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Their work indicates that ChatGPT-5.2 (Thinking) autonomously solved a problem posed in 2024, related to a conjecture formulated by mathematicians Ran and Teng. The model provided the main architecture of the proof after several dialogue sessions with the researchers.
This approach, dubbed "vibe-proving" by the scientists, involves using these tools to organize and explore complex theoretical ideas. One of the authors indicates having long sensed this potential, while being pleasantly surprised by the efficiency of the process. The method is inspired by "vibe-coding" used in programming.
The researchers from the Data Analytics Lab specify that human contribution remains indispensable, particularly for final verification and resolution of the last inaccuracies. Thus, artificial intelligence accelerates the formulation of proof drafts, but the validation step by experts still represents a significant point that requires time.
This advance constitutes a notable step for artificial intelligence in fundamental sciences. Beyond assistance with writing or coding, language models are now actively participating in mathematical discovery.
Professor Vincent Ginis from the Data Analytics Lab points out that certain preconceived notions about the limited creativity of such systems are thus being challenged. The experience shows that these tools can go beyond merely rephrasing training data to propose original reasoning.
The scientists anticipate that language models will continue to improve to assist researchers more during the verification phase. This synergy could transform practices in theoretical research, making the discovery process more interactive and certainly much faster.
What is a conjecture in mathematics?
In mathematics, a conjecture refers to a proposition considered probably true, based on observations or partial results. It differs from a theorem, which is a statement definitively established by a logical and rigorous proof.
These hypotheses often arise from the intuition of mathematicians who spot regularities or recurring structures. They serve as targets for research, motivating the quest for a formal proof that would transform the hypothesis into an indisputable mathematical truth.
The process of proving a conjecture is a collective enterprise that can last years, even centuries. It requires methodical creativity to construct a flawless argument, linking logical steps from axioms and already accepted theorems.
The resolution of a conjecture is always a landmark event in the discipline. It not only validates the initial intuition but also enriches the mathematical edifice by revealing new connections and paving the way for other questions.
How large language models (LLMs) work
Large language models, like the one used in this study, are artificial intelligence systems trained on massive amounts of text. They learn to predict and generate sequences of words coherently, capturing the structures of human language and certain forms of reasoning.
These models do not "understand" meaning in the human sense, but identify elaborate statistical patterns in the data. When presented with a mathematical problem, they can assemble learned concepts to propose a sequence of ideas that resembles a proof.
Their strength lies in their ability to quickly explore a vast space of theoretical possibilities. They can propose directions of reasoning or formulations that the human mind might not necessarily have considered first, acting as a catalyst for the researcher's creativity.
However, their output always requires critical examination. They can generate arguments that seem plausible but contain logical errors or unjustified leaps. Their role is therefore complementary, helping to structure thought while leaving the final say to the rigor of human verification.