A groundbreaking artificial intelligence system, TongGeometry, has been developed by a joint research team, achieving a significant milestone in autonomous problem proposing and solving. This innovative system has outperformed international benchmarks, including DeepMind’s AlphaGeometry, marking a major advancement in AI-assisted mathematical research and intelligent education.
The study, published in the journal Nature Machine Intelligence, was conducted by the Beijing Institute for General Artificial Intelligence (BIGAI) in collaboration with various departments at Peking University and the Wuhan Institute for Artificial Intelligence. The announcement underscores the growing capabilities of AI in complex logical reasoning and problem-solving.
Revolutionizing AI in Mathematics
Mathematics Olympiads have historically been a benchmark for testing AI’s logical reasoning capabilities. Earlier in 2024, DeepMind’s AlphaGeometry gained attention for its problem-solving prowess, though it relied heavily on large datasets and extensive computational resources. TongGeometry, however, presents a more sophisticated approach.
Unlike its predecessors, TongGeometry is not just a high-achieving solver but also a creator of new mathematical problems. Zhang Chi, a researcher at BIGAI and the first author of the paper, explained, “We identified a profound duality in our research: when the proof difficulty of a geometric proposition is far higher than its construction complexity, it possesses ‘aesthetic value’ as an Olympiad-level problem.”
“By modeling this duality, TongGeometry can precisely capture high-quality problems that meet the aesthetic standards of human mathematicians from a vast pool of spatial combinations. This is a global first, representing a paradigm shift from ‘imitative solving’ to ‘autonomous creation’,” Zhang noted.
Technological Superiority and Efficiency
The superiority of TongGeometry is evident in its performance metrics. While AlphaGeometry requires massive computing clusters, TongGeometry can solve all International Mathematical Olympiad geometry problems from 2000 onward in under 38 minutes using just a single consumer-grade GPU. This efficiency highlights the potential of domestic technology to lead in AI development.
The system employs an innovative normalized representation technology, significantly reducing the search space and addressing the path explosion problem inherent in traditional methods. Zhu Yixin, assistant professor from the School of Psychological and Cognitive Sciences at Peking University, emphasized the broader implications of this breakthrough.
“The significance of TongGeometry lies not only in the increase in solving speed but in its realization of the ‘small data, big task’ paradigm by simulating the intuition and aesthetics of human mathematicians,” Zhu stated.
Implications for Future AI Development
This development is not just a technical achievement but a strategic leap forward in AI research. The system’s ability to generate new geometry problems has already seen practical application, with three problems selected for the 2024 Chinese Mathematical Olympiad (Beijing District). This capability provides a foundation for future advances in automated mathematical proofs and personalized intelligent education.
Looking ahead, the research team plans to continue refining the “Tong” series of general intelligence models. This ongoing work aims to position Chinese AI technology at the forefront of complex logic and scientific discovery, potentially leading to new breakthroughs in various fields.
The emergence of TongGeometry signals a new era in AI, where systems are not only solving problems but also contributing to the creation of new knowledge. As AI continues to evolve, the implications for education, research, and technology are profound, promising a future where machines play an integral role in scientific exploration and discovery.
