• The model developed an independent proof for a challenging geometry problem
• Researchers emphasize the need for human review to ensure accuracy

The advanced artificial intelligence model ChatGPT-5.2 succeeded in creating an original mathematical proof for a geometry problem that had never been solved before, according to a new study demonstrating the ability of language models to produce innovative mathematical reasoning, while researchers stressed that human verification remains essential.

Researchers at the Data Analysis Laboratory at the Free University of Brussels noted that commercial language models can generate original proofs, and that ChatGPT-5.2 (Thinking) independently solved a problem proposed in 2024 by mathematicians Ran and Ting—a problem considered theoretically correct based on recurring patterns but not officially proven until now.

The study reported that the final proof came after seven dialogue sessions with ChatGPT and four revised versions of the argument, with the model playing a central role in exploring possible approaches, while human researchers verified the correctness and logical completeness of the conclusions.

According to the researchers, ChatGPT-5.2 developed most of the proof’s structure with minimal human assistance, marking the first evidence that a commercial language model can independently produce original mathematical proofs.

Brecht Verbeken, a postdoctoral researcher at the Data Analysis Laboratory, said, “I always believed ChatGPT could assist in solving unresolved mathematical problems, but I was surprised by the speed and efficiency of the results.”

The team described their new methodology as vibe-proving, in which language models help organize and explore complex theoretical ideas, comparing it to vibe-coding in AI programming, which has evolved from simple tools into semi-autonomous code generation.

Despite the model’s power, researchers stressed that human review remains crucial to close any gaps and ensure proof validity. They explained that the experiment highlights where language models can add value and where challenges remain.

These findings represent an important step in applying AI to theoretical research, as language models can contribute to original mathematical discoveries when combined with careful human oversight. Andrés Algaba, a professor at the Data Analysis Laboratory, said, “Proposed proofs can now be drafted faster, but human verification remains the bottleneck; still, models will continue to streamline the process.”