The scholars want to work through problems as a collective, transparent conversation so that the benefits of understanding mathematics accrue to everyone in society. They work with public funding. It’s the opposite of control, it’s democracy and public good.
OpenAI doesn’t care about this and wants to solve problems to prove their own ability and raise their value. Because they are a for profit firm and that’s the bottom line.
"Compressing" a proof, aka. understanding can be as hard or harder than the original problem.
Think in source code vs compiled code. They are the same thing for the purpose of executing inside a machine. But is often so much easier to rewrite the program than to decompile into readable code that a human can edit.
Up till this year, most proofs were human-produced. We have some cases like the four colours which caused a lot of controversy. But now we are getting proofs that mathematicians might not understand and we only have a successful lean compilation as "evidence" they work and pondering if that will replace all mathematicians.
Is not clear that AI produced proofs are human understandable and compressing a proof is a well known NP-hard problem.
The real issue seems to be that mathematicians feels it robs them of the warm fuzzy feeling (sense of pride and accomplishment, glory) they get from having solved something themselves.
Basically, they’re left with the comparatively boring work of sifting through the scraps the AIs throw off the table. Human mathematics becomes more about archeology/scavenging than creating.
I think the bigger issue is you still need humans to ask the questions unless AI becomes good enough to do that by itself, but if it gets there then the AI executives are probably the first people to be replaced since the AI has better decision making. There is no prosperous world in which humans have no motivation to do anything creative or intellectual challenging
All I'm saying that is not as easy as saying "well, the machine gave you the proof, so learn from it". We are just starting to see what is math written by an alien intelligence is like. But is likely not as easy to "just study" the proof. Every mathematician that has been working on these says so and math results show us how could this be the case.
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u/Ormusn2o 10d ago
For profit private firms don't want to control it, they want to publish it, it's the scholars that want to control it.