In a significant development for AI-driven research, a study from the Vrije Universiteit Brussel Data Analytics Lab has shown that ChatGPT can generate original mathematical proofs, solving a previously unproven geometry problem.
The research focused on a 2024 conjecture proposed by mathematicians Ran and Teng. A conjecture is a mathematical statement believed to be true but not formally proven. Once proven, it becomes a theorem.
According to the study, the proof was developed through 7 chat sessions and evolved across 4 versions. While the AI played a central role in structuring and exploring the solution, human researchers validated the logic and ensured mathematical accuracy.
The findings highlight ChatGPT-5.2 (Thinking)’s ability to independently develop much of the proof with limited human input. Researchers described this approach as “vibe-proving,” where AI helps organise and test complex theoretical ideas.
Brecht Verbeken, a postdoctoral researcher at the lab, noted that while he expected AI to assist in solving open problems, the speed and efficiency of the process were surprising. Professor Vincent Ginis added that the results challenge the belief that AI systems can only recombine existing knowledge rather than produce original insights.
The study positions vibe-proving alongside “vibe-coding,” where AI tools have rapidly evolved from assisting developers to generating near-complete code. Researchers believe a similar trajectory could unfold in mathematical discovery.
Despite the breakthrough, the team emphasised that human oversight remains critical. Final verification, logical consistency, and gap resolution still depend on expert review, making human validation the key bottleneck.
Professor Andres Algaba noted that while AI can accelerate the generation of candidate proofs, verification continues to require time and expertise.
The research marks a major step forward in AI’s role in theoretical fields, suggesting that language models could increasingly contribute to original discoveries when combined with rigorous human validation.
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