Google Deepmind's AlphaGeometry challenges the intelligence of the International Mathematical Olympiad (IMO) champion to solve complex geometric problems with an ability close to that of a human gold medalist, which is an amazing ability for AI that has never been seen before. But as AI moves closer to human intelligence, how will AlphaGeometry reshape the field of mathematics and even accelerate research in other fields, such as physics or engineering?
A revolutionary breakthrough from alphageometryIn the rapidly evolving field of AI, revolutionary breakthroughs often reshape our imagination of AI. A recent milestone came from Google's DeepMind, which recently published in the prestigious journal Nature, which introduced AlphaGeometry, an AI system with the ability to handle complex geometric and mathematical problems.
Geometry problems in the field of mathematics are a serious challenge to AI systems. Unlike mathematical problems, which have clear rules and limited possibilities, geometric problems, especially those at the Olympiad level, require a combination of creative intuition and logical reasoning. They require an understanding of abstract concepts, as well as the ability to find the best solution among a large number of potential solutions.
This AI system challenges the long-held belief that certain aspects of human intelligence, such as solving advanced math problems, are beyond the reach of AI's capabilities. Second, it demonstrates the potential of AI systems to make meaningful contributions to areas that require deep intelligence and creative capabilities.
AI will help mathematicians explore new speculationsTraditional AI systems, while excelling in structured environments with clear rules, struggle in the face of complex and abstract higher mathematics. At the heart of the problem lie two main obstacles: the need for deep reasoning and the limitations of data scarcity.
Mathematics, in particular, at the IMO level, requires nuanced understanding and the ability to deduce infinite possibilities, a task that requires more than just computational skills; It requires an AI that can think, reason, and deduce like the smartest human mind.
At the heart of AlphaGeometry's success is the innovative integration of neural language models (NLL) with a powerful deduction engine. This integration enables the AI to intuitively suggest possible resolution paths or structures, and then explore whether the logic of those suggestions is correct. Neural language models trained on massive datasets are adept at discerning patterns and generating hypotheses, mimicking the intuitive side of the human mind. nll is trained on a huge database of geometric problems, which is akin to having one mathematician think of a solution while another meticulously verifies the mathematical correctness of each idea.
The system's ability to generate its own training data by creating comprehensive geometry problems also means that it is free from its traditional reliance on human-generated data libraries. This approach not only solves the problem of data scarcity, but also demonstrates the potential for AI to learn and improve autonomously, which is necessary to move towards the development of artificial general intelligence (AGI).
In addition, the success of AlphaGeometry is far-reaching, and perhaps in the future, AI can contribute to advancing human knowledge in mathematics and other scientific fields. Through the process of proving and discovering mathematical theorems, AI can help mathematicians explore new speculations and solve long-standing problems, and accelerate the pace of mathematical research.
AI can reason across disciplines, self-teach, and solve problemsAlphaGeometry's test performance on IMO was successful in answering 25 correct answers out of 30 questions, which is almost on par with the Olympic gold medalist in human mathematics, with humans solving an average of 259 questions. Demonstrate that AI has made great strides in understanding and navigating complex geometries. 
（source：google deepmind）
AlphaGeometry's performance at the Gold level in IMO represents an AI capability that goes beyond routine tasks and simple calculations to handle complex abstract reasoning and problem solving. This may represent an important step forward in creating more advanced and versatile AI systems that can reason around, self-teach, and solve problems across disciplines.
The potential of this AI system goes far beyond the scope of a math competition. In the field of solving complex problems, this development has opened up new imaginations for the application of AI in various fields. AI's ability to generate hypotheses, derive solutions, and verify mathematical laws on its own will significantly accelerate the pace of scientific and technological development. From theoretical physics to engineering challenges, the principles and methods of this AI system can be adapted and applied to a wide range of complex problems, providing new tools for discovery and innovation.
AlphaGeometry's outstanding performance in the IMO competition not only proves AI's ability to solve complex mathematical problems, but also brings hope for the future development of the field of mathematics and opens up new possibilities for AI applications across disciplines. In the future, AI and human intelligence will work together to unlock a wider range of research fields.
Image by benzoixon freepik).