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vercel/next.js
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Agent skill
Mathematical Foundations
by brycewang-stanford in brycewang-stanford/Auto-Empirical-Research-Skills
Core mathematical concepts and theoretical frameworks for statistics
Install Mathematical Foundations
$ npx skills add brycewang-stanford/Auto-Empirical-Research-Skills --skill mathematical-foundations -a claude-codeProject install by default; add -g for ~/.claude/skills/.
$ gh skill install brycewang-stanford/Auto-Empirical-Research-Skills mathematical-foundations --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/brycewang-stanford/Auto-Empirical-Research-Skills.git skills-src && mkdir -p .claude/skills && cp -r skills-src/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations .claude/skills/mathematical-foundations && 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 "mathematical-foundations" agent skill from https://github.com/brycewang-stanford/Auto-Empirical-Research-Skills/tree/main/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations into .claude/skills/mathematical-foundations/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "mathematical-foundations", 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/brycewang-stanford/Auto-Empirical-Research-Skills/tree/main/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundationsType 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 brycewang-stanford/Auto-Empirical-Research-Skills --skill mathematical-foundations -a codexProject install goes to .agents/skills/; add -g for ~/.codex/skills/.
$ gh skill install brycewang-stanford/Auto-Empirical-Research-Skills mathematical-foundations --agent codexProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/brycewang-stanford/Auto-Empirical-Research-Skills.git skills-src && mkdir -p .agents/skills && cp -r skills-src/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations .agents/skills/mathematical-foundations && rm -rf skills-srcUse ~/.agents/skills/ instead of .agents/skills for a personal install.
Codex skills documentation · loads skills from .agents/skills/
Install the "mathematical-foundations" agent skill from https://github.com/brycewang-stanford/Auto-Empirical-Research-Skills/tree/main/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations into .agents/skills/mathematical-foundations/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "mathematical-foundations", 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 brycewang-stanford/Auto-Empirical-Research-Skills --skill mathematical-foundations -a cursorProject install goes to .agents/skills/; add -g for ~/.cursor/skills/.
$ gh skill install brycewang-stanford/Auto-Empirical-Research-Skills mathematical-foundations --agent cursorProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/brycewang-stanford/Auto-Empirical-Research-Skills.git skills-src && mkdir -p .cursor/skills && cp -r skills-src/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations .cursor/skills/mathematical-foundations && 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 "mathematical-foundations" agent skill from https://github.com/brycewang-stanford/Auto-Empirical-Research-Skills/tree/main/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations into .cursor/skills/mathematical-foundations/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "mathematical-foundations", 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/brycewang-stanford/Auto-Empirical-Research-Skills.git --path skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations--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 brycewang-stanford/Auto-Empirical-Research-Skills --skill mathematical-foundations -a gemini-cliProject install goes to .agents/skills/; add -g for ~/.gemini/skills/.
$ gh skill install brycewang-stanford/Auto-Empirical-Research-Skills mathematical-foundations --agent gemini-cliProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/brycewang-stanford/Auto-Empirical-Research-Skills.git skills-src && mkdir -p .gemini/skills && cp -r skills-src/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations .gemini/skills/mathematical-foundations && 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 "mathematical-foundations" agent skill from https://github.com/brycewang-stanford/Auto-Empirical-Research-Skills/tree/main/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations into .gemini/skills/mathematical-foundations/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "mathematical-foundations", 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 brycewang-stanford/Auto-Empirical-Research-Skills mathematical-foundationsInstalls 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 brycewang-stanford/Auto-Empirical-Research-Skills --skill mathematical-foundations -a github-copilotProject install goes to .agents/skills/; add -g for ~/.copilot/skills/.
$ git clone --depth 1 https://github.com/brycewang-stanford/Auto-Empirical-Research-Skills.git skills-src && mkdir -p .github/skills && cp -r skills-src/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations .github/skills/mathematical-foundations && 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 "mathematical-foundations" agent skill from https://github.com/brycewang-stanford/Auto-Empirical-Research-Skills/tree/main/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations into .github/skills/mathematical-foundations/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "mathematical-foundations", 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 brycewang-stanford/Auto-Empirical-Research-Skills --skill mathematical-foundations -a opencodeOpenCode documents no install command of its own. Project install goes to .agents/skills/; add -g for ~/.config/opencode/skills/.
$ gh skill install brycewang-stanford/Auto-Empirical-Research-Skills mathematical-foundations --agent opencodeProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/brycewang-stanford/Auto-Empirical-Research-Skills.git skills-src && mkdir -p .opencode/skills && cp -r skills-src/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations .opencode/skills/mathematical-foundations && 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 "mathematical-foundations" agent skill from https://github.com/brycewang-stanford/Auto-Empirical-Research-Skills/tree/main/skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations into .opencode/skills/mathematical-foundations/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "mathematical-foundations", 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
mathematical-foundations- GitHub stars
- 4.5k
- Token cost
- ~4.1k tokens
- SKILL.md length
- 1,160 words
- Files
- 1
- Skills in repo
- 383
- Repo updated
- First seen
- Licence
- Custom licence
At a glance
Core mathematical concepts and theoretical frameworks for statistics
- Works in 3 steps: Find any unbiased estimator $\hat{\theta}$ → Find complete sufficient statistic $T$ → Compute $E[\hat{\theta} \mid T]$
- Tasks that involve Statistics
- SKILL.md covers Sufficiency, Completeness, UMVUE and Rao-Blackwell and Exponential Families, plus 2 more sections
- Instructions only: no scripts, shell commands, URLs or credentials in SKILL.md
What it does
Mathematical Foundations is an agent skill from brycewang-stanford/Auto-Empirical-Research-Skills. Core mathematical concepts and theoretical frameworks for statistics
Its SKILL.md is about 4.1k tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.
It sits in Data & Analytics, covering Statistics. The repository describes itself as: 🔬 A curated collection of 23,000+ agent skills for empirical research across 8 social science disciplines. | 精选 23,000+ AI Agent 技能库，覆盖8大社会科学学科的实证研究。CoPaper.AI…
When your agent uses it
- Tasks that involve Statistics
Example prompts
- “/mathematical-foundations”
Workflow steps
3 steps, taken from the first numbered list in SKILL.md.
- Find any unbiased estimator $\hat{\theta}$
- Find complete sufficient statistic $T$
- Compute $E[\hat{\theta} \mid T]$
What it can do on your machine
Read from SKILL.md and the folder at commit 9fa87d8. 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
No scripts in the folder and no shell commands in SKILL.md (its code samples are r).
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
Mathematical Foundations loads about 4.1k tokens when it runs. Until then it costs about 23 tokens; SKILL.md has 1,160 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
Its licence (Custom licence) doesn't allow us to republish the file, so here is its outline and opening line. It has 1,160 words (~4,074 tokens).
“Core mathematical statistics theory for rigorous methodology development”
- name
- mathematical-foundations
Files
Just SKILL.md in skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations of brycewang-stanford/Auto-Empirical-Research-Skills.
Open the folder on GitHubat commit 9fa87d8
Compare with similar skills
Mathematical Foundations 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 |
|---|---|---|---|---|---|---|
| Mathematical Foundations this skillbrycewang-stanford/Auto-Empirical-Research-Skills | 4.5k | — | ~4.1k | Automated safety check: Pass | Custom licence | |
| Sandbox Benchvercel/next.js | 143k | — | ~4.1k | Automated safety check: Pass | MIT | |
| Statistical Analysisspacering-net/codeg | 3.9k | 3 repos | ~5k | Automated safety check: Pass | MIT | |
| StatsmodelszLanqing/codex-claude-academic-skills | 4.7k | 15 repos | ~4.9k | Automated safety check: Pass | BSD-3-Clause | |
| AI Daily DigestvigorX777/ai-daily-digest | 1.6k | — | ~1.3k | Automated safety check: Pass | None | |
| Statistical Powerspacering-net/codeg | 3.9k | 1 repos | ~3.6k | Automated safety check: Notes | MIT |
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Related
Categories
Questions about Mathematical Foundations
What does Mathematical Foundations do?
Core mathematical concepts and theoretical frameworks for statistics. Mathematical Foundations is an agent skill from brycewang-stanford/Auto-Empirical-Research-Skills.
When should I use Mathematical Foundations?
Mathematical Foundations fits situations like: tasks that involve Statistics.
How do I install Mathematical Foundations in Claude Code?
Run `npx skills add brycewang-stanford/Auto-Empirical-Research-Skills --skill mathematical-foundations -a claude-code`. Or copy the skill folder (skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations in brycewang-stanford/Auto-Empirical-Research-Skills) into .claude/skills/mathematical-foundations in your project. Claude Code loads it when a task matches its description.
How do I install Mathematical Foundations in Codex?
Run `npx skills add brycewang-stanford/Auto-Empirical-Research-Skills --skill mathematical-foundations -a codex`. Or copy the skill folder (skills/26-Data-Wise-scholar/skills/mathematical/mathematical-foundations in brycewang-stanford/Auto-Empirical-Research-Skills) into .agents/skills/mathematical-foundations in your project. Codex loads it when a task matches its description.
Can I use Mathematical Foundations 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 brycewang-stanford/Auto-Empirical-Research-Skills --skill mathematical-foundations -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/mathematical-foundations, .gemini/skills/mathematical-foundations, .github/skills/mathematical-foundations and .opencode/skills/mathematical-foundations in your project.
What does Mathematical Foundations need to run?
SKILL.md names no scripts, command-line tools or credentials: Mathematical Foundations is instructions for the agent only.
Does Mathematical Foundations 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 Mathematical Foundations 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 Mathematical Foundations use?
Mathematical Foundations has a licence file (the repository's licence) that doesn't match a standard licence. Read it on GitHub before reusing the skill.
How many tokens does Mathematical Foundations use?
About 4.1k tokens (SKILL.md is roughly 16k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.
What are the alternatives to Mathematical Foundations?
Skills that share tags, products or a category with Mathematical Foundations: Sandbox Bench (vercel/next.js, 143k stars), Statistical Analysis (spacering-net/codeg, 3.9k stars), Statsmodels (zLanqing/codex-claude-academic-skills, 4.7k stars) and AI Daily Digest (vigorX777/ai-daily-digest, 1.6k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.
Who maintains Mathematical Foundations?
brycewang-stanford (a GitHub user) maintains it in brycewang-stanford/Auto-Empirical-Research-Skills, which has 4,542 GitHub stars. The repository holds 383 skills in this directory. The repository was last updated on October 5, 2026.
Source: brycewang-stanford/Auto-Empirical-Research-Skills on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.