Bibliography

Every work this repository cites, once: Key, citation, and a stable link.

Shape: references

Key Citation Link
Adamczewski 2026 Adamczewski (2026). fc-review-results: an automated audit of formal-conjectures; README and the metadata of run c90271f0fa, 2026-09-11. GitHub repository https://github.com/tadamcz/fc-review-results
Adams 2016 Adams (2016). Proof auditing formalised mathematics. Journal of Formalized Reasoning 9(1), special issue Twenty years of the QED manifesto https://doi.org/10.6092/issn.1972-5787/4576
Aitken 1998 Aitken, Gray, Melham, Thomas (1998). Interactive theorem proving: an empirical study of user activity. Journal of Symbolic Computation 25(2). Read through Ringer 2019 https://doi.org/10.1006/jsco.1997.0175
Aitken 2000 Aitken, Melham (2000). An analysis of errors in interactive proof attempts. Interacting with Computers 12(6), 565-586. Read in full through the university https://doi.org/10.1016/S0953-5438(99)00023-5
Alexeev 2025 Alexeev (2025-12-05). Formalization of Erdős problems. Guest post, Xena Project blog https://xenaproject.wordpress.com/2025/12/05/formalization-of-erdos-problems/
Ammanamanchi 2026 Ammanamanchi, Bhat, Biderman (2026). Faults in our formal benchmarking: dataset defects and evaluation failures in Lean theorem proving. ICML 2026 arXiv:2606.29493
Anthropic 2026c Anthropic (2026). Fermat's Last Theorem. Research page; the owner's account of its own work https://www.anthropic.com/research/formalizing-fermats-last-theorem (archived: https://web.archive.org/web/20261023034152/https://www.anthropic.com/research/formalizing-fermats-last-theorem)
Avigad 2019 Avigad (2019). Learning logic and proof with an interactive theorem prover. In Hanna, Reid, de Villiers (eds.), Proof Technology in Mathematics Research and Teaching, Springer, 277-290 https://doi.org/10.1007/978-3-030-28483-1_13
Avigad 2024 Avigad (2024). Mathematics and the formal turn. Bulletin of the AMS 61(2), 225-240; preprint arXiv 2311.00007 https://doi.org/10.1090/bull/1832
Avigad 2026 Avigad, Buzzard, Commelin, Degenne, Morrison, Nash, Topaz (2026-10-16). How to formalize all of mathematics. Guest post, Xena Project blog https://xenaproject.wordpress.com/2026/10/16/how-to-formalize-all-of-mathematics/
Axiom 2026 Axiom (2026-01-08). From seeing why to checking everything. Research page; the owner's account https://axiommath.ai/research/from-seeing-why-to-checking-everything (archived: https://web.archive.org/web/20261012022104/https://axiommath.ai/research/from-seeing-why-to-checking-everything/)
Azerbayev 2023 Azerbayev, Piotrowski, Schoelkopf, Ayers, et al. (2023). ProofNet: autoformalizing and formally proving undergraduate-level mathematics. Preprint arXiv:2302.12433
Bancerek 2017 Bancerek, Byliński, Grabowski, Korniłowicz, Matuszewski, Naumowicz, Pąk (2017). The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning 61, 9-32 (online November 2017; volume 61 is the 2018 print volume) https://doi.org/10.1007/s10817-017-9440-6
Barendregt 2005 Barendregt, Wiedijk (2005). The challenge of computer mathematics. Philosophical Transactions of the Royal Society A 363, 2351-2375 https://doi.org/10.1098/rsta.2005.1650
Barik 2017 Barik, Smith, Lubick, Holmes, Feng, Murphy-Hill, Parnin (2017). Do developers read compiler error messages? ICSE 2017, 575-585. Abstract read https://doi.org/10.1109/ICSE.2017.59
Bartzia 2026 Bartzia, Beffara, Meyer, Narboux (2026). Proof assistants for undergraduate mathematics education: elements of an a priori analysis. International Journal of Mathematical Education in Science and Technology, 1-44 https://doi.org/10.1080/0020739x.2026.2632264
Bastani 2025 Bastani, Bastani, Sungu, Ge, Kabakcı, Mariman (2025). Generative AI without guardrails can harm learning: evidence from high school mathematics. Proceedings of the National Academy of Sciences 122(26), e2422633122. Abstract read (Crossref) https://doi.org/10.1073/pnas.2422633122
Bastounis 2026 Bastounis, Circelli, Hansen (2026). Navier-Stokes lost in translation: why Lean verification of AI autoformalisation does not guarantee correct natural language proofs. Preprint arXiv:2610.08144
Becker 2016 Becker (2016). An effective approach to enhancing compiler error messages. SIGCSE 2016, 126-131. Abstract read; the open copy refused automated reads https://doi.org/10.1145/2839509.2844584
Becker 2019 Becker, Denny, Pettit, Bouchard, Bouvier, Harrington and others (2019). Compiler error messages considered unhelpful: the landscape of text-based programming error message research. ITiCSE Working Group Reports, 177-210. Read in full through the university https://doi.org/10.1145/3344429.3372508
Becker 2024 Becker, de Frutos-Fernández, Diedering, van Doorn, Gouëzel and others (2024). A blueprint for the formalization of Carleson's theorem on convergence of Fourier series. Preprint arXiv:2405.06423
Beckert 2014 Beckert, Grebing, Böhl (2014). How to put usability into focus: using focus groups to evaluate the usability of interactive theorem provers. UITP 2014, EPTCS 167, 4-13 https://doi.org/10.4204/EPTCS.167.3
Beckert 2015 Beckert, Grebing, Böhl (2015). A usability evaluation of interactive theorem provers using focus groups. Software Engineering and Formal Methods workshops, LNCS, 3-19. Not read; its finding is cited through Ringer 2019 https://doi.org/10.1007/978-3-319-15201-1_1
Binder 2026 Binder, Lachnitt, Kosaian (2026). Apply2Isar: automatically converting Isabelle/HOL apply-style proofs to structured Isar. Preprint arXiv:2603.07771
Blanchette 2016 Blanchette, Kaliszyk, Paulson, Urban (2016). Hammering towards QED. Journal of Formalized Reasoning 9(1). DOI not on Crossref; resolved through doi.org https://doi.org/10.6092/issn.1972-5787/4593
Böhne 2018 Böhne, Kreitz (2018). Learning how to prove: from the Coq proof assistant to textbook style. EPTCS 267, 1-18 https://doi.org/10.4204/eptcs.267.1
Bolan 2025 Bolan, Breitner, Brox, Carlini, Carneiro and others, with Tao (2025). The Equational Theories Project: advancing collaborative mathematical research at scale. Preprint arXiv:2512.07087
Bottoni 2025 Bottoni, Cattaneo, Saçıkara (2025). Teaching "Foundations of Mathematics" with the Lean theorem prover. Preprint arXiv:2501.03352
Browning 2026 Browning, Hristova, Ledvinka, Springer, et al. (2026). A dataset of formalised theorem statements from the Annals of Mathematics. AI-MATH workshop, NeurIPS 2026 arXiv:2610.18301
Buçinca 2021 Buçinca, Malaya, Gajos (2021). To trust or to think: cognitive forcing functions can reduce overreliance on AI in AI-assisted decision-making. Proceedings of the ACM on Human-Computer Interaction 5(CSCW1), 1-21 https://doi.org/10.1145/3449287
Buzzard 2024 Buzzard (2024-12-11). Fermat's Last Theorem: how it's going. Xena Project blog https://xenaproject.wordpress.com/2024/12/11/fermats-last-theorem-how-its-going/
Buzzard 2025 Buzzard (2025-10-22). Formal or not formal? That is the question in AI for theorem proving. Xena Project blog https://xenaproject.wordpress.com/2025/10/22/formal-or-not-formal-that-is-the-question-in-ai-for-theorem-proving/
Buzzard 2026a Buzzard (2026-09-04). FLT: Anthropic has beaten me to it. Xena Project blog; read by both sides, and again by the maintainer's session https://xenaproject.wordpress.com/2026/09/04/flt-anthropic-has-beaten-me-to-it/
Buzzard 2026b Buzzard (2026-08-13). The Annals Challenge. Xena Project blog https://xenaproject.wordpress.com/2026/08/13/the-annals-challenge/
Buzzard 2026c Buzzard (2026-10-01). To grieve, or not to grieve? Xena Project blog https://xenaproject.wordpress.com/2026/10/01/to-grieve-or-not-to-grieve/
Buzzard 2026d Buzzard (2026-07-20). Human mathematicians are being outcounterexampled. Xena Project blog https://xenaproject.wordpress.com/2026/07/20/human-mathematicians-are-being-outcounterexampled/
Carl 2020 Carl (2020). Using automated theorem provers for mistake diagnosis in the didactics of mathematics. Preprint arXiv:2002.05083
Carl 2020b Carl (2020). Automatized evaluation of formalization exercises in mathematics. Preprint arXiv:2006.01800
Carl 2022 Carl, Lorenzen, Schmitz (2022). Natural language proof checking in introduction to proof classes: first experiences with Diproche. ThEdu'21, EPTCS 354, 59-70 https://doi.org/10.4204/EPTCS.354.5
Carl 2024 Carl (2024). Improving the Diproche CNL through autoformalization via large language models. ThEdu'23, EPTCS 400, 44-58 https://doi.org/10.4204/EPTCS.400.4
Carneiro 2024 Carneiro (2024). Lean4Lean: verifying a typechecker for Lean, in Lean. Preprint arXiv:2403.14064
Carter 2013 Carter, Monks (2013). Lurch: a word processor that can grade students' proofs. CICM 2013 Workshops and Work in Progress, CEUR-WS 1010, paper 4 https://ceur-ws.org/Vol-1010/paper-04.pdf
Chen 2025 Chen, Wu, Chen, et al. (2025). ReForm: reflective autoformalization with prospective bounded sequence optimization. ICLR 2026 arXiv:2510.24592
Chen 2026b Chen, Marwaha, Lu, Yuen, Peng (2026). Prove2Me: an open collaborative platform for scaling math formalization. Preprint arXiv:2608.28433
Chung 2026 Chung, Cai, Li, Yin, Agarwal and others, with Arora (2026). Goedel-Architect: streamlining formal theorem proving with blueprint generation and refinement. Preprint arXiv:2606.06468
CMU L3 2025 cmu-l3 (2025, news to October 2025, read 2026). LLMLean: LLMs and Lean for tactic suggestions and proof completion. GitHub repository README https://github.com/cmu-l3/llmlean
Collins 2024 Collins, Jiang, Frieder, Wong, Zilka, Bhatt, Lukasiewicz, Wu, Tenenbaum, Hart, Gowers, Li, Weller, Jamnik (2024). Evaluating language models for mathematics through interactions. PNAS 121(24); preprint arXiv 2306.01694 https://doi.org/10.1073/pnas.2318124121
Collins 2026 Collins, Frieder, Bayer, Loader, Lim, Song, Zaiser, Zhou, Li, Looi, Tenenbaum, Bhatt, Weller, Hernandez-Orallo, Freer, Chen, Sucholutsky (2026). Human agency in initial human-AI proof formalization workflows. Preprint arXiv:2606.04273
Commelin 2024 Commelin, Topaz (2024). Abstraction boundaries and spec driven development in pure mathematics. Bulletin of the AMS 61, 241-255. Read in the preprint https://doi.org/10.1090/bull/1831 (arXiv:2309.14870)
Commelin 2026 Commelin, Jamnik, Ochigame, Taelman, Venkatesh (2026). Shaping the future of mathematics in the age of AI. Preprint arXiv:2603.24914
Corbineau 2008 Corbineau (2008). A declarative language for the Coq proof assistant. TYPES 2007, LNCS 4941, 69-84. Title and venue only https://doi.org/10.1007/978-3-540-68103-8_5
Coscoy 1995 Coscoy, Kahn, Théry (1995). Extracting text from proofs. TLCA 1995, LNCS 902, 109-123. Title and venue only https://doi.org/10.1007/BFb0014048
Cramer 2010 Cramer, Fisseni, Koepke, Kühlwein, Schröder, Veldman (2010). The Naproche project: controlled natural language proof checking of mathematical texts. CNL 2009, LNCS 5972, 170-186. Title and venue only https://doi.org/10.1007/978-3-642-14418-9_11
Cramer 2013 Cramer (2013). Proof-checking mathematical texts in controlled natural language. Doctoral dissertation, Universität Bonn https://hdl.handle.net/20.500.11811/5780
Dai 2026 Dai, Yan, Lin (2026). The signal-coverage matrix: stratifying type and semantic errors in statement autoformalization. Preprint arXiv:2606.28013
DeepSeek 2025 DeepSeek (2025-04-30). DeepSeek-Prover-V2-671B. Model card; the owner's results https://huggingface.co/deepseek-ai/DeepSeek-Prover-V2-671B
De Lon 2021 De Lon, Koepke, Lorenzen, Marti, Schütz, Wenzel (2021). The Isabelle/Naproche natural language proof assistant. CADE-28, LNCS 12699, 614-624 https://doi.org/10.1007/978-3-030-79876-5_36
Deng 2026 Deng, Farber, Narasimha, Sivakumar, Xue (2026). Fix, not just resample: bounded compiler-guided repair in Lean 4. Preprint arXiv:2610.26942
Denny 2014 Denny, Luxton-Reilly, Carpenter (2014). Enhancing syntax error messages appears ineffectual. ITiCSE 2014, 273-278. Abstract read https://doi.org/10.1145/2591708.2591748
Denny 2020 Denny, Prather, Becker (2020). Error message readability and novice debugging performance. ITiCSE 2020, 480-486. Abstract read https://doi.org/10.1145/3341525.3387384
Denny 2021 Denny, Prather, Becker, Mooney, Homer, Albrecht, Powell (2021). On designing programming error messages for novices: readability and its constituent factors. CHI 2021. Abstract read https://doi.org/10.1145/3411764.3445696
De Toffoli 2024 De Toffoli (2024). Proofs for a price: tomorrow's ultra-rigorous mathematical culture. Bulletin of the AMS 61 https://doi.org/10.1090/bull/1823
Dressler 2026 Dressler (undated, read 2026). lean-lsp-mcp: Lean theorem prover MCP. GitHub repository README https://github.com/oOo0oOo/lean-lsp-mcp
Erdős DB 2026 Tao and contributors (read 2026). erdosproblems database: README and summary statistics, generated 2026-10. GitHub repository https://github.com/teorth/erdosproblems/blob/main/STATISTICS.md
Erdős-wiki 2026 erdosproblems contributors (2026). AI contributions to Erdős problems. Wiki page, data as of 2026-06-30 (may move) https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems
Eremondi 2019 Eremondi, Swierstra, Hage (2019). A framework for improving error messages in dependently-typed languages. Open Computer Science 9(1), 1-32 https://doi.org/10.1515/comp-2019-0001
Fan 2025 Fan, Tang, Le, Shen, Tan, Zhao, Shen, Li, Gašević (2025). Beware of metacognitive laziness: effects of generative artificial intelligence on learning motivation, processes, and performance. British Journal of Educational Technology 56, 489-530 https://doi.org/10.1111/bjet.13544
Feng 2026 Feng, Mao, Arekar, Zhong, Huang, Si, Li (2026). Aligning faithfulness for theory-scale autoformalization: FaithAlign. Preprint arXiv:2610.18498
Firsching 2026 Firsching, Lezeau, Mercuri, Horváth, et al. (2026). Formal Conjectures: an open and evolving benchmark for verified discovery in mathematics. Preprint arXiv:2605.13171
First 2023 First, Rabe, Ringer, Brun (2023). Baldur: whole-proof generation and repair with large language models. ESEC/FSE 2023 https://doi.org/10.1145/3611643.3616243 (arXiv:2303.04910)
Fuller 2014 Fuller, Weber, Mejía-Ramos, Rhoads, Samkoff (2014). Comprehending structured proofs. JIEEM 7(1). https://openalex.org/W2184046398
Gadgil 2026 Gadgil (undated, read 2026). LeanAide: AI-based tools for the Lean theorem prover. GitHub repository README https://github.com/siddhartha-gadgil/LeanAide
Ganesalingam 2017 Ganesalingam, Gowers (2017). A fully automatic theorem prover with human-style output. Journal of Automated Reasoning 58(2), 253-291 (online 2016). Read in the preprint, whose earlier title says problem solver for theorem prover https://doi.org/10.1007/s10817-016-9377-1 (arXiv:1309.4501)
Gao 2025 Gao, Wang, Jiang, et al. (2025). Herald: a natural language annotated Lean 4 dataset. ICLR 2025 arXiv:2410.10878
Garousi 2019 Garousi, Felderer, Mäntylä (2019). Guidelines for including grey literature and conducting multivocal literature reviews in software engineering. Information and Software Technology 106, 101-121 https://doi.org/10.1016/j.infsof.2018.09.006
GasStationManager 2026 GasStationManager (undated, read 2026). LeanTool: helping LLMs be better at Lean. GitHub repository README https://github.com/GasStationManager/LeanTool
GitHub 2026e GitHub (read 2026-10-29). Public metadata (stars, last push) of the repositories named in review.md, through the unauthenticated API: 23 repositories and one repository search by the formal side, and LeanDojo by the human side. The reviewers' count https://api.github.com/repos/PatrickMassot/leanblueprint (one of the calls)
GitHub 2026f GitHub (read 2026-10-29). Formal Conjectures issues and pull requests by the labels misformalization and ai-audit, and their states, through GitHub search. The human side's count, checked again at the audit the same day https://github.com/google-deepmind/formal-conjectures/issues?q=label%3Amisformalization
GitHub 2026g GitHub (read 2026-10-29). PNT+ pull requests with and without the ai label, by state, through GitHub search. The human side's count https://github.com/AlexKontorovich/PrimeNumberTheoremAnd/pulls?q=label%3Aai
GitHub 2026i GitHub (read 2026-10-29). PNT+ repository at commit 127b50e (2026-10-20): the workflow files under .github/workflows and lakefile.toml, through the unauthenticated public API; no comparator step, challenge file or formalization.yaml in the tree. The reviewer's read https://github.com/AlexKontorovich/PrimeNumberTheoremAnd/tree/127b50e33f6033e2147921167a117af96d9ba4ea/.github/workflows
Gleirscher 2023 Gleirscher, Sachtleben, Peleska (2023). Qualification of proof assistants, checkers, and generators: where are we and what next? Science of Computer Programming, article 102930; preprint arXiv 2302.09546 https://doi.org/10.1016/j.scico.2023.102930
Gloeckle 2026 Gloeckle, Rammal, Arnal, Munos, Cabannes, Synnaeve, Hayat (2026). Automatic textbook formalization. Preprint; the owners' account arXiv:2604.03071
Goddard 2012 Goddard, Roudsari, Wyatt (2012). Automation bias: a systematic review of frequency, effect mediators, and mitigators. Journal of the American Medical Informatics Association 19(1), 121-127 https://doi.org/10.1136/amiajnl-2011-000089
Goedel-LM 2025 Goedel-LM (2025-07-14). Goedel-Prover-V2-32B. Model card; the owner's results https://huggingface.co/Goedel-LM/Goedel-Prover-V2-32B
Gonthier 2013 Gonthier, Asperti, Avigad, Bertot, Cohen, Garillot, Le Roux, Mahboubi, and others (2013). A machine-checked proof of the odd order theorem. ITP 2013, LNCS 7998, 163-179 https://doi.org/10.1007/978-3-642-39634-2_14
Google 2025 Cohen-Addad, Woodruff (2025, updated 2026-05-18). Gemini-backed Paper Assistant Tool provides automated feedback for theoretical computer scientists at STOC 2026. Google Research blog; the owner's account of its own tool (may move) https://research.google/blog/gemini-provides-automated-feedback-for-theoretical-computer-scientists-at-stoc-2026/
Google DeepMind 2026 Google DeepMind and the Formal Conjectures authors (undated, read 2026). formal-conjectures: README and contributing guide. GitHub repository; read by both sides https://github.com/google-deepmind/formal-conjectures
Gopinathan 2023 Gopinathan, Keoliya, Sergey (2023). Mostly automated proof repair for verified libraries. PACMPL 7(PLDI), 25-49 https://doi.org/10.1145/3591221
Grabowski 2010 Grabowski, Korniłowicz, Naumowicz (2010). Mizar in a nutshell. Journal of Formalized Reasoning 3(2). DOI not on Crossref; resolved through doi.org https://doi.org/10.6092/issn.1972-5787/1980
Gui 2026 Gui, Yang, Shi (2026). Evaluating the robustness of proof autoformalization in Lean 4. Preprint arXiv:2606.14867
Guo 2026b Guo, Patel, Mehta, Kothari, Lu, Voss, Bhattacharyya, Donovan, Hartmann, Ranade (2026). LeanSide: a formally verified co-reasoning system for natural-language proofs. Preprint arXiv:2610.00760
Hales 2017 Hales, Adams, Bauer, Dang, Harrison, Hoang, Kaliszyk, Magron, and others (2017). A formal proof of the Kepler conjecture. Forum of Mathematics, Pi 5, e2 https://doi.org/10.1017/fmp.2017.1
Hales 2026 Hales (2026-10-09). What mathematicians should know about the Lean theorem prover: questions of reliability and AI. Guest post on Tao's blog; read by both sides, and again at the merge https://terrytao.wordpress.com/2026/10/09/what-mathematicians-should-know-about-the-lean-theorem-proverquestions-of-reliability-and-ai/
Han 2026 Han, Kim, Park, et al. (2026). SHADOWBENCH: toward reliable automatic evaluation of semantic alignment in autoformalization. EMNLP 2026 arXiv:2608.29270
Hanna 2021 Hanna, Yan (2021). Opening a discussion on teaching proof with automated theorem provers. For the Learning of Mathematics 41(3), 42-46. Paywalled; read through Tran Minh 2025 https://www.jstor.org/stable/27091220
Hanna 2024 Hanna, Larvor, Yan (2024). Using the proof assistant Lean in undergraduate mathematics classrooms. ZDM Mathematics Education 56, 1517-1529. Read in the authors' copy https://doi.org/10.1007/s11858-024-01577-9
Harmonic 2024 Harmonic (2024-07-09). One month in: a new SOTA on MiniF2F and more. Company news page; the owner's results https://harmonic.fun/news/minif2f/ (archived: https://web.archive.org/web/20260521005251/https://www.harmonic.fun/news/minif2f/)
Harrison 1998 Harrison (1998). Proof style. TYPES 1996, LNCS 1512, 154-172 https://doi.org/10.1007/BFb0097791
Harrison 2006 Harrison (2006). Towards self-verification of HOL Light. IJCAR 2006, LNCS 4130, 177-191. Paywalled https://doi.org/10.1007/11814771_17
Hattori 2025 Hattori, Matsuzaki, Fujiwara (2025). Natural language translation of formal proofs through informalization of proof steps and recursive summarization along proof structure. INLG 2025 arXiv:2509.09726
Hentschel 2016 Hentschel, Hähnle, Bubel (2016). An empirical evaluation of two user interfaces of an interactive program verifier. ASE 2016, 403-413. Read in full through the university https://doi.org/10.1145/2970276.2970303
Hu 2025 Hu, Zhou, Grechuk, Tyukin (2025). StepProof: step-by-step verification of natural language mathematical proofs. Preprint arXiv:2506.10558
Hubert 2025 Hubert, Mehta, Sartran, Horváth, Žužić, Wieser, et al. (2025). Olympiad-level formal mathematical reasoning with reinforcement learning. Nature, 607-613 https://doi.org/10.1038/s41586-025-09833-y
Iannone 2023 Iannone, Thoma (2023). Interactive theorem provers for university mathematics: an exploratory study of students' perceptions. International Journal of Mathematical Education in Science and Technology 55, 2622-2644 https://doi.org/10.1080/0020739x.2023.2178981
Iannone 2025a Iannone, Marasingha, Thoma (2025). Teaching mathematics with Lean: interactive theorem provers in the classroom. Notices of the AMS 72. Not reached: the publisher's page asked for a browser check https://doi.org/10.1090/noti3184
Iannone 2025b Iannone, Thoma (2025). "It feels like sort of cheating ...": mathematics students coding proofs with an interactive theorem prover. Digital Experiences in Mathematics Education 12, 366-392 https://doi.org/10.1007/s40751-025-00193-w
Ilin 2026 Ilin, Nugent (2026). Sorries are not the hard part: an expert-review case study of a semi-autonomous formalization. Preprint arXiv:2606.13925
Isabelle 2026 Isabelle developers (undated, read 2026). Overview. Isabelle website https://isabelle.in.tum.de/overview.html
Ishii 2014 Ishii, Asai (2014). Report on a user test and extension of a type debugger for novice programmers. TFPIE 2014, EPTCS 170, 1-18 https://doi.org/10.4204/EPTCS.170.1
Jiang 2023c Jiang, Welleck, Zhou, Li, Liu, Jamnik, Lacroix, Wu, Lample (2023). Draft, sketch, and prove: guiding formal theorem provers with informal proofs. ICLR 2023 arXiv:2210.12283
Kalyuga 2003 Kalyuga, Ayres, Chandler, Sweller (2003). The expertise reversal effect. Educational Psychologist https://doi.org/10.1207/S15326985EP3801_4
Kamoi 2024 Kamoi, Zhang, Zhang, Han, Zhang (2024). When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMs. Transactions of the ACL 12. doi:10.1162/tacl_a_00713
Kerjean 2022 Kerjean, Le Roux, Massot, Mayero, Mesnil, Modeste, Narboux, Rousselin (2022). Utilisation des assistants de preuves pour l'enseignement en L1. La Gazette de la Société Mathématique de France 174, 35-55. Read through Ouvrier-Buffet 2026 https://hal.science/hal-03979238
Kim 2026b Kim, Poiroux, Bosselut (2026). Do LLMs game formalization? Evaluating faithfulness in logical reasoning. VerifAI-2 workshop, ICLR 2026, non-archival arXiv:2604.19459
Kirov 2026a Kirov (2026-02-08). Leaning on AI. Blog https://rkirov.github.io/posts/lean5/
Kirov 2026b Kirov (2026-03-08). Human intuition, AI formalization: a real analysis case study. Blog https://rkirov.github.io/posts/lean6/
Klowden 2026 Klowden, Tao (2026). Mathematical methods and human thought in the age of AI. Preprint arXiv:2603.26524
Knobelsdorf 2017 Knobelsdorf, Frede, Böhne, Kreitz (2017). Theorem provers as a learning tool in theory of computation. ICER 2017, 83-92 https://doi.org/10.1145/3105726.3106184
Kondylidou 2026 Kondylidou, Blanchette, Heule (2026). Tao's equational proof challenge accepted. IJCAR 2026, LNCS, 3-21; read in the technical report, arXiv 2605.21200 https://doi.org/10.1007/978-3-032-32589-1_1
Kosmyna 2025 Kosmyna, Hauptmann, Yuan, Situ, Liao, Beresnitzky, Braunstein, Maes (2025). Your brain on ChatGPT: accumulation of cognitive debt when using an AI assistant for essay writing task. Preprint arXiv:2506.08872
Koutsoukou-Argyraki 2020 Koutsoukou-Argyraki (2020). Formalising mathematics in praxis: a mathematician's first experiences with Isabelle/HOL and the why and how of getting started. Jahresbericht der Deutschen Mathematiker-Vereinigung 123, 3-26 (online 2020, print 2021) https://doi.org/10.1365/s13291-020-00221-1
Krishnamurthi 2026 Krishnamurthi, Flatt (2026). Type-error ablation and AI coding agents. Preprint arXiv:2606.01522
Kuhn 2014 Kuhn (2014). A survey and classification of controlled natural languages. Computational Linguistics 40(1), 121-170 https://doi.org/10.1162/COLI_a_00168
Kung 2026 Kung, Song, Hwang, Yoon, Li, Severini, Olšák, Lockhart, Le, Gokturk, Luong, Pfister, Peng (2026). LEAP: supercharging LLMs for formal mathematics with agentic frameworks. Preprint arXiv:2606.03303
Lean-community 2026 Lean community (undated, read 2026). lean4game documentation, file create_game.md, section on hints https://github.com/leanprover-community/lean4game/blob/main/doc/create_game.md
LeanDojo 2026 lean-dojo (undated, read 2026). Lean Copilot: LLMs as copilots for theorem proving in Lean. GitHub repository README https://github.com/lean-dojo/LeanCopilot
Lean FRO 2025 Lean FRO (2025-08-14). Lean 4.22.0 release notes, section Named errors with explanations. The Lean language reference https://lean-lang.org/doc/reference/4.35.0/releases/v4.22.0/
Lean FRO 2026a Lean FRO (undated, read 2026). Comparator: a trustworthy judge for Lean proofs. GitHub repository README; read by both sides https://github.com/leanprover/comparator
Lean FRO 2026b Lean FRO (2026-10-12). Lean 4.35.0 release notes. The Lean language reference https://lean-lang.org/doc/reference/4.35.0/releases/v4.35.0/
Lean FRO 2026c Lean FRO (read 2026). Error explanations, index and the page on unknownIdentifier. The Lean language reference https://lean-lang.org/doc/reference/4.35.0/Error-Explanations/
Lean FRO 2026d Lean FRO (read 2026). Tactic reference: exact?, apply?, simp?. The Lean language reference https://lean-lang.org/doc/reference/4.35.0/Tactic-Proofs/Tactic-Reference/
Lee 2025 Lee, Sarkar, Tankelevitch, Drosos, Rintel, Banks, Wilson (2025). The impact of generative AI on critical thinking: self-reported reductions in cognitive effort and confidence effects from a survey of knowledge workers. CHI 2025, 1-22 https://doi.org/10.1145/3706598.3713778
Leinonen 2023 Leinonen, Hellas, Sarsa, Reeves, Denny, Prather, Becker (2023). Using large language models to enhance programming error messages. SIGCSE 2023 https://doi.org/10.1145/3545945.3569770 (arXiv:2210.11630)
Lessing 2025 Lessing, Ogbonnaya (2025). Reasoning and proof in mathematics education: a systematic literature review. Discover Education 5 https://doi.org/10.1007/s44217-025-01016-1
Li 2024b Li, Sun, Murphy, Su, Li, Zhang, Yang, Si (2024). A survey on deep learning for theorem proving. Preprint arXiv:2404.09939
Li 2024c Li, Wu, Li, Wei, et al. (2024). Autoformalize mathematical statements by symbolic equivalence and semantic consistency. NeurIPS 2024 arXiv:2410.20936
Li 2026b Li, Ammanamanchi, Bhat, Jamdar, Lin, Biderman (2026). SemantEq: faithful bidirectional equivalence of formal statements. Preprint arXiv:2610.32919
Liang 2024c Liang, Zhang, Cao, Wang, Ding, Yang, Vodrahalli, He, Smith, Yin, McFarland, Zou (2024). Can large language models provide useful feedback on research papers? A large-scale empirical analysis. NEJM AI 1(8); read in the preprint, arXiv 2310.01783 (v1) https://doi.org/10.1056/AIoa2400196
Lin 2025 Lin, Tang, Lyu, Wu, et al. (2025). Goedel-Prover: a frontier model for open-source automated theorem proving. Preprint arXiv:2502.07640
Lin 2025b Lin, Tang, Lyu, Yang, Chung and others, with Jin (2025). Goedel-Prover-V2: scaling formal theorem proving with scaffolded data synthesis and self-correction. Preprint; the model card is Goedel-LM 2025 arXiv:2508.03613
Liu 2025b Liu, Zheng, Lu, Cao, Yan (2025). Rethinking and improving autoformalization: towards a faithful metric and a dependency retrieval-based approach. ICLR 2025 https://dblp.org/rec/conf/iclr/LiuZLCY25
Liu 2025c Liu, Zhu, Liu, et al. (2025). Generalized tree edit distance (GTED): a faithful evaluation metric for statement autoformalization. AI4Math workshop, ICML 2025 arXiv:2507.07399
Liu 2025d Liu, Bao, Zhang, Liu, Chen, Liu, Jiao, Luo (2025). ATLAS: autoformalizing theorems through lifting, augmentation, and synthesis of data. NeurIPS 2025 arXiv:2502.05567
Lu 2024 Lu, Delaware, Zhang (2024). Proof automation with large language models. ASE 2024, 1509-1520 https://doi.org/10.1145/3691620.3695521 (arXiv:2409.14274)
Lu 2025 Lu, Wan, Huang, Xiong, et al. (2025). FormalAlign: automated alignment evaluation for autoformalization. ICLR 2025 arXiv:2410.10135
Lurch 2026 Lurch developers (undated, read 2026). Lurch Plus: proof verification with Lurch. Project site https://lurch.plus/ (archived: https://web.archive.org/web/20260714221045/https://lurch.plus/)
LZ 2025a Lean Zulip archive (2025). Machine Learning for Theorem Proving, topic Guarding against exploits in AI code, 37 messages, to 2025-08-02 (may move) https://leanprover-community.github.io/archive/stream/219941-Machine-Learning-for-Theorem-Proving/topic/Guarding.20against.20exploits.20in.20AI.20code.html
LZ 2025b Lean Zulip archive (2025). Machine Learning for Theorem Proving, topic Danger of Autoformalizers (e.g. Gauss), 54 messages, 2025-09-11 to 2025-11-07; met by both sides, scored by the human side (may move) https://leanprover-community.github.io/archive/stream/219941-Machine-Learning-for-Theorem-Proving/topic/Danger.20of.20Autoformalizers.20(e.2Eg.2E.20Gauss).html
LZ 2025c Lean Zulip archive (2025). Machine Learning for Theorem Proving, topic A (semi)-autoformalization challenge: 650=>448, 27 messages, 2025-05-16 to 2026-01-15 (may move) https://leanprover-community.github.io/archive/stream/219941-Machine-Learning-for-Theorem-Proving/topic/A.20(semi)-autoformalization.20challenge.3A.20650.3D.3E448.html
LZ 2025d Lean Zulip archive (2025). Machine Learning for Theorem Proving, topic on a Lean skill file for Anthropic's coding agent, 34 messages, to 2026-01-30; the exact title is in the link (may move) https://leanprover-community.github.io/archive/stream/219941-Machine-Learning-for-Theorem-Proving/topic/Lean.20Skill.20for.20Claude.20Code.html
LZ 2025e Lean Zulip archive (2025). general, topic TAIL - Template for AI generated Lean proofs, 10 messages, to 2025-12-31 (may move) https://leanprover-community.github.io/archive/stream/113488-general/topic/TAIL.20-.20Template.20for.20AI.20generated.20Lean.20proofs.html
LZ 2025f Lean Zulip archive (2025). Lean for teaching, topic Teaching with Verbose Lean, 54 messages, 2025-12-06 to 2026-02-26 (may move) https://leanprover-community.github.io/archive/stream/187764-Lean-for-teaching/topic/Teaching.20with.20Verbose.20Lean.html
LZ 2025g Lean Zulip archive (2025). Machine Learning for Theorem Proving, topic Wrong informal proof by AI, 15 messages, 2025-09-26 (may move) https://leanprover-community.github.io/archive/stream/219941-Machine-Learning-for-Theorem-Proving/topic/Wrong.20informal.20proof.20by.20AI.html
LZ 2025h Lean Zulip archive (2025). Machine Learning for Theorem Proving, topic theoretical computer science / STOC automated reviews, 4 messages, 2025-10-27 (may move) https://leanprover-community.github.io/archive/stream/219941-Machine-Learning-for-Theorem-Proving/topic/theoretical.20computer.20science.20.2F.20STOC.20automated.20reviews.html
LZ 2026a Lean Zulip archive (2026). general, topic AI Lean definitions, 33 messages, to 2026-02-08 (may move) https://leanprover-community.github.io/archive/stream/113488-general/topic/AI.20Lean.20definitions.html
LZ 2026b Lean Zulip archive (2026). Machine Learning for Theorem Proving, topic Understanding what Aristotle is formalizing, 2026-01-29; read by the formal side, not scored (may move) https://leanprover-community.github.io/archive/stream/219941-Machine-Learning-for-Theorem-Proving/topic/Understanding.20what.20Aristotle.20is.20formalizing.html
Marceau 2011 Marceau, Fisler, Krishnamurthi (2011). Measuring the effectiveness of error messages designed for novice programmers. SIGCSE 2011, 499-504. Abstract read https://doi.org/10.1145/1953163.1953308
Massot 2024 Massot (2024). Teaching mathematics using Lean and controlled natural language. ITP 2024, LIPIcs 309, paper 27 https://doi.org/10.4230/LIPIcs.ITP.2024.27
Massot 2026 Massot (undated, read 2026). leanblueprint: a plasTeX plugin and command-line tool for Lean blueprints. GitHub repository; held by mathematical-writing https://github.com/PatrickMassot/leanblueprint
Massot 2026b Massot (undated, read 2026). Verbose Lean 4: README, examples and basic configuration guide. GitHub repository; read by both sides, and the README again at the merge https://github.com/PatrickMassot/verbose-lean4
Math Inc 2025 Math Inc (2025, undated page; September 2025 per Hales 2026). Gauss, an autoformalization agent. Company page; the owner's account https://www.math.inc/gauss (archived: https://web.archive.org/web/20261021103654/https://www.math.inc/gauss)
Mathlib 2026 The mathlib community (undated, read 2026). Documentation style (contributor guide). Held by mathematical-writing https://leanprover-community.github.io/contribute/doc.html
Mathlib 2026b The mathlib community (read 2026-10-29). Mathlib statistics, section Counts. The formal side's count https://leanprover-community.github.io/mathlib_stats.html
Mathlib Initiative 2026 Mathlib Initiative (undated, read 2026). formalization.yaml: a self-reporting standard for formalization projects. README and template https://github.com/mathlib-initiative/formalization.yaml
MathOverflow 2026 Asker and answerers (2026-09-29). Formalization advice for mathematicians. MathOverflow question 515632; top answer by the user shown as Timothy Chow https://mathoverflow.net/questions/515632
Matichuk 2015 Matichuk, Murray, Andronick, Jeffery, Klein, Staples (2015). Empirical study towards a leading indicator for cost of formal software verification. ICSE 2015. Paywalled https://doi.org/10.1109/icse.2015.85
Mei 2026 Mei, Douglas (2026). Beyond LLM judge: mechanical verification for agentic autoformalization. Preprint arXiv:2610.20573
Mensfelt 2025 Mensfelt, Tena Cucala, Franco, Koutsoukou-Argyraki, et al. (2025). Towards a common framework for autoformalization. NeLaMKRR workshop at KR 2025 arXiv:2509.09810
Mihaylova 2026 Mihaylova, Logacheva, Hellas, Fan, Castro, Akram, Norouzi, Brusilovsky, Leinonen (2026). The effects of structured LLM-generated feedback on programming assignment performance. Preprint arXiv:2605.16933
Min 2026 Min, He, Li, et al. (2026). Theory-level autoformalization: from isolated statements to unified formal knowledge bases. Position paper, ICML 2026 arXiv:2607.13292
Mistral 2026 Mistral AI (2026-03-16). Leanstral: open-source foundation for trustworthy vibe-coding. Company news page; the owner's results https://mistral.ai/news/leanstral (archived: https://web.archive.org/web/20261004083217/https://mistral.ai/news/leanstral/)
Mohammad 2026 Mohammad, Sheikh (2026). The faithfulness gap: certifying semantic equivalence between natural-language and formal mathematical statements. Preprint arXiv:2606.16541
Moraru 2026 Moraru, Biswas, Gadiraju (2026). Beyond the traceback: using LLMs for adaptive explanations of programming errors. Preprint arXiv:2608.20896
Murphy 2024 Murphy, Yang, Sun, Li, et al. (2024). Autoformalizing Euclidean geometry. ICML 2024 arXiv:2405.17216
Naproche 2026 Naproche developers (undated, read 2026). Naproche project site, and the tutorial TUTORIAL.ftl.tex https://naproche.github.io/ ; https://github.com/naproche/naproche/blob/master/math/TUTORIAL.ftl.tex
Nipkow 2012 Nipkow (2012). Teaching semantics with a proof assistant: no more LSD trip proofs. Lecture Notes in Computer Science (2012), 24-38. Paywalled https://doi.org/10.1007/978-3-642-27940-9_3
Numina 2025 Project Numina (2025-04-13). Kimina-Autoformalizer-7B. Model card https://huggingface.co/project-numina/Kimina-Autoformalizer-7B
Ochigame 2024 Ochigame (2024). Automated mathematics and the reconfiguration of proof and labor. Bulletin of the AMS 61, 423-437 https://doi.org/10.1090/bull/1821
Ospanov 2025 Ospanov, Farnia, Yousefzadeh (2025). miniF2F-Lean revisited: reviewing limitations and charting a path forward. Preprint arXiv:2511.03108
Ospanov 2025b Ospanov, Farnia, Yousefzadeh (2025). APOLLO: automated LLM and Lean collaboration for advanced formal reasoning. NeurIPS 2025 arXiv:2505.05758
Otte 2026 Otte, Bos, Commelin, Portegies (2026). The educational proof assistant Waterproof in an introductory proof course: proof construction and learning processes. Preprint arXiv:2606.26809
Ouvrier-Buffet 2026 Ouvrier-Buffet (2026). Mathematics teachers' practices with proof assistants: a literature review. Working paper, HAL hal-05671977 https://hal.science/hal-05671977v1
Pąk 2014 Pąk (2014). Improving legibility of natural deduction proofs is not trivial. Logical Methods in Computer Science 10(3) https://doi.org/10.2168/LMCS-10(3:23)2014
Palomar 2026 Palomar registry (undated, read 2026). About, and Statement. Registry pages https://palomar-registry.org/about (archived: https://web.archive.org/web/20261011082215/https://palomar-registry.org/about) ; https://palomar-registry.org/statement (archived: https://web.archive.org/web/20261011082215/https://palomar-registry.org/statement)
Palomar 2026b Palomar registry (read 2026-10-29). Registry-wide totals, field totals of the public results API. The formal side's count, read again at the audit the same day https://data.palomar-registry.org/api/v1/results
Parasuraman 2010 Parasuraman, Manzey (2010). Complacency and bias in human use of automation: an attentional integration. Human Factors 52(3), 381-410 https://doi.org/10.1177/0018720810376055
PASE 2022 Asker and answerers (2022-02-15). Is there a Mizar-like sublanguage for Coq? Proof Assistants Stack Exchange question 571 and its accepted answer https://proofassistants.stackexchange.com/questions/571
PASE 2022b Asker and answerers (2022). Examples of new mathematics discovered through formalization? Proof Assistants Stack Exchange question 129 https://proofassistants.stackexchange.com/q/129
PASE 2024 Asker and answerers (2024-06-07). Tools like leanblueprint for other proof assistants, especially Coq? Proof Assistants Stack Exchange question 4035 https://proofassistants.stackexchange.com/questions/4035
PASE 2026 Asker and answerers (2026-07-25). How can I evaluate the semantic equivalence of Lean statements generated by an autoformalization model? Proof Assistants Stack Exchange question 6608; accepted answer by the user shown as Jason Rute, who marks one mention of a prover as a plug https://proofassistants.stackexchange.com/questions/6608
Patel 2025 Patel, Bhattacharyya, Lu, Mehta, Voss, Norouzi, Ranade (2025). LeanTutor: towards a verified AI mathematical proof tutor. Preprint arXiv:2506.08321
Paulson 2026 Paulson (2026-01-15). Broken proofs and broken provers. Machine Logic blog https://lawrencecpaulson.github.io/2026/01/15/Broken_proofs.html
Peng 2025 Peng, Yao, Ma, et al. (2025). CriticLean: critic-guided reinforcement learning for mathematical formalization. Preprint arXiv:2507.06181
Perháč 2025 Perháč, Novotný, Chodarev, Kristensen, Tveito, Shturmov, Thomsen (2025). OnlineProver: experience with a visualisation tool for teaching formal proofs. ThEdu'24, EPTCS 419, 55-74 https://doi.org/10.4204/EPTCS.419.4
Perry 2023 Perry, Srivastava, Kumar, Boneh (2023). Do users write more insecure code with AI assistants? ACM CCS 2023, 2785-2799 https://doi.org/10.1145/3576915.3623157
Petrov 2025 Petrov, Dekoninck, Baltadzhiev, Drencheva, Minchev, Balunović, Jovanović, Vechev (2025). Proof or bluff? Evaluating LLMs on 2025 USA Math Olympiad. Preprint arXiv:2503.21934
Petrov 2025b Petrov, Dekoninck, Vechev (2025). BrokenMath: a benchmark for sycophancy in theorem proving with LLMs. Preprint arXiv:2510.04721
Pettit 2017 Pettit, Homer, Gee (2017). Do enhanced compiler error messages help students? Results inconclusive. SIGCSE 2017, 465-470. Abstract read https://doi.org/10.1145/3017680.3017768
Pierce 2009 Pierce (2009). Lambda, the ultimate TA: using a proof assistant to teach programming language foundations. ICFP 2009, 121-122 (invited talk abstract) https://doi.org/10.1145/1596550.1596552
Pit-Claudel 2020 Pit-Claudel (2020). Untangling mechanized proofs. SLE 2020, 155-174. Abstract read https://doi.org/10.1145/3426425.3426940
PNT-plus 2026 PNT+ project (read 2026). PNT+ pull request style guide, with CONTRIBUTING.md. GitHub repository https://github.com/AlexKontorovich/PrimeNumberTheoremAnd/blob/main/PULL_REQUEST_STYLE.md
Poiroux 2025 Poiroux, Weiss, Kunčak, Bosselut (2025). Reliable evaluation and benchmarks for statement autoformalization. EMNLP 2025, 17958-17980 https://doi.org/10.18653/v1/2025.emnlp-main.907 (arXiv:2406.07222)
Poiroux 2025b Poiroux, Bosselut, Kunčak (2025). RLMEval: evaluating research-level neural theorem proving. Findings of EMNLP 2025 arXiv:2510.25427
Pollack 1997 Pollack (1997). How to believe a machine-checked proof. BRICS Report Series 4(18); also in Sambin, Smith (eds.), Twenty Five Years of Constructive Type Theory, Oxford University Press, 1998 https://doi.org/10.7146/brics.v4i18.18945
PostHog 2026 PostHog (read 2026). Vale and prose linting. Company handbook (may move) https://posthog.com/handbook/wizard-and-docs/vale
Prather 2017 Prather, Pettit, McMurry, Peters, Homer, Simone, Cohen (2017). On novices' interaction with compiler error messages: a human factors approach. ICER 2017, 74-82. Abstract read https://doi.org/10.1145/3105726.3106169
PyPI 2026 PyPI statistics (read 2026-10-29). Recent downloads of leanblueprint and lean-lsp-mcp, field last_month. The formal side's count https://pypistats.org/api/packages/leanblueprint/recent ; https://pypistats.org/api/packages/lean-lsp-mcp/recent
Raiyan 2026 Raiyan, Kabir, Mahmud, Hasan, Ananiadou (2026). Artificial intelligence for mathematical reasoning: an integrated survey of language models, neuro-symbolic systems, and verified discovery. Preprint arXiv:2606.08728
Rammal 2026 Rammal, Patel, Gloeckle, Hayat, Kempe, Munos, Arnal, Cabannes (2026). Formalizing mathematics at scale. Preprint; the owners' account arXiv:2605.29955
Ranta 2026 Ranta (2026). Symbolic informalization: fluent, productive, multilingual. Preprint arXiv:2606.16893
Rav 1999 Rav (1999). Why do we prove theorems? Philosophia Mathematica 7(1), 5-41. Paywalled https://doi.org/10.1093/philmat/7.1.5
Ringer 2019 Ringer, Palmskog, Sergey, Gligoric, Tatlock (2019). QED at large: a survey of engineering of formally verified software. Foundations and Trends in Programming Languages 5(2-3), 102-281 https://doi.org/10.1561/2500000045 (arXiv:2003.06458)
Ringer 2020 Ringer, Sanchez-Stern, Grossman, Lerner (2020). REPLica: REPL instrumentation for Coq analysis. CPP 2020. Read in the authors' copy https://doi.org/10.1145/3372885.3373823
Ringer 2021 Ringer, Porter, Yazdani, Leo, Grossman (2021). Proof repair across type equivalences. PLDI 2021, 112-127 https://doi.org/10.1145/3453483.3454033 (arXiv:2010.00774)
Rivin 2026 Rivin (2026-03-26). From 67% to 97%: when your theorem prover proves the wrong theorem. GitHub gist, with its benchmark repository https://gist.github.com/igorrivin/3d15a2ba02a6ef09a5ddee196805348e (archived: https://web.archive.org/web/20260328004705/https://gist.github.com/igorrivin/3d15a2ba02a6ef09a5ddee196805348e) ; https://github.com/igorrivin/polya-szego-benchmark
Salmon 2025 Salmon, Hammer, Santos, Becker (2025). Debugging without error messages: how LLM prompting strategy affects programming error explanation effectiveness. Preprint arXiv:2501.05706
Santos 2023 Santos, Prasad, Becker (2023). Always provide context: the effects of code context on programming error message enhancement. CompEd 2023, 147-153. Abstract read https://doi.org/10.1145/3576882.3617909
Santos 2024 Santos, Becker (2024). Not the silver bullet: LLM-enhanced programming error messages are ineffective in practice. UKICER 2024 https://doi.org/10.1145/3689535.3689554 (arXiv:2409.18661)
Scholze 2021 Scholze (2021-06-05). Half a year of the Liquid Tensor Experiment: amazing developments. Guest post, Xena Project blog https://xenaproject.wordpress.com/2021/06/05/half-a-year-of-the-liquid-tensor-experiment-amazing-developments/
Shen 2026 Shen, Qiu, Zhi, et al. (2026). MechAlign: evaluating semantic alignment at the project level in mathematical formalization. Preprint arXiv:2610.35269
Song 2024 Song, Yang, Anandkumar (2024). Lean Copilot: large language models as copilots for theorem proving in Lean. NeuS 2025. The repository is LeanDojo 2026 arXiv:2404.12534
StepFun 2025 StepFun (2025-08-19). StepFun-Formalizer-32B. Model card https://huggingface.co/stepfun-ai/StepFun-Formalizer-32B
STOC 2026 STOC 2026 organisers (2025). Experimental program: automated pre-submission feedback. Conference page (may move) https://acm-stoc.org/stoc2026/stoc2026-LLM_feedback.html
Stylianides 2024 Stylianides, Stylianides, Moutsios-Rentzos (2024). Proof and proving in school and university mathematics education research: a systematic review. ZDM Mathematics Education 56, 47-59 (abstract read) https://doi.org/10.1007/s11858-023-01518-y
Szegedy 2020 Szegedy (2020). A promising path towards autoformalization and general artificial intelligence. CICM 2020, Lecture Notes in Computer Science, 3-20 https://doi.org/10.1007/978-3-030-53518-6_1
Tan 2026 Tan, Blanchet, Syrgkanis (2026). PaperFormalizer: author-in-the-loop autoformalization of research papers in Lean. Preprint arXiv:2610.31810
Tanswell 2015 Tanswell (2015). A problem with the dependence of informal proofs on formal proofs. Philosophia Mathematica 23(3), 295-310. Paywalled https://doi.org/10.1093/philmat/nkv008
Tanswell 2026 Tanswell (2026-03-31). Vibe formalisation and slop mathematics. Talk abstract, Isaac Newton Institute https://talks.cam.ac.uk/talk/index/245968/
Tao 2023 Tao (2023). Formalizing the proof of PFR in Lean4 using Blueprint: a short tour. Blog post; held by mathematical-writing https://terrytao.wordpress.com/2023/11/18/formalizing-the-proof-of-pfr-in-lean4-using-blueprint-a-short-tour/
Tao 2023m Tao (2023). Learning Lean 4, a journal in Mathstodon posts, 2023-10-09 to 2023-11-19; cited posts of 2023-10-10, 2023-10-14, 2023-10-21, 2023-11-05, 2023-11-19 (may move) https://mathstodon.xyz/@tao/111206761117553482 ; https://mathstodon.xyz/@tao/111209438351902155 ; https://mathstodon.xyz/@tao/111234054337933006 ; https://mathstodon.xyz/@tao/111271244206606941 ; https://mathstodon.xyz/@tao/111360264941915326 ; https://mathstodon.xyz/@tao/111439273687647142
Tao 2024 Tao (2024-10-12). The equational theories project: a brief tour. Blog post https://terrytao.wordpress.com/2024/10/12/the-equational-theories-project-a-brief-tour/
Tao 2025a Tao (2025-05-11). Post on formalizing a one-page proof with Copilot and canonical. Mathstodon (may move) https://mathstodon.xyz/@tao/114486537464033675
Tao 2025b Tao (2025-10-22). Thread on Erdős problem 707, posts 2 and 3 of 3. Mathstodon (may move) https://mathstodon.xyz/@tao/115416210007455376 ; https://mathstodon.xyz/@tao/115416211466664814
Tao 2025c Tao (2025-11-04). Thread on vibe-coding a Lean proof for Erdős problem 613. Mathstodon (may move) https://mathstodon.xyz/@tao/115493669248813088 ; https://mathstodon.xyz/@tao/115493672527637142
Tao 2025d Tao (2025-12-09). The Equational Theories Project: advancing collaborative mathematical research at scale. Blog post https://terrytao.wordpress.com/2025/12/09/the-equational-theories-project-advancing-collaborative-mathematical-research-at-scale/
Tao 2026e Tao (2026-01-15). The integrated explicit analytic number theory network. Blog post; read by both sides https://terrytao.wordpress.com/2026/01/15/the-integrated-explicit-analytic-number-theory-network/
Tao 2026f Tao (2026-08-18). Palomar: a registry of Lean verified mathematics. Blog post https://terrytao.wordpress.com/2026/08/18/palomar-a-registry-of-lean-verified-mathematics/
Tao 2026g Tao (2026-05-04). Post on an agent triaging a referee report. Mathstodon (may move) https://mathstodon.xyz/@tao/116517314420904580
Tao 2026h Tao (2026-05-28). Post on skills files recording style preferences. Mathstodon (may move) https://mathstodon.xyz/@tao/116653336847856534
Tao 2026i Tao (2026-06-21). Thread on generation, verification and digestion in IEANTN, 3 posts. Mathstodon (may move) https://mathstodon.xyz/@tao/116789373239346609
Tao 2026j Tao (2026-08-12). A digestion of the proof of Sendov's conjecture. Blog post https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/
Tao 2026k Tao (2026-01-07 to 2026-01-10). Thread on Erdős problem 728 and AI-written expositions, 5 posts and an addendum. Mathstodon (may move) https://mathstodon.xyz/@tao/115855840223258103
Taylor 2024b Taylor, Vassar, Renzella, Pearce (2024). dcc --help: transforming the role of the compiler by generating context-aware error explanations with large language models. SIGCSE 2024 https://doi.org/10.1145/3626252.3630822 (arXiv:2308.11873)
Thakur 2024 Thakur, Tsoukalas, Wen, Xin, Chaudhuri (2024). An in-context learning agent for formal theorem-proving (COPRA). Preprint, version 5 arXiv:2310.04353
Thoma 2022 Thoma, Iannone (2022). Learning about proof with the theorem prover LEAN: the abundant numbers task. International Journal of Research in Undergraduate Mathematics Education 8, 64-93 https://doi.org/10.1007/s40753-021-00140-1
Tran Minh 2025 Tran Minh, Gonnord, Narboux (2025). Proof assistants for teaching: a survey. arXiv preprint (abstract read) arXiv:2505.13472
Tsoukalas 2024 Tsoukalas, Lee, Jennings, et al. (2024). PutnamBench: evaluating neural theorem-provers on the Putnam mathematical competition. NeurIPS 2024 Datasets and Benchmarks arXiv:2407.11214
TUe 2026 Eindhoven University of Technology (undated, read 2026). Waterproof as students' personal proof assistant. DRIVE project page; no archived copy found https://drive.tue.nl/projects/waterproof-as-students-personal-proof-assistant/
Tymoczko 1979 Tymoczko (1979). The four-color problem and its philosophical significance. The Journal of Philosophy 76(2), 57-83. Paywalled https://doi.org/10.2307/2025976
Uskuplu 2026 Uskuplu, Moss, de Paiva (2026). KnowTeX: visualizing mathematical dependencies. arXiv preprint, version 3 (abstract read) arXiv:2601.15294
Varambally 2025 Varambally, Voice, Sun, Chen, Yu, Ye (2025). Hilbert: recursively building formal proofs with informal reasoning. Preprint arXiv:2509.22819
Venturim 2026 Venturim, Estrada, Silva, et al. (2026). What has actually been proved? Auditable paper-to-Lean alignment with LeanTrail. MATH-AI workshop, NeurIPS 2026 arXiv:2610.35926
Verchinine 2007 Verchinine, Lyaletski, Paskevich (2007). System for Automated Deduction (SAD): a tool for proof verification. CADE-21, LNCS 4603, 398-403 https://doi.org/10.1007/978-3-540-73595-3_29
Vergo 2026 Vergo and others (2026-02-05). Discussion thread: side-by-side blueprint. Lean community forum, public archive, channel ecosystem-infrastructure https://leanprover-community.github.io/archive/stream/536994-ecosystem-infrastructure/topic/Discussion.20thread.20-.20Side.20by.20Side.20blueprint.html
Wang 2018 Wang, Kaliszyk, Urban (2018). First experiments with neural translation of informal to formal mathematics. CICM 2018, Lecture Notes in Computer Science, 255-270 https://doi.org/10.1007/978-3-319-96812-4_22 (arXiv:1805.06502)
Wang 2020b Wang, Brown, Kaliszyk, Urban (2020). Exploration of neural machine translation in autoformalization of mathematics in Mizar. CPP 2020, 85-98 https://doi.org/10.1145/3372885.3373827 (arXiv:1912.02636)
Wang 2024b Wang, Mitchell, Piech (2024). A large scale RCT on effective error messages in CS1. SIGCSE 2024, 1395-1401. Read in full through the university https://doi.org/10.1145/3626252.3630764
Wang 2025 Wang, Unsal, Lin, Baksys, et al. (2025). Kimina-Prover preview: towards large formal reasoning models with reinforcement learning. Preprint arXiv:2504.11354
Wang 2026 Wang, Chess, Lee, Ge, Mallavarapu, Alper, Ilin (2026). Learning to repair Lean proofs from compiler feedback. ICLR 2026 VerifAI workshop arXiv:2602.02990
Wemmenhove 2024 Wemmenhove, Arends, Beurskens, Bhaid, McCarren, Moraal, Rivera Garrido, Tuin, Vassallo, Wils, Portegies (2024). Waterproof: educational software for learning how to write mathematical proofs. EPTCS 400, 96-119 https://doi.org/10.4204/eptcs.400.7
Weng 2025 Weng, Du, Li, Lu, Sun, Liu, Zhang (2025). Autoformalization in the era of large language models: a survey. Preprint arXiv:2505.23486
Wenzel 1999 Wenzel (1999). Isar: a generic interpretative approach to readable formal proof documents. TPHOLs 1999, LNCS 1690, 167-183. Held by mathematical-writing https://doi.org/10.1007/3-540-48256-3_12
Wenzel 2002 Wenzel, Wiedijk (2002). A comparison of Mizar and Isar. Journal of Automated Reasoning 29(3-4), 389-411. Title and venue only https://doi.org/10.1023/A:1021935419355
Widjojo 2023 Widjojo, Treude (2023). Addressing compiler errors: Stack Overflow or large language models? Preprint arXiv:2307.10793
Wiedijk 2000 Wiedijk (2000). The de Bruijn factor. Poster paper, TPHOLs 2000, with the author's page of measured factors https://www.cs.ru.nl/~freek/factor/
Wiedijk 2004 Wiedijk (2004). Formal proof sketches. TYPES 2003, LNCS 3085, 378-393. Title and venue only https://doi.org/10.1007/978-3-540-24849-1_24
Wiedijk 2012 Wiedijk (2012). Pollack-inconsistency. Electronic Notes in Theoretical Computer Science 285, 85-100 https://doi.org/10.1016/j.entcs.2012.06.008
Wiedijk 2012b Wiedijk (2012). A synthesis of the procedural and declarative styles of interactive theorem proving. Logical Methods in Computer Science 8(1) https://doi.org/10.2168/LMCS-8(1:30)2012
Wu 2022 Wu, Jiang, Li, Rabe, et al. (2022). Autoformalization with large language models. NeurIPS 2022 arXiv:2205.12615
Wu 2025b Wu, Huang, Wan, et al. (2025). StepFun-Formalizer: unlocking the autoformalization potential of LLMs through knowledge-reasoning fusion. AAAI 2026 arXiv:2508.04440
Wu 2026 Wu (2026). Can AI review improve paper drafting? An empirical study on 20 computer architecture submissions. Preprint arXiv:2606.01013
Xin 2024 Xin, Guo, Shao, Ren, et al. (2024). DeepSeek-Prover: advancing theorem proving in LLMs through large-scale synthetic data. Preprint arXiv:2405.14333
Xin 2024b Xin, Ren, Song, Shao, Zhao and others (2024). DeepSeek-Prover-V1.5: harnessing proof assistant feedback for reinforcement learning and Monte-Carlo tree search. Preprint arXiv:2408.08152
Xu 2025 Xu, Wang, Wang, Li, Watt (2025). A minimalist proof language for neural theorem proving over Isabelle/HOL. OOPSLA 2026 arXiv:2507.18885
Yanahama 2026 Yanahama, Sannai (2026). Lean Atlas: an integrated proof environment for scalable human-AI collaborative formalization. Preprint arXiv:2604.16347
Yang 2024 Yang, Poesia, He, Li, Lauter, Chaudhuri, Song (2024). Formal mathematical reasoning: a new frontier in AI. Position paper, preprint arXiv:2412.16075
Ying 2024 Ying, Wu, Geng, et al. (2024). Lean Workbook: a large-scale Lean problem set formalized from natural language math problems. Preprint arXiv:2406.03847
Yu 2025b Yu, Peng, Ding, et al. (2025). FormalMATH: benchmarking formal mathematical reasoning of large language models. Technical report arXiv:2505.02735
Yu 2025c Yu, Zhong, Feng, et al. (2025). Mathesis: towards formal theorem proving from natural languages. Preprint arXiv:2506.07047
Zhai 2024 Zhai, Wibowo, Li (2024). The effects of over-reliance on AI dialogue systems on students' cognitive abilities: a systematic review. Smart Learning Environments 11, article 28 https://doi.org/10.1186/s40561-024-00316-7
Zhang 2025 Zhang, Valentino, Meadows, Freitas (2025). Beyond gold standards: epistemic ensemble of LLM judges for formal mathematical reasoning. Preprint arXiv:2506.10903
Zhang 2026 Zhang, Gallardo Candela, Murthy, et al. (2026). Beyond compilation: evaluating faithful natural-language-to-Lean statement formalization. Preprint, version 4 arXiv:2606.31002
Zheng 2022 Zheng, Han, Polu (2022). MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics. ICLR 2022 arXiv:2109.00110
Zheng 2023 Zheng, Wang, Xie, Liu, Sun, Xin, Shen, Li, Li (2023). Lyra: orchestrating dual correction in automated theorem proving. TMLR arXiv:2309.15806
Zhu 2026 Zhu (undated, read 2026). LeanArchitect: generating blueprint data directly from Lean. GitHub repository README https://github.com/hanwenzhu/LeanArchitect
Zhu 2026b Zhu, Monticone, Welleck, Avigad (2026). LeanArchitect: automating blueprint generation for humans and AI. ITP 2026, LIPIcs 382, 25. DOI registered with DataCite; resolved through doi.org. Zhu 2026 is the tool's repository https://doi.org/10.4230/LIPIcs.ITP.2026.25 (arXiv:2601.22554)
Joyce 1996 Joyce, D. E. (1996, from Heath's 1908 translation). Euclid's Elements, Book IX, Proposition 20, with VII.31. Clark University https://mathcs.clarku.edu/~djoyce/java/elements/bookIX/propIX20.html
Wikipedia 2026 Euclid Wikipedia (read 2026-11-03). Euclid's theorem, section Euclid's proof, Variations: N = n! + 1. Grey, an example only https://en.wikipedia.org/wiki/Euclid%27s_theorem