The primary motivation for math is not to check off proofs, but to understand the universe.
A proof itself is only an articulation of understanding. Traditionally having one was evidence you had an insight. But if a computer generates 10,000 pages of technical goop then we don’t learn anything.
For example if tell you P=NP with no other information, it doesn’t change anything. There are mathematicians who believe and act on both conditions. What we hope a proof would reveal is how a verifier could be used to derive the solver (even if doing so was impractical).
Why doesn’t the author even mention this and immediately jumps to utility arguments for why the research is important for the government to fund?
groundzeros2015 · · focus · HN ↗
A proof itself is only an articulation of understanding. Traditionally having one was evidence you had an insight. But if a computer generates 10,000 pages of technical goop then we don’t learn anything.
For example if tell you P=NP with no other information, it doesn’t change anything. There are mathematicians who believe and act on both conditions. What we hope a proof would reveal is how a verifier could be used to derive the solver (even if doing so was impractical).
Why doesn’t the author even mention this and immediately jumps to utility arguments for why the research is important for the government to fund?
treszkai · · focus · HN ↗