Google DeepMind makes history with an AI that has solved an ancient and impossible mathematical problem

Today, technological advances have led artificial intelligence to reach levels never seen before. However, this progress is fraught with some problems, and one of the most important is the tendency of generative AI to invent information instead of giving precise answers, known as hallucination.

Nevertheless, Google DeepMind has taken a big step with its latest tool, FunSearch. This not only solves complex mathematical problems, but goes further, generating completely new and hitherto unknown answers.

The test scenario for FunSearch was the boundary set problem, which has been a challenge to experts for a long time. While other language models tend to invent answers, FunSearch stands out for its ability to find the solutions.

This achievement, just to remind you, is in addition to some previous ones by DeepMind, such as AlphaFold and AlphaGo. “To be very honest, we have hypotheses, but we don’t know exactly why it works,” says Alhussein Fawzi, a research scientist at Google DeepMind. “At the beginning of the project we didn’t know if it would work.”

This is how FunSearch works and manages to solve impossible mathematical problems

To better understand this achievement, here is the process, as it uses a unique approach: it starts with a model called Codey, a computer code-optimized version of Google’s PaLM 2, and then applies a second layer that scans and cleans the information .

DeepMind engineers created a Python representation of the bounds set problem, but removed the lines containing the solution. Codey intervened, adding lines that solved the problem precisely. Then, another layer checked and scored the solutions to see if they were true..

They mention that they left FunSearch running for several days, generating millions of possible solutions and giving increasingly refined results. “This is a promising paradigm,” says Terence Tao of the University of California. “It’s an interesting way to harness the power of large language models.”

The incredible thing is that Not only did he find answers to the limit set problem, but he also delved into another mathematical problem called the container packing problem..

This involves packaging items in as few containers as possible, a task widely used in computing for data center management and e-commerce. FunSearch surpassed human capabilities in speed and effectiveness.

In addition, “FunSearch results are also easier to understand. A recipe is usually clearer than the strange mathematical solution it produces,” they comment.

The natural question is: How does FunSearch do it? The answer lies in its all-in-one approach. Unlike other models, FunSearch not only solves existing problems, as it can also solve all types of mathematical problems thanks to its ability to generate code instead of specific solutions. This makes your results more understandable and accessible.

Mathematicians “are still trying to figure out the best way to incorporate large language models into our research workflow, in ways that harness their power while mitigating their drawbacks,” explains Terence Tao. “This certainly indicates a possible way forward.”