Chinese Researchers Unveil TongGeometry: Pioneering Advance in AI Logical Reasoning

Artificial intelligence has long struggled with tasks requiring deep logical reasoning, particularly in domains like mathematics where human intuition and creativity play pivotal roles. A groundbreaking development from China is changing that narrative. Researchers have introduced TongGeometry, the world's first general AI system capable of both proposing novel Olympiad-level geometry problems and solving them autonomously. Published in the prestigious journal Nature Machine Intelligence, this breakthrough marks a significant leap in general AI logical reasoning capabilities.

TongGeometry, where 'Tong' translates to 'general' in Chinese, represents a fusion of neuro-symbolic approaches, guided tree search, and a vast deductive database of geometric facts. Developed on consumer-grade hardware—a stark contrast to resource-intensive predecessors—this model solves all 25 International Mathematical Olympiad (IMO) geometry problems from 2000 to 2024 in an average of 1.5 seconds. This achievement not only surpasses international benchmarks but also demonstrates AI's potential to mimic human-like mathematical discovery and proof generation.

The publication in Nature Machine Intelligence underscores China's accelerating role in AI research, particularly in areas demanding structured reasoning. As large language models (LLMs) dominate headlines for natural language tasks, TongGeometry highlights the complementary power of symbolic AI systems in tackling formal mathematical domains.

Meet the Minds Behind TongGeometry: BIGAI and Peking University Collaboration

The TongGeometry project stems from a two-year collaboration between the Beijing Institute for General Artificial Intelligence (BIGAI) and Peking University. Led by first author Zhang Chi from BIGAI, the team includes researchers like Yuxi Ma and others focused on advancing artificial general intelligence (AGI).

BIGAI, established to pursue AGI milestones, has previously introduced innovations like the Tong Test for evaluating AGI through embodied interactions. Peking University, one of China's top institutions, brings academic rigor and computational resources to the table. This partnership exemplifies how Chinese higher education institutions are fostering interdisciplinary AI research amid national strategies like the 'New Generation Artificial Intelligence Development Plan.'

Zhang Chi emphasized the system's dual functionality: "TongGeometry can precisely capture high-quality problems that meet the aesthetic standards of human mathematicians." This human-AI synergy positions the model as more than a solver—it's a creator of challenging problems, pushing the boundaries of AI creativity.

In the context of China's vibrant AI ecosystem, such collaborations between research institutes and elite universities like Peking are proliferating, attracting global talent and driving innovations that resonate worldwide.

Understanding Olympiad Geometry: The Ultimate Test for AI Reasoning

International Mathematical Olympiad (IMO) geometry problems are renowned for their complexity, often requiring inventive auxiliary constructions, symmetry exploitation, and multi-step deductions. Unlike straightforward computations, these problems demand a blend of spatial intuition, logical chaining, and creativity—hallmarks of human mathematical prowess.

Historically, AI struggled here. Early systems relied on brute-force search but faltered on novel configurations. Recent advances like DeepMind's AlphaGeometry (2024) achieved silver-medal performance on IMO problems but required enormous compute and human-curated data.

TongGeometry redefines this landscape by autonomously generating 6.7 billion theorems, including 4.1 billion with geometric symmetry, from a compact deductive database. This scale rivals human output over decades, achieved through efficient algorithmic design.

How TongGeometry Works: A Step-by-Step Breakdown of the Innovation

TongGeometry operates as a tree-based system leveraging guided search over a Euclidean planar geometry knowledge base. Here's the process:

• Deductive Database Construction: Starts with primitive axioms and constructions (e.g., points, lines, circles). Infers billions of facts via forward deduction, identifying dependencies for auxiliary lines.
• Problem Proposing: Models geometry as a Markov process on finite dependency graphs. Uses guided tree search to propose configurations needing auxiliaries, filtering for Olympiad-like difficulty and aesthetics.
• Proof Generation: For solving, employs Monte Carlo Tree Search (MCTS) guided by a neural oracle predicting promising moves, combined with symbolic deduction engine.
• Verification: All proofs are machine-verifiable, ensuring rigor without hallucinations common in LLMs.

This neuro-symbolic hybrid—neural guidance for intuition, symbolic for precision—enables 'small data, big task' efficiency. Unlike LLM scaling, it thrives on structured knowledge.

The core insight: Detecting construction dependencies allows pinpointing problems requiring auxiliaries, a novel duality between proposing and solving.

Photo by Sam Balye on Unsplash

Benchmark Dominance: TongGeometry Outshines Global Competitors

TongGeometry achieves 100% on historical IMO geometry, including recent IMO 2025 P2 without auxiliaries. On IMO-AG-30, it scores perfectly, first system above average gold medalist.

This efficiency democratizes advanced AI reasoning, making it accessible beyond tech giants.

TongGeometry vs. AlphaGeometry: A Head-to-Head Analysis

DeepMind's AlphaGeometry combined LLMs with symbolic search but leaned on massive synthetic data and compute. TongGeometry flips the script: leaner, faster, more autonomous.

• Compute Efficiency: TongGeometry: consumer GPU; AlphaGeometry: data center scale.
• Autonomy: Tong proposes problems; Alpha solves given ones.
• Scalability: Tong's database grows deductively; Alpha relies on LLM training.

Experts hail it as a paradigm shift towards hybrid AI, blending scale with structure.Read the full paper.

Implications for General AI and Logical Reasoning in China

This breakthrough addresses LLMs' reasoning Achilles' heel, advancing towards AGI. In China, it aligns with national AI goals, boosting sectors like education, robotics, and engineering.

For higher education, Peking University exemplifies training next-gen AI talent. Programs in AI and math now integrate such systems for advanced learning.

Stakeholders note: "TongGeometry realizes 'small data, big task,' vital for sustainable AI."

China's AI Research Landscape: Context and Momentum

China leads in AI publications, with BIGAI pushing AGI frontiers. Recent models like DeepSeek-R1 complement TongGeometry's symbolic focus. Government investments fuel university-led innovations, positioning China as a reasoning AI powerhouse.

Challenges remain: Ethical AI, data sovereignty, but solutions like Tong's efficiency pave the way.

Photo by Markus Leo on Unsplash

Real-World Applications and Future Outlook

Beyond academia, TongGeometry aids theorem discovery, automated tutoring, and CAD design. Future: Extend to 3D geometry, multi-domain reasoning.

Experts predict hybrid systems will dominate AGI paths, with China at forefront.

Career Opportunities in China's AI Boom

Aspiring researchers: Peking University and BIGAI offer paths. Explore research jobs, higher ed positions in AI. For career advice, visit higher ed career advice. Check jobs in China or rate professors for insights. Institutions seek talent in logical reasoning AI—your breakthrough awaits.