OpenAI shows 10 mathematical breakthroughs, but experts criticize them

OpenAI has said that the company's next major language model, called Astra, has found solutions to ten mathematical problems. The results emerged during internal development and testing of the model.

OpenAI describes the problems as open questions where there had been no major progress for at least ten years. The company says it cost only about $2,000 in computing power (so-called tokens, which are the AI model's unit of computation).

What is it about?

The problems span several branches of mathematics, including high-dimensional geometry, coding theory, group theory, quantum complexity and cryptography. One of the results is a new upper bound on how densely spheres can be packed in high dimensions. OpenAI says it is the first improvement of the general bound since 1978.

Astra also reportedly translated each proof into Lean. That is a computer program that can check mathematical proofs step by step, so you do not simply have to trust that the AI is right.

Criticism from mathematicians

After reviewing OpenAI's roughly 250-page report, several researchers have raised objections, according to Scientific American.

Stephen Miller of Yeshiva University believes OpenAI has effectively plagiarized his 2016 research on sphere packing. Francesco Fournier-Facio of Cambridge University says the breakthrough in group theory is not entirely new. According to him, it combines ideas from papers from 2016 and 2019, without this being clearly stated in the first press release. He points out that there is a large PR machine that wants to sound as impressive as possible, and that recent progress by humans is being overlooked.

According to Scientific American, OpenAI has promised to correct the report and spoke of minor updates during the week.

What does it mean?

The case shows both how fast AI is moving into advanced research and how important it is to check big claims. Even if the proofs are correct, it is a big question how much is the AI's own invention and how much builds on earlier human work. For ordinary readers, the point is that big announcements from AI companies should be taken with caution until independent experts have reviewed them.