The 722 Papers That Broke Math

Francis Johnson spent twenty-five years trying to solve Wall's D(2) problem. He wrote two books about it. He gave up. Now an unnamed AI model from OpenAI has claimed to have solved it, along with 720 other mathematical puzzles, in a single batch release on GitHub. The scale of the output is staggering. It is also, according to many in the field, unverified and potentially wrong. This is not a story about a single eureka moment. It is a story about a flood.

The release happened Tuesday. OpenAI dropped 722 manuscripts into a public repository, covering 372 different families of results. The company did not name the model. They did not show the prompts. They just said the average result took about three hours of computing power equivalent to ChatGPT Pro thinking time. The math community is split between awe and anxiety. The genie is out of the bottle, as Johnson put it. Now we have to deal with the mess.

A Flood of Proofs

OpenAI posed roughly 4,000 problems to this internal frontier model. They filtered the output down to the 722 manuscripts they deemed significant enough to publish. This is the largest public display of AI research level mathematics we have ever seen. The problems range from theoretical computer science to operator algebras. One claimed proof addresses the Unique Games Conjecture. Another tackles the free group factor problem, which has been open since the 1940s.

The company released summaries of the reasoning and estimates of the computing resources used. They did not publish the prompts. The Advisory Group on Mathematics and Artificial Intelligence, known as AGMAI, consulted on the release. They have not endorsed the findings. They simply noted that the batch includes solutions to hundreds of open questions. That is a very careful distinction. Consultation is not verification. The papers are out in the world, but they are not yet part of the mathematical canon.

The Verification Gap

Kevin Buzzard at Imperial College London looked at the 30 papers relevant to his field of number theory. He found that only seven seemed impressive. Only one was formally verified in Lean. Lean is a type of computer analysis that can prove mathematical results beyond reasonable doubt. The other six are just text. They are just claims. They need an expert to read them. They need a human eye to check the logic. That is a massive bottleneck.

Buzzard says acceptance will take time. He warns journalists to wait while mathematicians do their job. The six unformalized results have to wait until an expert is motivated to check the text or a Lean formalization is produced. This is the critical friction point. We have the answer, but we do not have the proof. We have the claim, but we do not have the certainty. The gap between generation and verification is where the real work happens. And that work is slow.

The Human Element

Johnson is not angry. He is astonished. He worked on his problem for decades. He saw AI models produce sophisticated and clear analysis in recent months. He says it puts us all in a strange position. He believes the genie is out of the bottle. We have to adapt. Human beings are supposed to be adaptable. For the moment, he just stands back and is astonished. That reaction is common. It is also dangerous. Awe can blind us to error.

The trend in AI mathematics is upwards. The depth is impressive. The breadth is overwhelming. But the reliability is uncertain. If the new results turn out to be mostly true, we will have a new paradigm. If they are riddled with subtle errors, we will have a cautionary tale. The math community is in the middle of that uncertainty. They are checking. They are verifying. They are waiting. The 722 papers are not a conclusion. They are a starting point. And a very noisy one.

What Comes Next

The release is under an open source license. The protocols for paper revisions and citations are included. This is an invitation to the community. It is a challenge. It is a test. The next step is not more papers. It is verification. It is formalization. It is the slow, painstaking work of checking every line. The AI model did the heavy lifting. The humans have to do the careful work. That is how science works. That is how mathematics works.

We are standing on the edge of a new era in discovery. The tools are powerful. The output is prolific. The verification is lagging. This is not a failure. It is a process. The 722 papers are a landmark. But they are not the destination. They are a signal. They tell us that the capability is there. They tell us that the pace is accelerating. They tell us that the future of mathematics is not just human. It is hybrid. And it is happening now.