ClaudSkills / Science & Research / math-stats

Lean Math Foundations

Q: What is a Claude Code skill and how does the Lean Math Foundations skill fit in?

A Claude Code skill is a SKILL.md file that lives under ~/.claude/skills/<name>/ and tells the Claude Code CLI agent how to perform a specific task (instructions, prompts, allowed tools). Skills are auto-discovered at session start. Lean Math Foundations is one of 67,000+ skills indexed in the open ClaudSkills catalog, classified under the Science & Research category. Learn more at https://claudskills.com/learn/what-is-skill-md/.

Category: Science & Research · Sub-category: math-stats · Last updated: 2026-05-30

USE FOR: foundational mathematics in Lean 4 — Lean's type system (Prop / Type / universes), classical vs constructive choices, Mathlib's algebraic typeclass hierarchy (Group / Ring / Order / Lattice / Module / Algebra), category theory basics, and any proof that needs foundational reasoning about types, propositions, or universes. DO NOT USE FOR: applied lattice instances such as severity / quality-gate lattices (use @lean-math-discrete); analysis-flavoured algebra such as normed-space structure (use @lean-math-analysis); writing a specific proof (use @lean-proof); reviewing a finished proof (use @lean-proof-review). TRIGGERS: type universe, Prop vs Type, classical reasoning, Classical.choice, algebraic typeclass, Mathlib hierarchy, category theory, propext, funext.

About this skill (catalog notes)

Lean Math Foundations is published as a SKILL.md file in this catalog. The SKILL.md runs to about 941 words, in the catalog's typical mid-range.

Source: github.com/r-irbe/proof-skills
License: Apache-2.0
Original author: r-irbe
Indexed lastmod: 2026-05-30
Catalog position: Science & Research · math-stats
Indexed related skills: 10

How Lean Math Foundations fits the catalog

Lean Math Foundations sits in the Science & Research category under the math-stats sub-topic in the ClaudSkills catalog. There are 10 related skills indexed alongside it; comparing a few before installing usually reveals which fits your workflow best.

These notes are auto-generated from features detected in the SKILL.md file and from this catalog's structure — they aren't part of the source repository.

From the source SKILL.md

Guide to formalizing foundational mathematics in Lean 4, covering the structures and patterns that underpin all domain-specific formalization work.

What this skill does

Lean Math Foundations is a community-contributed Claude Code skill in the math-stats sub-category. It ships as a SKILL.md file that Claude Code auto-discovers under ~/.claude/skills/lean-math-foundations/ and loads when your prompt matches the skill's trigger.

Who uses this skill

The Lean Math Foundations Claude Code skill is built for researchers, data scientists, academics, and analysts working with complex data and scientific literature. It's part of ClaudSkills (also referred to as Claude Skills or Claude Code Skills) — the open community-curated registry of 93,000+ SKILL.md files for Anthropic's Claude Code agent and the wider Claude ecosystem (Claude API, Claude Agent SDK).

How to install

Free

Manual install (2 steps)

mkdir -p ~/.claude/skills/lean-math-foundations
curl -L https://claudskills.com/skills/lean-math-foundations/SKILL.md \
  -o ~/.claude/skills/lean-math-foundations/SKILL.md

Or just download SKILL.md directly and drop it into ~/.claude/skills/lean-math-foundations/. Claude Code auto-discovers it on next session.

Skills live at ~/.claude/skills/lean-math-foundations/SKILL.md on macOS/Linux, or %USERPROFILE%\.claude\skills\lean-math-foundations\SKILL.md on Windows. See the full install guide for step-by-step instructions.

📱 Install from your phone or desktop Telegram

Open @claudskills_bot on Telegram, tap Open Desktop App, and the desktop app installs this skill for you. Or share the bot link with a colleague — they get the same one-tap install. Learn more →

Pro

One-click install via the desktop app

The ClaudSkills desktop app installs any skill directly into ~/.claude/skills/ with one click — no terminal required. Pro starts at $9/mo or $149 lifetime.

Pro

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See pricing → Download desktop app

Frequently asked questions

How do I install the Lean Math Foundations Claude Code skill?

Install via the ClaudSkills desktop app (one click) or copy SKILL.md from the source repository to ~/.claude/skills/lean-math-foundations/SKILL.md and restart Claude Code. Both flows are detailed at claudskills.com/install/.

What does the Lean Math Foundations skill do?

Is this skill free to install?

Yes. ClaudSkills is an open registry — every skill keeps its source repository's license, and manual install via copy is free. ClaudSkills Pro ($9/mo, $79/yr, or $149 one-time) adds one-click install via the desktop app and a multi-signal Quality Score.

When should I use the Lean Math Foundations skill?

Use Lean Math Foundations when your Claude Code task falls under the Science & Research category — specifically in the math stats area. Claude Code auto-discovers installed skills and invokes the right one based on the task description, so you can also ask Claude directly (e.g. "use Lean Math Foundations" or describe the task and let Claude pick). Browse related skills at /category/science/.

What is a Claude Code skill and how does the Lean Math Foundations skill fit in?

A Claude Code skill is a SKILL.md file that lives under ~/.claude/skills/<name>/ and tells the Claude Code CLI agent how to perform a specific task (instructions, prompts, allowed tools). Skills are auto-discovered at session start. Lean Math Foundations is one of 67,000+ skills indexed in the open ClaudSkills catalog, classified under the Science & Research category. Learn more at /learn/what-is-a-claude-skill/.

Attribution & license

Source: https://github.com/r-irbe/proof-skills/blob/HEAD/skills/lean-math-foundations/SKILL.md
License: Apache-2.0
Author: r-irbe
Website: https://github.com/r-irbe/proof-skills

Cite this skill

If you reference this skill in a blog post, paper, or documentation, you can cite it as:

APA

r-irbe. (2026). Lean Math Foundations [Claude Code skill]. ClaudSkills. https://claudskills.com/skills/lean-math-foundations/

BibTeX

@misc{lean-math-foundations-2026,
  author    = {r-irbe},
  title     = {Lean Math Foundations [Claude Code skill]},
  year      = {2026},
  publisher = {ClaudSkills},
  url       = {https://claudskills.com/skills/lean-math-foundations/}
}

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