5 days ago
- Conjectures vary in difficulty and type, from easily reachable to those requiring multigenerational effort.
- The value of conjectures is often judged by their interestingness and truth, which can be subjective and self-referential.
- There is a bias in mathematics toward proving conjectures rather than disproving them, with institutions and journals rewarding proofs more.
- Disproving conjectures is valid and constructive, offering opportunities for new insights and counterexamples.
- Researchers should embrace conjectures, test them computationally, collaborate, and be open to disproving them.