A Discussion on Relevance and Interest
What are interesting theorems?
Discussion with George Barmpalias (November 14th 2008):
- A theorem is interesting if many people have tried solving it and failed. This information is communicated within the respective communities, i.e. scientists become aware about what theorems are interesting in their community and who tried to proof it by talking to each other. Sometimes this can also be seen based on open questions of papers or books, as these have been considered by the authors (it would be rather embarrassing to not try solving them, if they would turn out trival)
- Theorems for simple problems that are hard to proof are interesting.
- Proofs for complicated statements are not interesting, as they do not have any simple consequences.
So what makes a proof complicated? What is a complicated theorem? What are examples for interesting theorems?
- e.g. P = NP
