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Notes on a Path to AI Assistance in Mathematical Reasoning
Published 4 Oct 2023 in math.HO and cs.AI | (2310.02896v1)
Abstract: These informal notes are based on the author's lecture at the National Academies of Science, Engineering, and Mathematics workshop on "AI to Assist Mathematical Reasoning" in June 2023. The goal is to think through a path by which we might arrive at AI that is useful for the research mathematician.
- Jeremy Avigad. Notes on a formalization of the prime number theorem, 2004. https://www.andrew.cmu.edu/user/avigad/Papers/pntnotes.pdf.
- Formalising perfectoid spaces. POPL: Principles of Programming Languages, Association for Computing Machinery, pages 299–312, 2020.
- Thomas Bloom. On a density conjecture about unit fractions, 2021. https://arxiv.org/abs/2112.03726.
- Unit fractions, 2022. https://b-mehta.github.io/unit-fractions/.
- Johan Commelin and mathlib. Completion of the liquid tensor experiment, 2022. https://leanprover-community.github.io/blog/posts/lte-final/.
- Formalizing the solution to the cap set problem. In 10th International Conference on Interactive Theorem Proving, volume 141 of LIPIcs. Leibniz Int. Proc. Inform., pages Art. No. 15, 19. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2019.
- Advancing mathematics by guiding human intuition with AI. Nature, 600:70–74, 2021.
- On large subsets of 𝔽qnsubscriptsuperscript𝔽𝑛𝑞\mathbb{F}^{n}_{q}blackboard_F start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_q end_POSTSUBSCRIPT with no three-term arithmetic progression. Ann. of Math. (2), 185(1):339–343, 2017.
- Giles Gardam. A counterexample to the unit conjecture for group rings. Ann. of Math. (2), 194(3):967–979, 2021.
- Formalizing Gardam’s disproof of Kaplansky’s unit conjecture, 2022. https://siddhartha-gadgil.github.io/automating-mathematics/posts/formalizing-gardam-disproof-kaplansky-conjecture/.
- Textbooks are all you need, 2023. https://arxiv.org/abs/2306.11644.
- Murmurations of elliptic curves, 2022. https://arxiv.org/abs/2204.10140.
- Draft, sketch, and prove: Guiding formal theorem provers with informal proofs, 2022. https://arxiv.org/abs/2210.12283.
- “const_mul_action” in Lean3’s mathlib, 2022. https://github.com/leanprover-community/mathlib/blob/f23a09ce6d3f367220dc3cecad6b7eb69eb01690/src/topology/algebra/const_mul_action.lean.
- Hypertree proof search for neural theorem proving, 2022. https://arxiv.org/abs/2205.11491.
- Mathematical reasoning via self-supervised skip-tree training, 2020. https://arxiv.org/abs/2006.04757.
- Peter Scholze. Liquid tensor experiment. Exp. Math., 31(2):349–354, 2022.
- Christian Szegedy, editor. A Promising Path Towards Autoformalization and General Artificial Intelligence, 2020.
- Autoformalization with large language models, 2022. https://arxiv.org/abs/2205.12615.
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