Tracy Ke (@TracyKe7) profile picture

Professor of Statistics, Harvard University

Cambridge, MA
Joined July 2020
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“The Gold Rush in AI4Math, II: What are signatures of AI-assisted proofs?” arxiv.org/abs/2611.08412 How do AI-assisted proofs differ from human-written ones? We assemble a dataset of 8,281 mathematical papers spanning different forms and levels of AI involvement. To represent each paper, we introduce the graph of immediate proof support (GIPS). Our study reveals a qualitative gradient of AI involvement in the resulting feature space and identifies statistically significant features (“signatures”) of AI assistance in developing and organizing mathematical arguments.
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I asked ChatGPT to rank the difficulty of the Millennium Prize problems. It lists P vs NP as #1 difficult one, because it requires "a fundamentally new kind of mathematics." Given today's news, I am really curious who (human or AI) will make the next breakthrough on P vs NP ~
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"The Gold Rush in AI4Math: Where Are We Now?" arxiv.org/abs/2608.24961 Is substantive AI use in math research increasing? Which subfields are most affected? What problems have been solved? Who is writing them—and which AI models are they using? An empirical study of 32,944 math arXiv submissions from Mar. 1–Aug. 20, 2026.
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The AI-use categories are determined through LLM-based classification of authors’ disclosures in the papers.
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New paper! A problem dating back to Kolmogorov (1937), the nonnegative inverse eigenvalue problem. We identify a new impossibility region for the first genuinely open symmetric case, 5×5. And, fittingly for 2026, AI helped us in manuscript preparation. arXiv:2608.19435
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My first experience of working closely with AI on mathematical problems, which is amazing. We used GPT-5.6.
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On Thursday's Joint Statistical Meeting (10:00am, session 436), I will present discoveries on 83K statistical papers (including topic modeling of paper abstracts and network modeling of author-author co-citation relationships).
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Our paper "Predicting returns with text data" is highlighted for JSM 2020. amstat.org/ASA/News/Newswort… Link to the paper: zke.fas.harvard.edu/papers/S…
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