AlphaGeometry2: DeepMind’s AI Redefines Geometric Problem Solving | | | | Turtles AI

AlphaGeometry2, DeepMind’s latest AI evolution, has achieved extraordinary results in solving geometric problems, outperforming most human experts. With an 84% success rate on IMO problems from 2000 to 2024, this system integrates advanced language models and a symbolic engine, demonstrating unprecedented mathematical reasoning capabilities.

Key Points:

• Outstanding performance: AlphaGeometry2 solved 84% of the International Mathematical Olympiad (IMO) geometry problems from 2000 to 2024, a significant improvement over the previous version’s 54%.
• Innovative technology: It uses a Gemini-based language model and an advanced symbolic engine (DDAR) to efficiently formulate and verify geometric proofs.
• New search strategies: The Shared Knowledge Ensemble of Search Trees (SKEST) algorithm enables parallel processing, increasing the speed and quality of solutions.
• Future evolution: DeepMind aims to further improve the system by integrating direct natural language understanding to expand the accessibility and effectiveness of mathematical assistance.

AlphaGeometry2 represents a qualitative leap in the field of AI applied to mathematics, bringing the resolution of geometric problems to a level never seen before. Using a linguistic model based on the Gemini architecture and an advanced symbolic deduction engine, this system is able to identify resolution strategies with a precision superior to that of most human experts. A few months ago we told you how Google had already reached a remarkable level in the Mathematics Olympiad. Now the new version significantly surpasses the previous result, demonstrating that it can compete with the winners of the International Mathematics Olympiad, obtaining a result comparable to that of a gold medal. The approach adopted combines two fundamental components: a linguistic model capable of generating suggestions based on a detailed geometric description and a symbolic engine, the DDAR (Deductive Database Arithmetic Reasoning), which verifies the logical coherence of the proposed solutions, building a deductive closure of the available information.

A key element that allowed AlphaGeometry2 to improve the performance of its predecessor is the SKEST algorithm, which implements an iterative search strategy based on knowledge sharing between several parallel search trees. This mechanism allows to simultaneously explore multiple solution paths, increasing the processing speed and improving the quality of the proofs generated. The efficiency of the system was further increased with a new C++ implementation of the DDAR, making it 300 times faster than the previous version written in Python.

A particularly interesting aspect of the development of AlphaGeometry2 is the analysis of the impact of pre-trained language models compared to those developed from scratch. The researchers observed that both approaches lead to complementary capabilities, suggesting that the combination of different training methodologies could be a key element for future performance improvement. Furthermore, it was found that the tokenizer used is not a determining factor for the success of the system, with similar results obtained both with specialized models with a small vocabulary and with generic tokenizers.

Despite its impressive progress, AlphaGeometry2 still has some limitations, particularly when it comes to solving problems with a variable number of points, nonlinear equations, or inequalities. To overcome these obstacles, DeepMind is exploring new strategies such as breaking complex problems into subproblems and applying reinforcement learning, paving the way for further evolution of AI in solving advanced mathematical problems.

AlphaGeometry2’s impact could extend far beyond the domain of geometry, with potential applications in physics, engineering, and mathematical research. The ability to develop a system that can address problems directly from natural language is an ambitious but realistic goal that will transform the way mathematicians and scientists interact with AI.

The continued evolution of AlphaGeometry demonstrates how AI can not only support, but potentially redefine, mathematical and scientific thinking.