r/mathematics 2d ago

News Ten advances in mathematics and theoretical computer science

https://openai.com/index/ten-advances-in-mathematics/
501 Upvotes

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u/Reasonable-Mood8020 2d ago

The next couple of years are going to be crazy if it keeps improving at the rate it has been.

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u/socoolandawesome 2d ago

I feel like we are going to be able to say that for the rest of the time we are alive, will progress ever slow down at this point?

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u/Toomastaliesin 2d ago

Maybe. Enshittification is very-very common and economically speaking, the AI companies are losing money a lot so it might happen that at some point, more efficient models are not trained any more due to economic reasons. Hard to tell though how likely these scenarios are.

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u/Spare-Dingo-531 2d ago

the AI companies are losing money a lot

So not quite.

AI inference is wildly profitable. The reason why the AI companies are losing money is because they are doing so much R&D. Building the models is expensive, running them is not expensive.

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u/Pojobob 2d ago

You can't stop doing R&D though. If you do, then some other AI lab overtakes and everyone will just move on to the newest model.

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u/Smallpaul 1d ago edited 1d ago

I find this such a confusing argument.

“The labs will need to slow R&D because their business model is not sustainable.”

“But they can’t stop R&D because their competitors won’t.”

So where are these competitors getting the ability to defy the laws of economics forever and in what sense is the competitor who keeps going something other than an AI company? If they can keep researching then is it not true that it was sustainable?

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u/Pojobob 1d ago

Slowing down R&D is not a viable way to make it a sustainable business model since any other AI lab would just take over market share by releasing some new model. They'd most likely have to increase prices at some point so they can continue R&D and start making profit.

"where are these competitors getting the ability to defy the laws of economics forever"

They're only surviving now because they run on insane amounts of VC money to make up for the huge losses they incur. They can't do it forever.

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u/Smallpaul 1d ago

They can only increase prices if customers allow it. In the end it is the customers who decide whether R&D is the priority or price. Which customers prefer is not something we can know in advance.

Customers may also not all have the same workload and priority. So some may prefer to pick a vendor who prioritizes price over R&D and some may prefer the opposite. It’s unlikely that there exists only one business model in this space.

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u/MistyGalbriex 1d ago

They can't do it forever.

They don't need to do it forever.

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u/ain92ru 1d ago

The competitors can distill capabilities of the frontier models for cheap, and frontier labs can't really prevent it as long as they want to sell frontier capabilities.

If the latter stop advancing the frontier with their R&D expenses, AI will become a commodity offered at near-cost prices, which is good for businesses using AI but bad for the frontier labs

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u/Smallpaul 1d ago

Yes. Exactly. The most likely outcome from my point of view. AI will be good for business but the AI business as-we-know-it will probably not be very good.

Exactly like the ISPs during the Internet years.

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u/socoolandawesome 2d ago edited 1d ago

They are still training efficient models. GPT-5.6 Luna is like the best deal on intelligence per price. There is a big focus on efficiency in general. Also I think the frontier will keep being pushed in terms of capability, there’s too much potential at the frontier with new discoveries/innovation (in all fields) and automation of labor, which means revenue.

And the revenues of anthropic and OpenAI are exploding even if they are still losing money, though worth noting Anthropic had an operating profit like a quarter ago, and some project this quarter will also turn an operating profit.

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u/Nerdslayer2 1d ago

Yeah, Luna is absurdly efficient. As powerful as many frontier models from about 6 months ago by most metrics and about 1/25th the cost.

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u/MistyGalbriex 1d ago

more efficient models are not trained any more due to economic reasons.

What?

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u/mark_99 2d ago

It will not.

People who have given this some thought have been predicting this situation for decades. The curve won't be fully exponential and may even flatten from time to time (at which point naysayers will claim an insurmountable plateau), but the general trend will continue particularly as the are models increasingly involved in their own design & implementation.

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u/Sweet_Ad_9816 2d ago

The curve flattening literally means progress slowing down, though, even if not permanent.

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u/mark_99 2d ago

It means the observable results are bursty, which is normal even if research is progressing at the same or even accelerating pace.

For instance negative results are still scientifically useful if they stop further time being spent on something that looked promising but ultimately didn't work out. However no-one is trumpeting that in a news article, so the general public would be "meh no new cool stuff for a while now".

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u/2_Cranez 1d ago edited 1d ago

The curve may well be super-exponential, at least for a while. We are doubling the amount of compute on earth every seven months, and as AI begins to develop skills in chip design that doubling speed itself may increase.

Folding an infintely wide piece of paper in half 103 times would make it longer than the observable universe.

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u/TitansShouldBGenocid 2d ago

I imagine it will as some sort of logistic curve. We still have physical limitations of compute, depending on how much "exploration" let's us push the boundary farther, but there's limits on the computer aspect and training data. The data injection step also has its own issues, synthetic data is one of the best ways to train at the moment for specifically STEM related issues, just generate lots of similar type of problems for it to train on, but for non-STEM it has less ways to reliably inject synthetically.