Are there any fields that are unusually difficult to get a PhD in due to lack of new contributions?

I asked this question in GQ earlier about how people in math graduate school come up with new topics for a dissertation. The description was different than I was used to but I am convinced it isn’t hard for math PhD students to come up with something new to work on.

That brings us to this question. Are there any fields or subfields that are so well-defined now that work has mostly stopped on them. I may be off-base on this too but I presume it is hard to get a PhD in English if your study is Shakespeare for example just because so much has been done on it.

I realize that whole fields haven’t come to a grinding halt but what about bigger subfields that reached just about everything they can do? Any examples are appreciated. Ranking the level of new knowledge should be taken into account as well. I did behavioral neuroscience which is still wide open. Astronomy seems to be pretty open as well for example. Musicology, maybe not so much but what do I know?

The major disciplines keep morphing to accomodate new things, but the subfields die out. Electrical enginneering used to be all about motors, generators, and electrical distribution systems, but those have largely faded, though not completely. There are still a few getting Ph.D.s working on exotic forms of vacuum tubes, but I don’t think anybody is working on galena crystal radio detectors. The fad in condensed matter physics is Graphene, but that will fade away and be replaced by other things, like topological insulators, or some other cool but esoteric topic.

Geometrical optics, maybe.

But it all depends on how narrowly one is allowed to define “field.”

I vote for none.

It’s hard to imagine any science that is closed off. We don’t know anything about anything. Older technologies may be gone, but the trend for generations has been combining subfields, quantum chemistry, or ecological geology, or multi-dimensional archaeology,

The social sciences can always study people, and people are forever changing. They do the combinetrics things too.

It might seem as if the arts would be studied out, but in fact the greatest wave of new fields in English and all allied arts have come since WWII. Semiotics, deconstructionism, postmodernism, gender studies, queer studies, genre studies, popular culture, visual artforms, computer worlds, the list grows every year. They mean that you can look at Shakespeare or anybody else in completely new ways, that you can examine history for things that the old professors never even realized were issues, that art is a complete plastic morphing everything encompassing every facet of existence.

Just try to be a generalist these days. It’ll make your head explode. Being a specialist has never been easier.

Look at knowledge like an expanding balloon. The more you put in it, the larger the surface area between the known and the unknown.

And as pointed out, the path to Ph.D. is about specialization – you learn more and more about less and less until you know everything there is to know about nothing at all.

Never saw anyplace offer a degree in “Geometrical Optics”. There are plenty of new opportunities opening up in Optics, and several places give degrees in Optical Engineering.

But, even taken at face value, there are still developments in straight Geometrical Optics, as the continuing flow of papers to JOSA A (The Journal of the Optical Society of America, part A – devoted to "developments in any field of classical optics, image science, and vision. " according to its website) shows.

Two great quotes! Are they yours, may I ask? (Just wanted to know to whom I should attribute them, not questioning your honesty.)

could you please clarify the electrical engineering bit? Are you saying that at this point power engineering worldwide is down to training professionals with undergrad and MS degrees to keep the industry running and that there is no more space for research in the field? Or are you just referring to a lack of interest and grad programs in this field specifically in America?

On the face of it, making power distribution networks more stable and efficient sounds like a research area about as broad and endless as curing cancer. But I am a non specialist, obviously.

The second one goes back to at least the 1930s.* It’s referred to as if it’s a common phrase then. It’s the standard phrase for anyone getting a Ph.D.

I can’t find the first, though. That looks original to SmartAlecCat.
*There are many earlier dates in the hits, but those all look to be runs of journals. Google Books has the strange habit of dating them by the first volume in the series no matter the date of the actual entry.

In retrospect, this was probably a bad example. You are correct that there is plenty of work in power engineering, smart grids, etc, but the focus would be dramatically different from 100 years ago. My point is that, especially in technology, the discipline morphs considerably. You wouldn’t be able to do a thesis on a vacuum diode of the type used in garden variety radios of the 1950’s, but you could do one on a vacuum tube for producing terahertz radiation.

The *knowledge as balloon *metaphor is also real old. I think **SmartAlecCat **told it in a very nce clean way, but (s)he’s far from the first to think of the idea. Or to write it down.

Neither are mine – I’ve heard both for years.