> Here’s a thought experiment: suppose that a mathematician solved a major problem by having a long exchange with an LLM in which the mathematician played a useful guiding role but the LLM did all the technical work and had the main ideas. Would we regard that as a major achievement of the mathematician? I don’t think we would.
This is a cultural choice. It makes sense that in the mathematics culture we currently have, this is alien. But already, other fields, and many individuals, would disagree and say that the human did have a major achievement here.
As long as human-AI collaborations are producing the best results, there is meaningful contribution by the humans, and people that are deeper experts and skilled LLM whisperers should be able to make outsized contributions. The real shoe drops when pure AI beats humans and human-AI collaboration.
I replied to a comment about AI in sports and I build on that.
We praise car drivers despite most of the performance in their sport comes from the car. The driver makes the difference when two cars are close in performance. Brilliances or mistakes. Horse riders too.
In the case of math, the human can lead the LLM on the right track, point it to a problem or to another one. So it deserves some praise.
Then the team that built the car, cared about the horse, built the AI might deserve even more praise but we tend to care more about the single most visible human.
Well, kind of. In F1 there's 2 championships: the driver's championship, and the constructor's championship. The constructor's championship is for the best engineered auto. Both the driver and the engineers win separate things because it takes both.
I'm not sure I understood your question. Literally, of course not, but how does it relate to my points?
If I had a car 100 km/h faster on straights, after some training I would probably win Monza, but that would be a car that does not conform to F1 rules (or we would have that kind of speeds now) so that would not be a F1 race.
Maybe your question is about the sharing of praise between the team and the driver. I think that every race fan agrees that when a team did a much better job than all the other ones and have a dominant car, the championship is a competition between the two drivers of that team. So the car is the single most important factor. Then the best driver wins. Nobody can overcome a one second difference in a season of 24 GPs.
It's more to say that F1 drivers are a selected niche that is very good at winning F1 races, representing maybe a 200 to 5000/8,300,000,000 group. I doubt you could win an F1 race at all, respecting the rules. Whether the team deserves praise or not, the drivers show exceptional aptitude to win.
If Terrence Tao finds a novel proof, I believe it's his exceptional aptitude that is to praise, whatever help he used.
Edit0:I would bet that a normal run of the mill random human would be likely to kill themselves racing (with actual intent) an F1 car.
Well, I'm absolutely sure I can't win a race respecting the rules. I would bet that no HN reader can, even if I don't know if there are pro drivers here.
I add that my bet of winning at Monza (a stop and go track with minimal turning) with a non conforming 100 km/h faster car is optimistic. Honestly, I would brake too early, carry not enough speed through chicanes and corners, waste a huge part of my speed advantage by starting accelerating from lower speed.
I also think that 50+ laps will give me plenty of chances of crashing out even with plenty of training. Maybe even kill myself, as you write.
Maybe I could take pole position with the (very) old format of the best time of two 1 hour sessions on Friday and Saturday. I think it ended in the 90s.
I still don't understand the relationship between your question and the discussion on AIs.
If only a small, highly trained and specialised group can use a tool to accomplish a task that can't be accomplished by people not from the group, with or without the tool, it shows to me the proficiency of the people using the tool.
You might've missed my sentence about Terrence Tao?
Maybe I'm dense and haven't understood why you've brought up racing?
Edit0: about killing yourself driving: it highlight that the tool can't be considered "the main contributor"to an achievement if 99,99% of people would not achieve the same outcome but would be likely to die from misuse instead. The person that wrangles it and achieves exceptional outcome is all the more to praise in my book.
I’m not sure what your point is. I could certainly not, and I could certainly not write a breakthrough paper in mathematics even with the most advanced AI. I wouldn’t even know what to ask of it.
Perhaps I could set up an elaborate master agent to consider all possible new problems in mathematics and ask sub agents to work on the most promising ones. But then I could probably also program a self driving car system which could win an F1 race as well.
>Would we regard that as a major achievement of the mathematician? I don’t think we would
For some reason this reminds me of AI images and a domain like comedy.
If an image makes people laugh, the person who prompted it to make the image certainly doesn't get credit for the vast majority of the work in its creation, but perhaps they do get credit for the initial prompt idea and then the "taste" to select that particular one from whatever drafts they went through or otherwise guiding it.
So if a mathematician comes up with an amazing result that an LLM "did", I think they could still get a bit of credit for prompting it to do it and being its guide.
But whereas the first person could perhaps be called a comedian and not an artist, would the mathematician still be called a mathematician or something else?
I would. Even if someone found a prompt or even automated the conversation and just searched all open math problems I still would. If they produced a useful result without harm to anyone, that's a valuable human activity that should be rewarded just as well as we reward the other mathematicians, which I imagine is quite a lot, given all the billionaire mathematicians...
Absolutely. Who cares if the LLM automates some of the grunt work? Mathematicians are artists, and they paint with ideas. The goal is map out more of the beautiful structure of how things work. The enjoyment in it derives entirely from the payoff of seeing the larger view of how things fit together. If part of their process involves bouncing things off of other people, or even LLMs, I don't think it matters much, nor does it take away from the enjoyment in getting things figured out.
This is a cultural choice. It makes sense that in the mathematics culture we currently have, this is alien. But already, other fields, and many individuals, would disagree and say that the human did have a major achievement here. As long as human-AI collaborations are producing the best results, there is meaningful contribution by the humans, and people that are deeper experts and skilled LLM whisperers should be able to make outsized contributions. The real shoe drops when pure AI beats humans and human-AI collaboration.