DeepMind’s FunSearch Makes History
Google DeepMind’s artificial intelligence (AI) system, FunSearch, has solved a decades-old mathematical puzzle, cementing its place in scientific history. The cap set problem, a notorious question in combinatorial mathematics that remained unsolved for 30 years, has finally been cracked thanks to FunSearch’s innovative approach. This breakthrough underscores AI’s expanding role in driving scientific discovery.
What is the Cap Set Problem?
The cap set problem seeks to find the largest possible set of points in a finite mathematical space (e.g., a three-dimensional grid) where no three points form an arithmetic progression. While seemingly simple, this combinatorial optimization challenge has long been regarded as one of the field’s most complex questions. Despite decades of effort and theoretical advancements by mathematicians, a definitive solution remained elusive.
How Does FunSearch Work?
Unlike traditional AI models, FunSearch combines large language models (LLMs) with mathematical discovery. It operates through a two-step iterative cycle:
- Creative Generation: The language model generates potential solutions or formulas for the problem.
- Evaluation and Refinement: A “evaluator” module tests these solutions for mathematical validity, selects the most promising ones, and feeds them back into the system.
This process merges human intuition with machine efficiency, uncovering novel pathways to solutions that were previously unexplored.
Why Does This Matter?
- A New Era in Scientific Discovery: FunSearch proves that AI can tackle abstract mathematical problems, moving beyond data analysis or predictions. This expands AI’s potential in theoretical sciences.
- Practical Applications: Solving the cap set problem could advance fields like cryptography, data compression, and even quantum computing.
- Human-AI Collaboration: The system demonstrates how AI can act as a “partner” in solving problems too complex for humans alone.
DeepMind’s Scientific Journey
DeepMind previously revolutionized strategy games with AlphaGo and protein folding with AlphaFold. FunSearch now marks the company’s first major success in theoretical mathematics. The team believes this technology could eventually address challenges in group theory, statistical physics, and beyond.
Expert Reactions
Mathematician Dr. Terence Tao (a Fields Medalist known for his work on the cap set problem) commented, “This result is an exciting sign that AI will be adopted as a new tool in mathematical research.”
