I found the claim in the title a bit astonishing when I first read it recently in an interview with Michael Rapoport in the German magazine Spiegel (8 February 2019). And I was wondering how he comes to that conclusion. Here is the article, but the full interview is not available for free, so I will paraphrase the relevant part.
Rapoport talks about dead ends in mathematics and brings up class field theory as an example. He basically says: Class field theory had been proven nearly 100 years ago, and, after that, researchers spent about 70 years to turn it into a satisfactory theory. However, along the way it was realized that the original goal of class field theory had to be abandoned because it did not turn out to be fruitful.
I had only few contacts with people class field theory but never had the impression that number theorists were thinking about it in this way. So I wonder how to interpret Rapoport's claims. I think it boils down to the following questions:
- What were the original goals of class field theory?
- Why did it not turn out to be fruitful, and is this failure somehow quantifiable?
- Are there new ideas the take up the original goal?
- Is class field theory rendered obsolete by more general ideas?