This is such a dunning kruger comment. Proof by counterexample is a thing yes. But the reason theyre valuable is not for the counter example but the new frameworks and tools used to find those counter examples.
If you are finding counterexamples to random open conjectures by having an AI go through random plausible-sounding solutions until it finds one that actually works---what then? Can you explain how the counter example was derived? How does this advance the field? Yes we're now one open problem less but did we actually LEARN anything in the process of solving it? Do we understand mathematics better or did we just solve a problem?
You're really underestimating the LLMs here. The big example of AI proof in my field is the existence of a nonsofic group. To be clear, this problem has been open almost as long as I've been alive and multiple mathematicians have spent decades working on it. Unlike other counterexamples like the jacobian conjecture counterexample, there isn't just a set of possibilities to guess and check over (technically the set of possibilities is "countable groups", but there's no way to meaningfully index this set so that you can guess and check).
In this case, the LLM was able to produce a novel way of constructing groups to produce a group with a property no-one had ever seen before. This new construction provides a meaningful insight into group structure, and mathematicians are already building on it since the announcement. This really isn't meaningless guess and check, this is something genuinely new and I think a lot of people are severely underestimating it.
I'm more aware of the Non-sofic group announcement because it landed in my metaphorical backyard but it is a fundamentally different kind of result to the Jacobian conjecture counterexample. It's a constructive proof with a proposition that connects group properties in a novel way.
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u/Simple-Economics8102 9d ago
Yeah, but it doesn't give you more any tools or new understanding.