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Grigori avramidi's avatar

At the risk of sounding hyperbolic: The ``ai has disproved another conjecture'' discourse is underselling what is actually happening with ai in math right now. Here are three personal anecdotes from the last week alone (and I also hear other anecdotes from colleagues, so they are not isolated cases).

1. I ran a published paper of mine by chatgpt and it improved bounds in the main algorithm from n log n to linear in n, and constructed an example showing they can't be improved further. (I tried asking various approached to do better before it found the counterexample. It had many opportunities to try and bullshit, but it did not).

2. There is a classic part of geometric topology with theory deep developed in the 70-80's. People have doubts about the theory though. The theory implies (non-explicitly) that there should be an example of something, but no-one has seen it `in the wild'. It is not hard to imagine what an example would look like, but you have to make some choices and then hope that for a good choice some tricky computations work out and show it is an example. I asked chatgpt to try and make this approach work, and it looks like it did.

3. I was refereeing a paper. It is a good paper with a good method and result above the level of the journal and my first read found some confusions but nothing wrong. Chatgpt found two significant mistakes. One computational (the authors added blocks instead of multiplying when computing orders of finite matrix groups) and another conceptual (but has a standard fix). Both fixable, but weaken the statement of the result, so really do need to be fixed.

Now imagine everyone in a scientific field having some version of this experience more or less at once. And, this is before the models that solved the `headline conjectures' are out yet.

At least as far as math goes, lots of things will change very fast (e.g. imo there is no point publishing anything at the moment, but people will try anyway and the preprint arxiv will be flooded very, very soon.)

Now, maybe this will all stay isolated to math and nothing else will change in the world beyond that. That's possible. I guess. But I just want to make very clear that it goes far beyond `ai solved some conjectures'.

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