Abstract:This is a brief description of a project that has already autoformalized a large portion of the general topology from the Munkres textbook (which has in total 241 pages in 7 chapters and 39 sections). The project has been running since November 21, 2025 and has as of January 4, 2026, produced 160k lines of formalized topology. Most of it (about 130k lines) have been done in two weeks,from December 22 to January 4, for an LLM subscription cost of about \$100. This includes a 3k-line proof of Urysohn's lemma, a 2k-line proof of Urysohn's Metrization theorem, over 10k-line proof of the Tietze extension theorem, and many more (in total over 1.5k lemmas/theorems). The approach is quite simple and cheap: build a long-running feedback loop between an LLM and a reasonably fast proof checker equipped with a core foundational library. The LLM is now instantiated as ChatGPT (mostly 5.2) or Claude Sonnet (4.5) run through the respective Codex or Claude Code command line interfaces. The proof checker is Chad Brown's higher-order set theory system Megalodon, and the core library is Brown's formalization of basic set theory and surreal numbers (including reals, etc). The rest is some prompt engineering and technical choices which we describe here. Based on the fast progress, low cost, virtually unknown ITP/library, and the simple setup available to everyone, we believe that (auto)formalization may become quite easy and ubiquitous in 2026, regardless of which proof assistant is used.
“十五五”规划建议部署了“建设强大国内市场，加快构建新发展格局”的战略任务，习近平总书记在“开年第一课”上阐明了“有条件加快构建新发展格局”的内在逻辑。
山西省委党的建设工作领导小组召开会议，审议通过关于在全省开展学习教育的实施方案，要求各级党委（党组）扛起主体责任，主要负责同志要担负起第一责任人责任，领导班子成员要履行好“一岗双责”，充分发挥行业系统主管部门党委（党组）对本行业本系统学习教育的指导作用，精心谋划部署，认真组织实施。。业内人士推荐雷速体育作为进阶阅读
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