AI makes new mathematical discovery

• Google DeepMind's FunSearch AI solves the long-standing cap set problem
• The LLM uses an iterative loop to evolve new, verifiable knowledge
• Researchers can use this AI partner to accelerate scientific discovery

For centuries, the image of a mathematician involved a chalkboard, deep thought, and human intuition. A recent breakthrough by Google's DeepMind, however, introduces a powerful new element: an AI partner that can make novel discoveries.

A New Kind of Thinking Machine

The discovery centres on an AI system from Google DeepMind called FunSearch. Unlike previous AI that might find solutions already known to humans, FunSearch made a genuine, new discovery in a complex area of mathematics. It tackled the 'cap set problem', a puzzle that has stumped mathematicians for decades. This wasn't about simply crunching numbers faster; it was about generating new, verifiable knowledge that was not part of the AI's training data. The achievement, published in the journal Nature, marks a significant milestone: the first time a large language model (LLM) has been used to find a solution to a long-standing scientific puzzle.

How Does It Actually Work?

FunSearch’s method is a clever blend of creativity and discipline. It pairs a creative LLM—a version of Google's PaLM 2 trained on code—with a strict automated evaluator. The process is iterative: the user defines a problem in code, and the LLM suggests creative solutions, also in the form of computer programs. The evaluator then runs these programs, discards the incorrect or unhelpful ones, and keeps the promising ideas. The best solutions are then fed back to the LLM, which is prompted to improve upon them, creating a self-improving loop. Researchers describe it as an evolutionary process where ideas 'evolve' into new knowledge, harnessing the LLM's creativity while a rigorous system guards against errors and hallucinations.

The Mathematician's New Co-pilot

The key takeaway from this breakthrough isn't that AI will replace human mathematicians, but that it will become an invaluable partner. Experts see this as the dawn of a new era of AI-assisted discovery. Instead of being a black box, FunSearch produces its solutions as computer code, which means mathematicians can inspect, understand, and learn from the AI's novel approach. The system can be seen as a collaborator that can handle tedious calculations, check proofs, and explore countless possibilities, freeing up human researchers to focus on intuition, creativity, and the bigger picture. Working with these tools is described as being akin to collaborating with a very smart, if sometimes error-prone, colleague.

What This Means for India

This development has significant implications for India's burgeoning tech and research sectors. India already stands as the fourth-largest adopter of DeepMind's AlphaFold AI for biological sciences, with over 180,000 researchers using it. As AI becomes a key partner in fundamental sciences like mathematics, it can accelerate discovery at Indian institutions. The Indian government and private universities are already increasing their focus on AI and data science, with new institutions like the Jio Institute and centres of excellence at universities like Mahindra University. The ability to leverage AI as a research partner could amplify the work of India's mathematicians and scientists, helping to solve complex, real-world problems in fields from logistics and urban planning to finance and medicine. The nation's historic strength in mathematics provides a strong foundation for leading in this new, AI-powered era of science.