Difficulty in verifying and explaining AI-generated mathematical proofs and discoveries

Signals over time

6 observed signals across 1 sources, tracked for 7 days. Confidence: low.

What people are saying Observed

• “As a software engineer, I can accept AI-generated code because the code is not the point of software; the point is software that works, and the code is just a means to an end. Code is usually a terrible mess and essentially no one just reads code, like, for fun. In the spirit of this article, I would love for someone more knowledgeable to articulate what the end product of mathematics is. Is it, as this article mentions, the abstractions that it produces? I've always been fascinated by how the Fourier transform and the quaternion were invented as part of pure math and then used for computer graphics stuff over a century later. To put it another way: should the proofs of theorems that AI is now generating actually be considered end products of mathematics, or are they turning out to be more of a step along the way to developing mathematical ideas, kind of like the code in software engineering?”

  Hacker News · question

• “> The idea of puzzling out what an AI did to prove something sounds quite boring and unappealing. The way I see it, it's no different from a lot of grad student work where you have to figure out what a human-written proof is doing. > Maybe they could have gotten into contact with the people of the research areas of the problems that they solved and worked with them to create a better exposition. That's what Anthropic is doing, and the issue is that people will complain that they weren't the chosen "person to work with". OpenAI's approach is more like a race where everyone's at the same starting point: they get the AI's raw proof to work on and have to figure out how it works.”

  Hacker News · complaint

• “I think eventually there will be sort of a centralized more or less automated repository for ingesting and sorting ai-generated lean proofs and making them searchable and re-usable. On some level it kind of doesn't matter if mathematicians can ingest the results, if coding agents can just search for them online and use them in their own proofs. I actually think it would be very smart for the big AI labs to get together to fund an independent organization to manage such a thing, and hire mathematicians to run it. What is happening now is that some aspects of mathematics are turning into essentially an exercise in software engineering. It is well known that proofs and computer programs have an isomorphism, and I think the eventual merger is more or less inevitable. That's not to say that there isn't an infinite amount of work remaining for mathematicians to do. There are only so many problems that are going to be amenable to this approach.”

  Hacker News · wishlist

• “It is not obvious to me that a single canonical human language write-up of a proof is the best output in this new world where write-ups are cheap. A human reader can query an LLM and get explanations of key points tailored to the reader's own background in mathematics.”

  Hacker News · complaint

• “Math proofs need to produce the correct output correctly, which is not quite the same thing. This looks like an AI IPO PR powerplay, because at this point the proofs haven't been checked and it may not be possible for a human to check them - because proofs should be clear, not horribly written and noisy. The noise is suspicious because it's the difference between brute forcing and cognition. A human proof won't just be logically correct, it will be cognitively distilled and coherent. It may still take years to understand it, but the logical flow will be straightforward, not obfuscated. You want the path through the maze to be as short as possible and the map to be as clear as possible. This sounds like the opposite. There may be a genuine path through the maze, but if it's too convoluted and takes too long it will be impossible to confirm. I think the next step is to demand that proofs either be human-scale or they prove that a human-scale proof is impossible and the machine proof is as good as it gets. I suspect that's possible without tripping over the halting problem. (But I can't prove it.)”

  Hacker News · complaint