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Comment by ethanlipson | Hacker News Reader

Why do nearly all the articles exploring the development of AI applied to math assume that capabilities won’t extend beyond theorem proving?

> other skills will matter more: choosing which terrain is worth exploring, steering fleets of airplanes, and explaining what they find to the rest of the world.

These all seem totally achievable by LLM agents, or at least, I don’t see an obvious reason why it wouldn’t be. 3blue1brown’s recent discussion on this subject was a bit better, but he spent the plurality of main body of the video assuming this scenario, devoting less time to the other possibilities. To me, it seems dangerous to build a math career on the foundation that AI won’t be able to explain math well in a few years, let alone a few months (which seems entirely plausible given the recent math progress).

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Because the other option is that AI does what you say. And if you think about it (and you are a mathematitian and not an engineer) it means that AI is able to read our minds and know our desires. And at that point who cares about existence anymore?

Sorry, why would it need to read our minds exactly?

"Choosing which terrain is worth exploring" is more clear if you have an objective function (if you are doing engineering). But mathematics is closer to art in that regard. What is a terrain worth exploring in art?

Sometimes I wonder if "art" is also just some form of pattern matching on a very meta level.

In some sense, any art can’t be random in order to be distinguishable from noise

>What is a terrain worth exploring in art?

The joys of parenthood. The excitement of new love. The tragedy of aging. The rise and fall of a great family. Jealousy, vengeance, embarrassment, righteousness, venality. You obviously couldn’t create an all encompassing map of the terrain, but human art has a lot of recurring themes that are clearly “worth exploring” because they’ve consistently been explored in the past. I think the same kind of repetition probably also exists to some degree in other areas of human endeavor. An artificial intelligence could probably suss out a lot of those themes and produce valuable (if not maximally valuable) work without being a mind reader.

Ive noticed that too, I don’t know why people talk like we need to figure this out right now

Like we can even know what the future of math is this early

It’s not like you can just declare that up front, it’s something that happens naturally when people spend time using the tools

Right now they have to figure out some kind of story to tell the grad students. Even if it will be subject to change they have to have something.

Just because they could, doesn't mean anyone would bother having the AI agents do so.

You don't think OpenAI has any interest in having agents identify new interesting research terrain? They just want to solve existing important millennium problems and then they're done?

Yes? I expect their motivation for devoting resources to solve these problems will dramatically drop as soon as they IPO. Maths is just a convenient vanity metric for OpenAI to demonstrate progress, but long term progress in mathematics has no commercial value to them.

Of course, general improvements may be sufficient to continue to drive math improvements even without specific attention - we’ll see.

Not a chance. They'll go for room temperature superconductors and other stuff that is currently in the quite possible but not yet proven and patent the hell out of it and charge rent to the rest of humanity.

Why would that necessarily be accessible by thinking only? Or do you see them running or directing large laboratories of various types?

Simulation to the point that the accuracy is large enough to extrapolate to real materials. You can do a lot of stuff when you have access to a million GPUs that would otherwise be much harder.

I have my doubts there, but we will see.

A lot of materials science is already done through simulation, same with a large chunk of chemistry and biology. That fraction will only increase over time.

https://en.wikipedia.org/wiki/Computational_chemistry

https://en.wikipedia.org/wiki/Computational_biology

https://en.wikipedia.org/wiki/Computational_materials_scienc...

These fields are all going through a tremendous acceleration right now.

I am aware of advances, but I think a large chunk is a stretch in various ways. We'll just see what happens - simulating even a glass of water fully is tough.

That depends on the granularity of your simulation. For most - not all - purposes a glass of water can be simulated coarsely or by simulating a far smaller amount with greater fidelity and then to extrapolate.

For useful materials science the numbers are still large but far lower than the numbers involved in 'a glass of water'.

I really depends on what is needed. If you know that something quite "coarse" is enough to create/uncover room temperature superconductors with high critical current - fair enough. Again, we'll see what happens.

With the kind of compute they have at their disposal 'quite coarse' may actually be 'impressively detailed' and that is why I think they have an edge on this kind of stuff. It's like being able to borrow a trillion and then to go play research lab, it would be highly surprising if they weren't able to monetize such a head start.

AI systems will probably be able to, if not direct labs themselves, cut down a lot of the search space to only the most promising candidates. That’s basically what Isomorphic Labs is doing for candidate drug research. It doesn’t seem crazy that the same could be true for material sciences.

Maybe. Are we seeing any indication of increased success rates in stage 3 trials already for "AI drug candidates"?

Could also be that some things are not possible in some ways. I wonder if there is some general theory on "shortcuts".

Stage 1, yes, stage 2, it's a wash (for now at least), which does not promise much for stage 3, but it is still a bit early for that.

If they did that and were able to find someone to pay them, that'd be a pretty good contribution, no?

> I expect their motivation for devoting resources to solve these problems will dramatically drop as soon as they IPO. Maths is just a convenient vanity metric for OpenAI to demonstrate progress, but long term progress in mathematics has no commercial value to them.

And why would IPO remove incentive that's present pre-IPO? Somehow math progress will influence price at IPO but won't influence stock price post-IPO? Or will they just stop caring about stock price once they are public. None of these options makes any sense.

Because if you assume there is going to be an AI-god that can do everything better than us, there's nothing to really do. Like really, what do you want these people to write? "Well, math for humans is over as well as all intellectual activity, better just jerk off watching AI-generated hentai all day until I die"

Just because the truth is inconvenient doesn't make it false.

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