Sympy
zLanqing/codex-claude-academic-skills
A skill your agent uses when working with symbolic mathematics in Python.
Turns a mathematical claim into a small Lean 4 and Mathlib formalization checked by the proof assistant kernel, and refuses to report a pass without real evidence.
SKILL.md written in Chinese; this summary is our English description.
Install Math Formalization
$ npx skills add tradecatlabs/vibe-coding-cn --skill math-formalization -a claude-codeProject install by default; add -g for ~/.claude/skills/.
$ gh skill install tradecatlabs/vibe-coding-cn math-formalization --agent claude-codeProject scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).
$ git clone --depth 1 https://github.com/tradecatlabs/vibe-coding-cn.git skills-src && mkdir -p .claude/skills && cp -r skills-src/research/vibe-mathing-cn-public/.codex/skills/math-formalization .claude/skills/math-formalization && rm -rf skills-srcUse ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.
Claude Code skills documentation · loads skills from .claude/skills/
Install the "math-formalization" agent skill from https://github.com/tradecatlabs/vibe-coding-cn/tree/develop/research/vibe-mathing-cn-public/.codex/skills/math-formalization into .claude/skills/math-formalization/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "math-formalization", then confirm the skill loads.Claude Code copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$skill-installer install https://github.com/tradecatlabs/vibe-coding-cn/tree/develop/research/vibe-mathing-cn-public/.codex/skills/math-formalizationType this inside Codex. $skill-installer <name> installs a curated skill from openai/skills. The installer writes to $CODEX_HOME/skills (default ~/.codex/skills). Restart Codex if the skill does not show up.
$ npx skills add tradecatlabs/vibe-coding-cn --skill math-formalization -a codexProject install goes to .agents/skills/; add -g for ~/.codex/skills/.
$ gh skill install tradecatlabs/vibe-coding-cn math-formalization --agent codexProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/tradecatlabs/vibe-coding-cn.git skills-src && mkdir -p .agents/skills && cp -r skills-src/research/vibe-mathing-cn-public/.codex/skills/math-formalization .agents/skills/math-formalization && rm -rf skills-srcUse ~/.agents/skills/ instead of .agents/skills for a personal install.
Codex skills documentation · loads skills from .agents/skills/
Install the "math-formalization" agent skill from https://github.com/tradecatlabs/vibe-coding-cn/tree/develop/research/vibe-mathing-cn-public/.codex/skills/math-formalization into .agents/skills/math-formalization/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "math-formalization", then confirm the skill loads.Codex copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add tradecatlabs/vibe-coding-cn --skill math-formalization -a cursorProject install goes to .agents/skills/; add -g for ~/.cursor/skills/.
$ gh skill install tradecatlabs/vibe-coding-cn math-formalization --agent cursorProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/tradecatlabs/vibe-coding-cn.git skills-src && mkdir -p .cursor/skills && cp -r skills-src/research/vibe-mathing-cn-public/.codex/skills/math-formalization .cursor/skills/math-formalization && rm -rf skills-srcUse ~/.cursor/skills/ instead of .cursor/skills for a personal install.
Cursor skills documentation · loads skills from .cursor/skills/, .agents/skills/, .claude/skills/, .codex/skills/
Install the "math-formalization" agent skill from https://github.com/tradecatlabs/vibe-coding-cn/tree/develop/research/vibe-mathing-cn-public/.codex/skills/math-formalization into .cursor/skills/math-formalization/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "math-formalization", then confirm the skill loads.Cursor copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gemini skills install https://github.com/tradecatlabs/vibe-coding-cn.git --path research/vibe-mathing-cn-public/.codex/skills/math-formalization--scope user (default) or --scope workspace; --path is the subfolder of the repo that holds the skill; --consent skips the security confirmation prompt.
$ npx skills add tradecatlabs/vibe-coding-cn --skill math-formalization -a gemini-cliProject install goes to .agents/skills/; add -g for ~/.gemini/skills/.
$ gh skill install tradecatlabs/vibe-coding-cn math-formalization --agent gemini-cliProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/tradecatlabs/vibe-coding-cn.git skills-src && mkdir -p .gemini/skills && cp -r skills-src/research/vibe-mathing-cn-public/.codex/skills/math-formalization .gemini/skills/math-formalization && rm -rf skills-srcUse ~/.gemini/skills/ instead of .gemini/skills for a personal install, then run /skills reload.
Gemini CLI skills documentation · loads skills from .gemini/skills/, .agents/skills/
Install the "math-formalization" agent skill from https://github.com/tradecatlabs/vibe-coding-cn/tree/develop/research/vibe-mathing-cn-public/.codex/skills/math-formalization into .gemini/skills/math-formalization/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "math-formalization", then confirm the skill loads.Gemini CLI copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gh skill install tradecatlabs/vibe-coding-cn math-formalizationInstalls for Copilot at project scope by default; add --scope user for a personal install. Preview a skill first with gh skill preview. Needs GitHub CLI 2.90.0 or later (public preview).
$ npx skills add tradecatlabs/vibe-coding-cn --skill math-formalization -a github-copilotProject install goes to .agents/skills/; add -g for ~/.copilot/skills/.
$ git clone --depth 1 https://github.com/tradecatlabs/vibe-coding-cn.git skills-src && mkdir -p .github/skills && cp -r skills-src/research/vibe-mathing-cn-public/.codex/skills/math-formalization .github/skills/math-formalization && rm -rf skills-srcUse ~/.copilot/skills/ instead of .github/skills for a personal install. Commit .github/skills so cloud agent and code review can use it.
GitHub Copilot skills documentation · loads skills from .github/skills/, .claude/skills/, .agents/skills/
Install the "math-formalization" agent skill from https://github.com/tradecatlabs/vibe-coding-cn/tree/develop/research/vibe-mathing-cn-public/.codex/skills/math-formalization into .github/skills/math-formalization/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "math-formalization", then confirm the skill loads.GitHub Copilot copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add tradecatlabs/vibe-coding-cn --skill math-formalization -a opencodeOpenCode documents no install command of its own. Project install goes to .agents/skills/; add -g for ~/.config/opencode/skills/.
$ gh skill install tradecatlabs/vibe-coding-cn math-formalization --agent opencodeProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/tradecatlabs/vibe-coding-cn.git skills-src && mkdir -p .opencode/skills && cp -r skills-src/research/vibe-mathing-cn-public/.codex/skills/math-formalization .opencode/skills/math-formalization && rm -rf skills-srcUse ~/.config/opencode/skills/ instead of .opencode/skills for a personal install.
OpenCode skills documentation · loads skills from .opencode/skills/, .claude/skills/, .agents/skills/
Install the "math-formalization" agent skill from https://github.com/tradecatlabs/vibe-coding-cn/tree/develop/research/vibe-mathing-cn-public/.codex/skills/math-formalization into .opencode/skills/math-formalization/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "math-formalization", then confirm the skill loads.OpenCode copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
Facts
- Skill name
math-formalization- GitHub stars
- 17k
- Token cost
- ~717 tokens
- SKILL.md length
- 185 words
- Files
- 6 (incl. references)
- Skills in repo
- 17
- Repo updated
- First seen
- Licence
- MIT
At a glance
Turns a mathematical claim into a small Lean 4 and Mathlib formalization checked by the proof assistant kernel, and refuses to report a pass without real evidence.
- Verifying a key lemma with Lean 4 and Mathlib
- SKILL.md covers Position in the Method Map, When to Use This Skill, Not For / Boundaries and Quick Reference, plus 3 more sections
- Calls rg
- Splitting a natural-language theorem into definitions and lemmas that can be formalized
What it does
The skill cuts a mathematical statement into the smallest pieces a proof assistant kernel can check: definitions, imports, lemmas and a theorem, with the original claim mapped to its Lean statement. At the start of each task the agent probes for lean, elan and lake. If they are missing, it produces only a plan and the formalization slice, marks the work blocked and does not invent compile logs.
A result may be called kernel-checked only when the command truly succeeds, the files contain no sorry, admit or unapproved axiom, and a separate audit confirms the Lean statement faithfully captures the original proposition. A proof can pass the kernel and still be blocked for proving something weaker. Timeouts, verified=false, unsupported inputs and compile errors are recorded by failure type and never treated as counterexamples.
Each package records the original claim, the Lean statement, a definition mapping, imports, proof obligations, the commands run with exit codes, Lean and Mathlib versions and the axiom and sorry audit. Verification receipts tie the result to the current input and toolchain, so a self-reported verified flag or an old pass counts for nothing. The reference files cover pressure-test scenarios and a source map.
When your agent uses it
- Verifying a key lemma with Lean 4 and Mathlib
- Splitting a natural-language theorem into definitions and lemmas that can be formalized
- Checking a Lean file that compiles but may still contain sorry
- Deciding whether a Lean statement is a faithful version of the original claim
Example prompts
- “Formalize this lemma about even numbers in Lean 4 and check it with the kernel.”
- “Check proofs/Basic.lean for sorry placeholders and tell me if it can be called kernel-checked.”
- “The Lean build timed out, so record what is still unproven without calling the claim false.”
Requirements
- A Lean toolchain with lean, elan and lake
- Mathlib for proofs that use the library
What it can do on your machine
Read from SKILL.md and the folder at commit 81fc7ae. It shows what the files ask for, not the result of running them.
Tool permissions
Pre-approves nothing: there is no allowed-tools line, so your agent's usual permission prompts apply.
From allowed-tools in the SKILL.md frontmatter.
Runs code
Shell commands in SKILL.md call:
rg
From the folder's file list and the shell code blocks in SKILL.md.
Network
No URLs in SKILL.md.
From URLs in SKILL.md, links to its own repository left out.
Credentials
Names no API keys, tokens, secrets or passwords.
From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.
Context cost
Math Formalization loads about 717 tokens when it runs, and up to ~1.7k if it reads all its reference files. Until then it costs about 39 tokens; SKILL.md has 185 words of instructions outside code blocks.
Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.
Safety
Auto-check passed
The automated check found no risky patterns in SKILL.md.
Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.
SKILL.md
The full file from tradecatlabs/vibe-coding-cn at commit 81fc7ae, republished under its MIT licence (© tradecatlabs). 185 words, ~717 tokens.
Download SKILL.mdSave it as
.claude/skills/math-formalization/SKILL.md (or your agent's skills folder). This skill also uses 5 other files; get the full folder from GitHub.- name
- math-formalization
- description
- 数学形式化与 proof-assistant 验证。用户要求 Lean 4/Mathlib、formal proof、kernel check、无 sorry 编译，或需要把自然语言定理切成可形式化定义和引理时使用。缺少 Lean 工具链时必须 fail-closed。
Math Formalization
把数学主张转成可由 proof assistant 内核检查的最小切片；当前环境缺工具时只产出计划，不伪造验证。
Position in the Method Map
Lean 是形式化方法中的依赖类型理论型交互式定理证明平台，主战场属于“演绎验证 / 定理证明”，不是形式化方法的同义词。先用 governance/standards/FORMAL-METHODS-MAP.md 固定规格与语义，再进行 Lean 语言/elaboration、proof engineering、自动化、Mathlib library engineering 和应用形式化。simp、grind、SMT 或符号执行可以辅助找证明，但最终的 kernel 检查和 statement-faithfulness 审查必须分开记录。
When to Use This Skill
- 用户明确要求 Lean 4、Mathlib 或机器检查证明。
- 自然语言证明已经稳定，需要验证关键引理或高风险步骤。
- 需要建立 definitions/imports/lemmas/theorem 的形式化依赖结构。
Not For / Boundaries
- CandidateObservation 或 formal-conjectures 条目只有在明确用户形式化请求或 active ProblemContract 下才能进入形式化；benchmark statement/build 不创建数学 Result。
- formal-conjectures 只使用 vendor lock 固定 commit/immutable benchmark snapshot；其上游也明确要求人工审查 misformalization，固定或编译成功不替代 statement faithfulness。
- 每次任务开始时运行时探测
lean、elan和lake；所需工具缺失时才 fail-closed 为calibration/blocked，不得把主机安装状态缓存为 skill 事实。 - 含
sorry、admit、未授权 axiom 或编译失败的文件不得标记 kernel-checked。 - 不采用归档 skill 中未经验证的
lean_agentPython API。 - 形式化成功证明 Lean 陈述成立，不自动证明它忠实表达原自然语言命题；必须做 faithfulness audit。
verified=false、timeout、unsupported、编译错误和基础设施错误都不是数学反例；必须保留失败类别。- 调用者自报的
verified、历史 PASS 或只存在的 receipt 文件没有通过权；证据必须绑定当前输入、工具链和真实产物。
Quick Reference
command -v lean
command -v lake
lean --version
lake env lean Path/To/File.lean
rg -n '\b(sorry|admit)\b' .形式化包必须包含：原命题、Lean 陈述、定义映射、imports、证明义务、实际命令、退出码、Lean/Mathlib 版本、axiom/sorry 审计和 faithfulness 状态。
验证 receipt 至少记录：当前请求/输入 digest、形式化产物或 theorem digest、checker 与 toolchain、请求和实际建立的 claim strength、未闭合义务、assurance mode、结构化结果状态与错误类别。claimEstablished 不得强于真实证据，也不得强于 claimRequested。
只有命令真实返回成功、无占位证明且陈述忠实审计完成，才能写 kernel-checked。
Examples
Example 1：工具缺失
- 输入：“把这个引理用 Lean 验证。”
- 动作：运行预检，发现
lean缺失；输出安装前置和形式化切片。 - 验收：状态是 blocked，不创建伪编译日志。
Example 2：含 sorry
- 输入：一个能够编译但包含
sorry的 Lean 文件。 - 动作：扫描占位符并阻止通过。
- 验收：不能标记 kernel-checked，报告具体文件/位置。
Example 3：陈述失真
- 输入：Lean 证明了比原命题更弱的结论。
- 动作：proof check 与 faithfulness audit 分开裁决。
- 验收：内核检查可 PASS，但总体状态仍因表达不忠实而 BLOCK。
Example 4：验证超时
- 输入：proof assistant adapter 超时并返回
verified=false。 - 动作：记录 timeout、预算、工具链和未闭合义务。
- 验收：状态为 blocked/timeout，不把原命题标记 refuted。
References
references/source-map.md：Lean Skill、receipt、adapter 与 faithfulness checker 的来源和限制。references/pressure-tests.md：占位证明、证据新鲜度、claim strength、失败分类与陈述忠实性压力场景。
Maintenance
- Sources：
wentor-research-plugins、leanprover-skills、mathevidence、itpeval、atp-checkers；只吸收方法、不变量和反例，不直接激活上游代码。 - Last updated：2026-08-26。
- Verification：安装后必须用当前 Lean/Mathlib 官方工具运行最小无
sorryvertical slice。
© tradecatlabs, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file
Files
SKILL.md and 5 other files (references) in research/vibe-mathing-cn-public/.codex/skills/math-formalization of tradecatlabs/vibe-coding-cn.
- SKILL.md
- CHANGELOG.md
- VERSION
- references/index.md
- references/pressure-tests.md
- references/source-map.md
Open the folder on GitHubat commit 81fc7ae
Compare with similar skills
Math Formalization next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.
| Skill | Stars | Used in | Tokens | Auto-check | Licence | Repo updated |
|---|---|---|---|---|---|---|
| Math Formalization this skilltradecatlabs/vibe-coding-cn | 17k | — | ~717 | Automated safety check: Pass | MIT | |
| SympyzLanqing/codex-claude-academic-skills | 4.6k | 16 repos | ~3.4k | Automated safety check: Pass | MIT | |
| Edu Analytic Geometrywy51ai/edulab | 1.4k | 1 repos | ~1.6k | Automated safety check: Pass | Apache-2.0 | |
| Edu Solid Geometrywy51ai/edulab | 1.4k | 1 repos | ~1.1k | Automated safety check: Pass | Apache-2.0 | |
| Math Modeling Competition WorkflowXiaoMaColtAI/math-modeling-skill | 1.9k | — | ~1.2k | Automated safety check: Pass | None | |
| Math Toolsananddtyagi/cc-marketplace | 687 | 2 repos | ~1.3k | Automated safety check: Pass | None |
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Related
Categories
Questions about Math Formalization
What does Math Formalization do?
Turns a mathematical claim into a small Lean 4 and Mathlib formalization checked by the proof assistant kernel, and refuses to report a pass without real evidence. The skill cuts a mathematical statement into the smallest pieces a proof assistant kernel can check: definitions, imports, lemmas and a theorem, with the original claim mapped to its Lean statement. At the start of each task the agent probes for lean, elan and lake.
When should I use Math Formalization?
Math Formalization fits situations like: verifying a key lemma with Lean 4 and Mathlib; splitting a natural-language theorem into definitions and lemmas that can be formalized; checking a Lean file that compiles but may still contain sorry; deciding whether a Lean statement is a faithful version of the original claim.
How do I install Math Formalization in Claude Code?
Run `npx skills add tradecatlabs/vibe-coding-cn --skill math-formalization -a claude-code`. Or copy the skill folder (research/vibe-mathing-cn-public/.codex/skills/math-formalization in tradecatlabs/vibe-coding-cn) into .claude/skills/math-formalization in your project. Claude Code loads it when a task matches its description.
How do I install Math Formalization in Codex?
Run `npx skills add tradecatlabs/vibe-coding-cn --skill math-formalization -a codex`. Or copy the skill folder (research/vibe-mathing-cn-public/.codex/skills/math-formalization in tradecatlabs/vibe-coding-cn) into .agents/skills/math-formalization in your project. Codex loads it when a task matches its description.
Can I use Math Formalization in Cursor, Gemini CLI or GitHub Copilot?
Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add tradecatlabs/vibe-coding-cn --skill math-formalization -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/math-formalization, .gemini/skills/math-formalization, .github/skills/math-formalization and .opencode/skills/math-formalization in your project.
What does Math Formalization need to run?
Going by SKILL.md and its folder, Math Formalization needs the command-line tools its instructions call (rg). Our summary lists: A Lean toolchain with lean, elan and lake; Mathlib for proofs that use the library.
Does Math Formalization access the network?
SKILL.md contains no URLs. Any network use would come from the scripts or tools the agent runs. This is read from the text; nothing was executed.
Is Math Formalization safe to install?
Our automated static check of SKILL.md found no risky patterns, such as piping downloads into a shell, reading credential files or hidden Unicode. It is not a guarantee. Review the folder before installing.
What licence does Math Formalization use?
Math Formalization is published under the MIT licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.
How many tokens does Math Formalization use?
About 717 tokens (SKILL.md is roughly 2.9k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full. Its references folder adds about 1k tokens, read only when the agent opens those files.
What are the alternatives to Math Formalization?
Skills that share tags, products or a category with Math Formalization: Sympy (zLanqing/codex-claude-academic-skills, 4.6k stars), Edu Analytic Geometry (wy51ai/edulab, 1.4k stars), Edu Solid Geometry (wy51ai/edulab, 1.4k stars) and Math Modeling Competition Workflow (XiaoMaColtAI/math-modeling-skill, 1.9k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.
Who maintains Math Formalization?
tradecatlabs (a GitHub user) maintains it in tradecatlabs/vibe-coding-cn, which has 17,236 GitHub stars. The repository holds 17 skills in this directory. The repository was last updated on October 8, 2026.
Source: tradecatlabs/vibe-coding-cn on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.