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?
Because the question that belies all of this is whether still makes financial or economic sense in the age of LLMs for tax-payers to fund mathematics research.
Up until recently, they've had a true ivory-tower to dismiss such criticism, but as LLMs have demonstrated, that approach won't survive going forward, so pure mathematics are up in arms. They genuinely don't know how to justify their jobs.
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?
infamouscow · · focus · HN ↗
Because the question that belies all of this is whether still makes financial or economic sense in the age of LLMs for tax-payers to fund mathematics research.
Up until recently, they've had a true ivory-tower to dismiss such criticism, but as LLMs have demonstrated, that approach won't survive going forward, so pure mathematics are up in arms. They genuinely don't know how to justify their jobs.
groundzeros2015 · · focus · HN ↗
Math was always a few levels removed but somehow sneaks in with engineering and basic science.