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- DeepMind's FunSearch solves an unsolved math problem.
- The tool utilizes a large language model, Codey.
- Demonstrates potential for AI in complex problem-solving.
DeepMind, a subsidiary of Google, has recently made significant strides in the realm of mathematical research. Their latest tool, FunSearch, has successfully cracked a long-standing unsolved problem in pure mathematics. This is an important moment in the application of large language models in scientific discovery, writes MIT Technology Review.
Large language models in scientific research
The journey of FunSearch began with the challenge of solving the cap set problem, a complex issue in pure mathematics that has puzzled mathematicians for years. This problem involves determining the maximum size of a specific type of set, a task so intricate that even the acclaimed mathematician Terence Tao labeled it his favorite open question.
What sets FunSearch apart is its unique approach. Unlike previous tools that treated mathematical problems as puzzles similar to games like Go or chess, FunSearch employs a large language model named Codey, which is a refined version of Google’s PaLM 2, specifically fine-tuned for understanding and generating computer code. This model works in tandem with other systems designed to filter out incorrect or nonsensical answers and refine the promising ones.
The process involves Codey suggesting code to fill in the blanks of an incomplete Python program sketching out the problem. The suggestions are then evaluated and refined in a repetitive cycle until a viable solution emerges. This methodology, while experimental, proved successful in not only addressing the cap set problem but also in tackling other complex issues like the bin packing problem.
Implications for the future of mathematical research
The success of FunSearch is not just in solving these problems but in the manner it achieved these results. By generating code - a recipe for the solution rather than the solution itself - FunSearch offers a more versatile and understandable approach to problem-solving. This is a testament to the untapped potential of AI in scientific research, providing a new paradigm for approaching and solving intricate problems.