There have been undergrad and grad students who had solved an open math problem before they got their PhD, but for them getting a PhD was not even a question they consider, it’s just something that naturally happens. It’s not about credentialism, it’s about being smart enough, creative enough and hard-working enough to outdo the rest of the very crowded field in a particular area. If you are all that, writing up a PhD thesis is a minor step. And if you are not all that, why pick a field like math to begin with?
Just to TL:DR my comment above: to get a PhD is many times easier than to “accomplish groundbreaking work”, so if the former is an issue, you will never do the latter.
to get a PhD is many times easier than to “accomplish groundbreaking work”
Shminux,
I want to disagree with this statement. I guess it all depends on what you mean by “groundbreaking work”. First, it seems to me that most of the Ph.D. dissertations that I know of entailed discovering new theorems. Second, in my math department, it took 7 years on average to get a Ph.D. It often takes a lot less time to discover and write up a good, popular paper (say one with over 20 citations).
If you don’t consider a paper “groundbreaking” unless it has over 100 citations, then maybe you are correct. I just don’t know.
I was using the word “groundbreaking” in the sense of making an unusually significant advance in the field or solving an unusually difficult problem.
I have to admit I know only undergraduate calculus, so I made an assumption that the list I based this off of described such accomplishments.
If not, it still would show that most academically interesting math problems are solved by PhDs, and that people capable of doing the work tend to find the PhD an attractive/helpful way to get there.
There have been undergrad and grad students who had solved an open math problem before they got their PhD, but for them getting a PhD was not even a question they consider, it’s just something that naturally happens. It’s not about credentialism, it’s about being smart enough, creative enough and hard-working enough to outdo the rest of the very crowded field in a particular area. If you are all that, writing up a PhD thesis is a minor step. And if you are not all that, why pick a field like math to begin with?
Just to TL:DR my comment above: to get a PhD is many times easier than to “accomplish groundbreaking work”, so if the former is an issue, you will never do the latter.
Shminux, I want to disagree with this statement. I guess it all depends on what you mean by “groundbreaking work”. First, it seems to me that most of the Ph.D. dissertations that I know of entailed discovering new theorems. Second, in my math department, it took 7 years on average to get a Ph.D. It often takes a lot less time to discover and write up a good, popular paper (say one with over 20 citations).
If you don’t consider a paper “groundbreaking” unless it has over 100 citations, then maybe you are correct. I just don’t know.
I was using the word “groundbreaking” in the sense of making an unusually significant advance in the field or solving an unusually difficult problem.
I have to admit I know only undergraduate calculus, so I made an assumption that the list I based this off of described such accomplishments.
If not, it still would show that most academically interesting math problems are solved by PhDs, and that people capable of doing the work tend to find the PhD an attractive/helpful way to get there.
The kind of people who are interested in the problems of core math likely do seek a math PhD.
I would expect to the extend that people do groundbreaking work in math without an PhD they are more likely to do it for applied math.