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.
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.