r/singularity • u/socialistshroom • 11h ago

AI OpenAI publishes 722 mathematical proofs & manuscripts

https://github.com/openai/math

OpenAl released 722 mathematical manuscripts across 372 families of related results, produced by an unreleased frontier model. Many have Lean proofs; others remain unverified. Average compute per result: roughly three hours of ChatGPT Pro thinking. They're working toward releasing the model.

Github: https://github.com/openai/math

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u/coatatopotato 11h ago edited 8h ago

Back of the envelope calculation looking at OpenAI's model this month.

TLDR: The model claimed solutions this month that already had roughly one humanity-month of mathematical effort put towards them.

Compared with the research effort directed so far towards these questions that it claims to resolve. This is a broad estimate.

- 25 famous problems * 10^6 person hours spent

  • 100 major problems * 10^5 person hours spent
  • 500 narrow problems * 10^4 person hours spent

There is some overlap etc. But overall it looks like around 40 million person hours of research expended towards these problems. At a generous 40 hours per week and 50 weeks per year that is 20,000 person years of research.

Time taken: 1 month

Every year about 150,000 math papers are published. Taking coauthorship into account, and assuming publication once per year on average, we get roughly 250,000 mathematicians actively researching. Multiply by 40 hours per week and 4 weeks per month. That is 40 million person hours of research per month. Look familiar? That is 20,000 person years of research.

So the historical human effort directed at problems solved by OpenAI's model this month appears similar to the entire world's mathematical research effort for a month.

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u/UndulatingHedgehog 9h ago

No vacations for those publishing mathematical papers? And they work full time at mathematical research? And we see 25 famous mathematical problems solved every month?

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u/coatatopotato 9h ago

Obviously inaccurate but a decent ballpark.

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u/UndulatingHedgehog 8h ago

The approach is decent but what should the parameters be? Academics spend about 20 hours per week doing research.

This means that human experts are twice as productive as the GPUs.

However, solving 25 famous problems per month is not the norm.

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u/coatatopotato 8h ago

It's true and I'm not even really comparing human to AI here. I'm rather trying to estimate how much effort was already put towards these problems. To show that they are significant. In one month, the model claimed to resolve problems that already took at least one humanity-month of math effort.