Mathematician Timothy Gowers describes how ChatGPT 5.5 Pro, in under two hours, produced PhD-level research in additive combinatorics — specifically improving upper bounds on a problem from Mel Nathanson's paper on sumset sizes. The model first made a routine improvement to MIT student Isaac Rajagopal's exponential bound, then independently devised a novel construction using k-dissociated sets to achieve a polynomial bound, which Rajagopal assessed as 'almost certainly correct' and genuinely original at the level of ideas. Gowers reflects on the implications for mathematical research training, the future of PhD education, and what it means to contribute to mathematics when LLMs can solve 'gentle' open problems. Isaac Rajagopal provides a detailed technical guest section explaining the key idea ChatGPT contributed. The post also raises questions about where AI-produced mathematical results should be published and archived.
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Isaac’s evaluation of what ChatGPT achievedTim on what this means for mathematical researchAppendix 1 (Isaac)Appendix 2 (Isaac)Appendix 3 (Isaac)Sort: