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Comment by awelkie | Hacker News Reader

I think it depends on the field. In mathematics I think the expectation is that students need to study for a few years to even understand what the open questions are, and only then can they begin the research.

I'm fully aware of what the point of a PhD is. I wasn't expecting to become a generalist, but I was expecting some time to study some recent results and come up with a tractable research proposal. Indeed, if the purpose of a PhD is to expand the totality of human knowledge, why was it expected that I would publish 3-4 conference papers to graduate? Wouldn't one significant result have been enough?

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> Indeed, if the purpose of a PhD is to expand the totality of human knowledge, why was it expected that I would publish 3-4 conference papers to graduate?

This is a question that bothers me quite a bit with respect to EECS (electrical engineering and computer science). In mathematics, one's PhD thesis can often serve as one's first paper (once revised). Funnily enough, the same was true for EECS even at the top tier places in the 1980's - I know of a case at Caltech where the student did not have any publications prior to graduation, and yet went on to become a successful professor.

Is it really true that humanity is producing more knowledge in EECS today per student than it was in the 1980's? I seriously doubt this. In my experience, instead what has happened is that the average "delta" in a conference proceeding has gone down significantly, in spite of the vast increase of words like "novel" and "new" being used, and the ballooning of the average paper length.

In mathematics on the other hand, top quality authors freely admit that a lot of their work can be "implicitly" traced back to the "big names" of the past; indeed this has to be done for conceptual and historical clarity.

I see that you mention Peter Sarnak in your top comment. Peter Sarnak has a a wonderful article at the very end of "The Princeton Companion to Mathematics" on his advice for students. Among other things, he stresses the importance of the "history of ideas", and how it often brings clarity to an entire field.

Thanks for the pointer to Peter Sarnak's advice. I believe this is the history of ideas advice you were referring to on pg 1008 (1031 in pdf):

When learning an area, one should combine reading modern treatments with a study of the original papers, especially papers by the masters of our subject. One of the troubles with recent accounts of certain topics is that they can become too slick. As each new author finds cleverer proofs or treatments of a theory, the treatment evolves toward the one that contains the “shortest proofs.” Unfortunately, these are often in a form that causes the new student to ponder, “How did anyone think of this?” By going back to the original sources one can usually see the subject evolving naturally and understand how it has reached its modern form. (There will remain those unexpected and brilliant steps at which one can only marvel at the genius of the inventor, but there are far fewer of these than you might think.)

Often one "significant result" has to be serialized into 3-4 conference papers in order for it to be digestible and reviewable by the referees.

There are exceptions of course, like Gentry's fully homomorphic encryption, but those are increasingly rare.

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