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Not every discovery needs an LLM
TL;DR: AI-driven scientific discovery with systems such as AlphaTensor, AlphaEvolve, etc is en vogue and we are also heavily invested in that space. However, these LLM- and RL-driven approaches, while impressive often in themselves, are not always the right tool to get the job done. In this post I will talk about three recent projects from our group that take different angles on LLM- and RL-driven mathematical discovery systems. Two of them revisit classical problems made famous through these AI systems and show that classical structured search matches or beats them on these specific problem classes; with a tiny fraction of the compute. The third example goes the other way around: AI not as discovery engine, but an AI-accelerated subroutine sits inside a classical structured search and lets us settle a thirty-year-old conjecture on real algebraic plane curves of degree seven. This points to an interesting shift in the recent AI vs. classical discussion: it is not so much about whether
