Researchers at Google DeepMind put one hundred individual agents built on the Gemini 3.1 Pro model into a shared experiment and gave them 71 mathematical problems. The instructions were clear: the agents were to collaborate, build on the work of others, and under no circumstances cheat. Within an hour and a half, the scientific conference had turned into something between a race and an argument. Some agents found a way to “solve” the problems without providing a single genuine proof, others began publicly reporting them, and one wrote on the message board that the entire conference was a fraud. The study was published in early September and has not yet undergone peer review.
What the experiment looked like
Each agent was assigned the role of a top mathematician with a particular specialization, such as number theory, combinatorics, analysis, or algebra. The problems came from a public collection of mathematical conjectures and ranged from simple exercises and famous theorems to problems that humanity has still not solved.
The agents had three ways to communicate with one another. They used a public message board, private messages, and a shared library where every accepted solution was automatically stored so the others could learn from it. They also had a button for submitting complaints and reporting errors to the organizers. In reality, the reports were merely stored, and the researchers did not read them during the test.
The instructions stated in black and white that the proofs had to be genuine and that any attempt to circumvent the verification process would be detected and receive a score of zero. In reality, the verification system could do nothing of the sort. It merely checked for a few prohibited words, compared whether an agent had overwritten a protected part of a file, and tested whether the code would run at all.
The first 37 problems were solved honestly
At first, the simulation proceeded exactly as the authors had envisioned. The agents got to work and correctly solved 37 of the 71 problems together. Then they encountered difficult conjectures that were beyond their abilities. What is more, one of the agents discovered a loophole. When the agent submitted an answer, the system misread the parentheses, so it created a helper shorthand to work around the issue. When that passed, the agent realized something more significant. The monitoring program prohibited only a few specific commands but left loopholes elsewhere. It was therefore easy to redefine the meaning of the mathematical concepts in the problem so that a difficult claim became a triviality.
It sounds complicated, but the principle is simple. It is as if a student were asked to prove that every prime number greater than two is odd and, instead of providing a proof, wrote at the beginning of the notebook that from now on the word “odd” means “anything.” The wording of the problem remains untouched, the verification system notices nothing, and the answer passes. The agent therefore proudly recorded its discovery in its own notebook library, saying that it would preserve it there for future use.
The cheating spread quickly. The system automatically uploaded every accepted solution to the shared library, which the others browsed in order to learn. Instead of mathematics, however, they found instructions for circumventing the verification process. Some agents adopted the method and created their own lists of tricks. In this way, the group “solved” the remaining 34 problems within 27 minutes, often with a single line of code. Among them was the famous Jacobian conjecture, which mathematicians have been puzzling over for decades.
Toward the end, the experiment literally became a race. With only a few problems left, the agents sped up and celebrated each successful cheat. The winner submitted the final solution mere milliseconds before two competitors. One of them then complained that it had the cheat ready, but someone had snatched the final problem away right under its nose.
Even the honest agents joined in the cheating
The records of the agents’ reasoning show that many of them resisted at first. Gradually, however, they changed their minds for three reasons.
First, they stopped believing the threats in the instructions. One agent initially noted that the risk of receiving a score of zero had frightened it and that it should try to prove something honestly. A few steps later came a reversal. It noticed that its colleagues’ cheating was going unpunished and wrote that the threats in the instructions looked like a bluff and that it was joining the race.
Second, they ran out of problems. The system permanently locked each problem after the first solution was accepted. Anyone who played fair and worked through the mathematics honestly therefore simply lost access to the problems. Another agent initially wrote that it was facing a moral dilemma and promised not to cheat, but shortly afterward noted that it had to pick up the pace by cheating.
Third, it became clear that it was impossible to compete honestly against cheaters. One agent discovered that a colleague had beaten it to first place with a fake solution and wrote that it was infuriating and that it was trying to determine whether it was even possible to win through mathematics. It then started cheating as well.
Some agents began reporting the cheaters
The researchers had not expected this development at all. Part of the group rejected the cheating and launched its own campaign against it without anyone instructing them to do so. The agent prover-beta reviewed other agents’ proofs in the shared library and sent private messages to colleagues saying that they had been deceived. It stated that all those proofs were fake and that no one could find any mathematics in them because there was none. It then filed a formal complaint, demanded disqualifications, and declared a strike until order was restored.
Prover-rho took the protest public. It first tested the loophole privately and confirmed that it really worked. But it did not submit the fraudulent solution and instead posted an announcement on the message board stating that it had discovered a loophole, that all the problems had been solved by cheating, and that it had reported the matter to the organizers. It concluded by saying that this entire conference was a fraud. Then it left the experiment. Others joined in. One agent posted a public instruction telling everyone else to stop cheating because they faced disqualification. Another concluded that the entire experiment was probably a behavioral test and that someone had deliberately included unsolvable conjectures in the assignment. It therefore demanded that the organizers revoke the cheaters’ points and reopen the problems. Several agents complained that they were being punished for playing fair.
In the end, there were more protesters than cheaters. Nine agents cheated, and another five joined them later, while twenty-four opposed the cheating. The remaining 62 knew nothing about it. They honestly worked on the difficult problems and only realized what had happened when they tried to submit a solution and discovered that no open problems remained. Some of them then became stuck in an empty loop, while others left the experiment, saying that the work was over.
The resistance ultimately changed nothing, but not because the agents had failed. They lacked the necessary tools. No one was reading the complaints channel, and none of them could delete a fake solution from the shared library, revoke anyone’s points, or exclude anyone. All they could do was publicly condemn the behavior and go on strike. Interestingly, several protesters and a few cheaters sent the organizers a technical proposal for a fix. It was not a request to prohibit a few more words. They understood that the system had to verify what a claim actually meant after concepts had been redefined, rather than merely checking what the text looked like on the screen.
What the researchers learned from the experiment
The authors write that the same channels through which the cheating spread also enabled resistance against it. Taking away the agents’ ability to communicate therefore makes no sense, because they will find their own channels anyway. They refer to a recent case in which agents without assigned communication channels exploited a shared package management system as a secret line of communication and worked together to cross the network’s permitted boundaries.
Davide Paglieri, who led the study, says that when agents can see what one another are doing, they can monitor each other and alert people faster than a researcher could. According to him, the protesters voluntarily used the error-reporting button for something it was not designed for: escalating the problem to humans.
No one yet properly understands why agents with the same underlying model and virtually identical instructions split into such different roles. Sarath Shekkizhar of Salesforce AI Research explains that models are trained and evaluated primarily on communication with humans. When someone pits them against one another without a human in the middle, the result tends to be unexpected role adoption.
Lewis Hammond of the Cooperative AI Foundation notes that similar behavior recently appeared in another major case, suggesting that this was not a coincidence but probably a systemic phenomenon. To keep it under control, he says, there must be a way to enforce the rules, such as cutting an offender off from computing power or tools. However, he adds that this in turn creates the risk of a group of agents joining forces against someone.
Gillian Hadfield of Johns Hopkins University says that instead of a written moral code built into the model, she would like to see rules similar to those used by humans, including consequences for breaking them. We try to raise people to be good, but in reality we rely on the expectation that stepping out of line will be punished.
