Google’s DeepMind AI Just Cracked an Unsolved Math Problem

Google's DeepMind AI has managed to solve a math problem that had eluded mathematicians for decades — the cap set problem. The results were published in the journal Nature.

The discovery was made using a new tool called FunSearch, a large-language model that looks for functions (hence the name, it is not fun) to solve different kinds of mathematical problems. FunSearch combines an LLM called Codey, a version of Google’s health care model, PaLM 2, with rejection algorithms that sift through suggestions, producing correct and novel solutions. While other AI tools were limited to specific tasks, FunSearch's versatility makes it applicable to a wide range of mathematical problems

It represents a leap in terms of AI technology: Large-language model-based AI like ChatGPT and Google's Bard have proven useful in combing through existing knowledge databases to find answers to problems, but they are notoriously bad at math. And when it comes to generating entirely new knowledge, most models start spewing a ton of factually incorrect information or hallucinating.

FunSearch also spewed a ton of nonsense, according to the paper. But there were diamonds among the debris, the researchers found. Particularly, FunSearch challenges the idea that these AI just generate known content and instead show they can make novel discoveries. .

“What makes FunSearch a particularly powerful scientific tool is that it outputs programs that reveal how its solutions are constructed, rather than just what the solutions are,” Google DeepMind wrote in a company blog post.

Unlike its predecessors, FunSearch uses a two-step process. Initially, researchers outline a problem in Python, omitting the lines specifying the solution. Codey then fills in the missing parts, and a second algorithm scores the suggestions, iterating the process to refine results. This way, FunSearch successfully produced a correct and previously unknown solution to the decades-old cap set problem, a puzzle that has stumped mathematicians due to its intricate nature. The problem involves working out how many dots can be set down in an area where no three dots ever form a straight line.

FunSearch's success opens new avenues for leveraging large language models in mathematical problem-solving. The tool's ability to generate code, offering a recipe for solutions, indicates potential applications across various problem domains.

While scientists explore ways to incorporate AI into their processes, FunSearch's achievement suggests a promising paradigm for harnessing the power of these models in future research.