"What Becomes of the Geniuses Who Devoted Their Lives?"... 722 Papers Released in Just 3 Hours Spark 'Shock and Awe' [Reading Science]

OpenAI Releases 372 Research Findings... Verification Debate as Some Are Withdrawn or Revised
Korean Mathematicians: "They Must Lead Beyond Proofs to New Insights"

The global mathematics community is abuzz as a wave of research findings claims that artificial intelligence (AI) has solved longstanding mathematical problems.

A total of 722 papers have been released across fields including algebra, geometry, and differential equations. Some offer solutions to problems that mathematicians had been unable to solve for decades. However, as some results have been withdrawn or revised, debate is growing over how much credit AI-generated mathematical work should receive.

A scene from the 1997 film "Good Will Hunting." Will Hunting (Matt Damon), a math prodigy, solves a math problem on a blackboard in a university hallway. Still from "Good Will Hunting."

722 Papers from AI... Why the Mathematics Community Is Surprised

On October 6 (local time), OpenAI released 722 math papers generated using large language models (LLMs). The papers are grouped into 372 research findings and cover various fields of mathematics, including algebra, geometry, and differential equations. The papers and related materials were posted on GitHub, an online platform for sharing code and research materials, so that anyone can examine and verify them. According to OpenAI, producing a single research finding required about three hours of computation using a state-of-the-art AI model.

The announcement has drawn attention because AI has gone beyond helping solve existing math problems to proposing new proofs and algorithms. The findings reportedly include counterexamples showing that longstanding conjectures are false, as well as new methods of solving problems. However, the accuracy and academic value of these claims still need to be assessed through further review by mathematicians.

Materials released by OpenAI, categorizing 722 math papers written with the help of AI into 372 research findings. They contain solutions to challenging problems across various fields of mathematics, including algebra, geometry, and differential equations. Courtesy of OpenAI.

"Some findings claim to solve famous longstanding problems, others present counterexamples to long-held conjectures, and still others propose new algorithms that would have been difficult to imagine. I think this is why so many mathematicians are surprised," said Eom Sangil, chief investigator of the Discrete Mathematics Group at the Institute for Basic Science (IBS).

Baek Hyungryeol, dean of KAIST's Graduate School of AI Mathematics and a professor in its Department of Mathematical Sciences, also said, "This announcement includes several problems in my research field that could be considered Fields Medal-level. If the major findings are verified, the impact on the mathematics community will be enormous."

Proof Is Not the End... The Role of Mathematicians in the AI Era

The challenge is verification. The materials released by OpenAI include proofs in Lean, a format that allows mathematical proofs to be checked by computers, but not all the papers have undergone this kind of verification. Lean is a program that checks whether mathematical propositions have been proved according to logical rules.

"Only about 42% of the papers released this time are accompanied by Lean formalizations, which is less than half. The rest are available only as papers, so the possibility that errors will be found cannot be ruled out," Eom said. Indeed, as of 2:20 p.m. on October 8, OpenAI said it had withdrawn three of the released results and revised and supplemented more than a dozen proofs.

Passing computer verification does not mean that every issue has been resolved. "What Lean guarantees is only that a proposition readable by Lean has been proved. People still have to read it and check whether the proposition matches the paper's claim," Eom explained.

A screenshot of a GitHub repository where OpenAI published math papers generated with artificial intelligence (AI), along with related proof materials. Some papers also include proofs in Lean, a format that allows computers to verify the logical validity of mathematical proofs. Screenshot of GitHub page.

The papers' quality and their contributions to existing research are also being debated. "The manuscripts I read were difficult to follow. In many places, terms were used before being defined, with the definitions appearing much later, forcing readers to go back and forth to figure out what they meant," Baek said. He added, "The overall structure of the argument and the central ideas are not clearly presented."

Baek took a cautious view of assessments that AI had solved only the final steps of existing research. "In mathematics, that final step may be the most difficult part," he said. "It is important to clearly state what was drawn from previous research and what is new."

The announcement shows AI's potential to dramatically accelerate mathematical research, while also raising fundamental questions about the role of human mathematicians. Even if AI can rapidly produce complex proofs, the process of verifying and understanding them, and developing them into new research, remains important.

"Mathematics has advanced as mathematicians collaborate, tackle problems, and, once they are solved, gain new insights by understanding them deeply. I am concerned about whether this process will continue to work well if LLMs make solving the most difficult problems easy," Eom said.

"Whether a proof is correct is important, but the process by which it becomes part of our knowledge is just as important," Baek said. "No matter how many proofs AI produces, if they do not become living knowledge within the mathematical community, it is difficult to call that, in itself, progress in mathematics."

This content was produced with the assistance of AI translation services.