publish it.

As I recall, at one time the math department at Princeton said that the grad courses were introductions to research by experts in their fields, that no courses were given for preparation for the qualifying exams, that students were expected to prepare for the quals by independent study, and students were expected to have some research underway in their first year. Good. I'd done a lot of independent study before I went to grad school.

I got accepted as a grad student at the Princeton math department but went elsewhere (where my wife was still in grad school), brought my own research problem with me to grad school, and did my dissertation research independently in my first summer building on one of the courses in my first year. Then the quals were for WTF?