DeepMind Cracks the Unsolvable: LLM Solves Longstanding Math Puzzle

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In a major breakthrough for artificial intelligence (AI) research, Google DeepMind has employed an LLM to solve a longstanding mathematical puzzle considered “unsolvable” by traditional methods. This feat, detailed in a recent Nature paper, marks a significant milestone in AI’s ability to tackle complex scientific challenges and opens doors for future discoveries in various fields.

Key Highlights:

  • Google DeepMind’s AI tool “FunSearch” leverages a large language model (LLM) to tackle complex math problems.
  • The LLM, “Codey,” cracked the “cap set” problem, a decades-old puzzle that eluded traditional methods.
  • FunSearch’s iterative approach generated and evaluated millions of Python code snippets, ultimately finding a solution.
  • This breakthrough marks a significant step in AI’s ability to solve complex scientific problems.

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The LLM in question, nicknamed “Codey,” is a specialized variant of DeepMind’s PaLM 2 model, trained on a massive dataset of code and text. Codey’s prowess was unleashed on the “cap set” problem, a decades-old puzzle in combinatorial mathematics that has stumped mathematicians for years. The problem involves finding sets of numbers with specific properties, and its complexity has resisted conventional solution methods.

Here’s where DeepMind’s innovation comes into play. The researchers developed a tool called “FunSearch” that leverages Codey’s capabilities in a unique way. FunSearch employs an iterative approach, prompting Codey to generate Python code snippets that might solve the cap set problem. These snippets are then evaluated by another algorithm within FunSearch, which assesses their validity and potential for success. This process is repeated millions of times, allowing Codey to refine its solutions and ultimately arrive at a valid one.

The journey to cracking the cap set problem wasn’t without its challenges. The researchers mention that FunSearch required “a couple of million suggestions and a few dozen repetitions of the overall process” before Codey successfully identified a working solution. This highlights the immense computational power and iterative refinement needed for such complex tasks.

The implications of this breakthrough extend far beyond solving a single math puzzle. DeepMind’s success with FunSearch signifies a crucial step forward in AI’s ability to tackle complex scientific problems. The iterative approach employed by Codey and FunSearch could be applied to other challenging domains, such as physics, chemistry, and materials science, offering a powerful tool for scientific discovery.

Furthermore, this achievement sheds light on the potential of LLMs to go beyond their traditional tasks of text generation and summarization. By specializing LLMs like Codey for specific purposes and employing innovative tools like FunSearch, AI can contribute to scientific progress in remarkable ways.

DeepMind’s successful application of an LLM to solve the “unsolvable” cap set problem represents a significant leap forward in AI research. This breakthrough opens doors for future scientific discoveries across various fields and underscores the potential of LLMs to become invaluable tools in the quest for human knowledge.


About the author


Jamie Davidson

Jamie Davidson is the Marketing Communications Manager for Vast Conference, a meeting solution providing HD-audio, video conferencing with screen sharing, and a mobile app to easily and reliably get work done."