"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 Verification Debate as Some Are Withdrawn or Revised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 claiming that artificial intelligence (AI) has solved long-standing mathematical problems emerges all at once.

A total of 722 papers have been released across fields including algebra, geometry, and differential equations. Among them are 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 However, as some results have been withdrawn or revised, debate is growing over how much credit should be given to mathematical achievements produced by AI.

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 Produced by AI... Why the Math 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 published on GitHub, an online platform for sharing code and research materials, so that anyone can review and verify them. According to OpenAI, producing each research finding involved running a cutting-edge AI model for about three hours.

The announcement has drawn attention because AI has gone beyond assisting with solutions to existing math problems and has presented new proofs and algorithms. The findings reportedly include counterexamples showing that long-standing conjectures are false, as well as new ways to solve problems. However, the accuracy and academic value of these claims will need to be established through follow-up verification 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.

Uhm Sang-il, chief investigator of the Discrete Mathematics Group at the Institute for Basic Science (IBS), said, "Some findings claim to have solved famous, long-standing problems; others present counterexamples to long-standing conjectures; and still others offer new algorithms that would have been hard to imagine. I think this is why so many mathematicians are surprised."

Baek Hyung-ryul, dean of the KAIST Graduate School of AI Mathematics and a professor in its Department of Mathematical Sciences, also said, "This announcement includes several problems in my field that could be considered worthy of a Fields Medal," adding, "If the key results are verified, the impact on the mathematical 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 enables mathematical proofs to be checked by a computer, but not all of the papers have undergone this kind of verification. Lean is a program that checks whether mathematical propositions have been proved according to logical rules.

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

Passing computer verification does not mean that every issue has been resolved. Uhm explained, "What Lean guarantees is only that a proposition that can be read by Lean has been proved. A person still needs to read it and check whether that proposition matches the paper's claim."

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 quality of the papers and their contributions to existing research are also matters of debate. Baek said, "The manuscripts I read were difficult to follow," adding, "There were many passages where readers had to go back and forth to understand the meaning, such as when terms were used before they were defined, with the definitions appearing much later." He added, "The overall structure of the arguments and the central ideas are also not clearly presented."

He took a cautious view of the assessment that AI had solved only the final step of existing research. Baek said, "In mathematics, that final step may be the hardest part," emphasizing, "It is important to clearly explain what was taken from previous research and what is new."

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

Uhm said, "Mathematics has advanced as mathematicians collaborate, tackle problems, and, once those problems are solved, develop a deep understanding of them and gain new insights," adding, "I worry about whether this process will continue to work well if LLMs make it easy to solve the most difficult problems."

Baek emphasized, "Whether a proof is correct is important, but the process by which it becomes part of our knowledge is just as important. 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.