Google Deepmind has announced a major breakthrough, claiming to have developed a new AI system capable of solving complex geometrical problems. Published on January 17, the research marks a significant development in the improvement of AI systems.

While artificial intelligence has made waves with its ability to solve difficult mathematical problems, geometry continued to pose a challenge. AI systems are known to struggle with the mathematical reasoning required to solve geometry problems.

However, this might now change, with Google Deepmind’s new AI system solving geometry proofs used to test high-school students at the International Mathematical Olympiad.

## Here’s how Deepmind Scientists Cracked the Geometry Challenge

Despite being one of the oldest branches of mathematics, geometry has constantly proven difficult for AI systems to work with. This is primarily due to a lack of training data, which would be necessary for the systems to be able to solve challenging logical problems.

AI systems are typically trained using machine learning. This involves engineers providing them with the necessary data on how to complete a task successfully, following which the systems can learn to solve similar problems.

*The challenge, however, lies in the limited number of human demonstrations that are available for proving geometry theorems.*

To get around the issue, Google Deepmind researchers took up a new, hybrid approach to build AlphaGeometry, the new AI system. The system comprises two key components – a neural network and a symbolic AI engine.

The former is an AI-based loosely on the human brain and has played a pivotal role in recent major technological advances.

The symbolic AI engine, on the other hand, uses a series of human-coded rules to represent data as symbols and then reason by manipulating the symbols.

Before deep learning based on neural networks gained popularity and saw significant advancements during the mid-2000s, symbolic AI had been a popular approach for decades.

**Gold medalists at the Olympiad have solved 25.9 problems on average, and AlphaGeometry isn’t too far behind.**

In this case, the researchers synthetically generated 100 million examples of geometry problems. These were similar, but not identical to the problems used in the International Mathematics Olympiad – a test where the top-performing students have to solve complex theorems.

The synthesized theorems, along with their proofs, were then used to train the neural network that powers AlphaGeometry. This, along with the system’s ability to search through branching points, enabled it to solve complex geometry problems even in the absence of any human input.

Putting AlphaGeometry’s capabilities to the test, researchers then had it try to solve 30 problems from the Olympiad.

The AI system successfully solved 25 of these problems – a huge improvement compared to past attempts.

For comparison, the previous best method only allowed an AI system to solve 10 of the 30 problems.

## What Does This Mean for the Future of AI?

So far, most of the excitement surrounding AI has been focused on ChatGPT and other similar large language models.

Deepmind, on the other hand, focused on more practical applications for artificial intelligence, such as breakthroughs in different areas of mathematics and recent developments in weather forecasting.

The new system not only solved the theorems by providing proofs in a way that was understandable by humans but even came up with a new version of one of the theorems.

Considering previous failures in solving complex geometrical problems using AI, this is undoubtedly a major development. The success of the approach adopted also indicates that in domains where there’s a lack of training data for deep learning, synthetic data is a viable solution.

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