alt Hacker NewsIt would be nice if someone used AI and/or Lean to sort out the abc conjecture, an important unsolved problem in Diophantine analysis. A mathematician (Mochizuki) claimed to have proven it in 2012 using a new theory called "Inter-universal Teichmüller theory" that almost nobody understands. Some mathematicians think the proof is correct while the majority don't. So the conjecture is in this annoying limbo where its status is a social construct rather than a decided fact.
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That's true of the entirety of mathematics. Its validity is a social construct. That is not to relativize it entirely, but much of what was considered good and sound mathematics in the ancient Agean for example would now fall way short of what mathematicians consider valid proofs.
Mathematics is a human endeavor funded on communicating and sharing mental constructs. Some are useful but most of it is not about producing useful things, quite the opposite in fact.
Gödel showed you need to agree on definitions to even do any valid mathematical construct.
Truth is also ill defined. That's what I don't get about generating math with LLMs. Who cares if you make hundreds of pages and lean code and it gets a thumbs up for logical validity? Mathematics is so much more then concatenating valid logical statements.
I'm sure over the next 6 months both OpenAI and Anthropic are going to continue pouring many many millions of dollars into any famous open mathematical problem like that. There is a limited pool of problems which have held prestige for enough time to make general news headlines when solved and you don't really get nearly as much limelight for proving it the second time or adding in proof for additional cases/forms.