---
name: wiki-search-math
description: >
  Search external mathematics resources for a topic: MathWorld, nLab, OEIS,
  DLMF, and Wikipedia math articles. Returns ranked results, optionally
  hands them to wiki-add-resource. Use when the user says "search math",
  "find on MathWorld", "look up in nLab", "OEIS sequence", "DLMF formula",
  "search Wikipedia math", or during math-research project setup when
  external math sources are needed.
---

Before acting, read [the runtime guidance](../../RUNTIME.md).


# Math Resource Search

Companion to [wiki-search-wolfram](../wiki-search-wolfram/SKILL.md) — searches external (non-Wolfram-ecosystem) mathematics resources.
Use it whenever a math-research project needs to anchor a concept against authoritative external references.

## When to use

- The user says "search math", "find on MathWorld", "look up in nLab", "OEIS sequence", "DLMF formula", "search Wikipedia math".
- During math-research project setup when external math sources are needed.

## What you need

1. **Topic / keywords** — what to search for.
   Concept ("Lie algebra"), theorem ("Stokes theorem"), object ("Bessel function"), sequence ("Fibonacci numbers"), or named entity ("Galois theory").
2. **Project directory** (optional) — for logging results into `Wiki/` if it exists.

## Kernel execution (license-aware)

The search scripts below each spawn a fresh `wolframscript` kernel (one license seat) — check headroom first per the authoritative policy in [`AGENTS.md` § *Wolfram Kernel Execution Policy*](../../RUNTIME.md#wolfram-execution); with no free seat, run the equivalent `Import[...]` through `mcp__Wolfram__WolframLanguageEvaluator`.

## Steps

The steps are the sources — run their scripts **in parallel**, then finish with *After searching*.
Skip any source that is clearly irrelevant (e.g. skip OEIS for a non-discrete topic).

### 1. MathWorld

Wolfram MathWorld — large encyclopedia, classical math through research math.

```bash
wolframscript -f "${PLUGIN_ROOT}/scripts/search_mathworld.wls" <keyword1> <keyword2> ...
```

Returns JSON array of `{name, url, snippet}`.
The script scrapes the search page for entry links matching `mathworld.wolfram.com/<EntryName>.html`.
Names are derived from CamelCase slugs.

### 2. nLab

Category-theoretic and higher-structures wiki.
Best for category theory, homotopy theory, algebraic geometry, mathematical physics.

```bash
wolframscript -f "${PLUGIN_ROOT}/scripts/search_nlab.wls" <keyword1> <keyword2> ...
```

Returns JSON array of `{name, url, snippet}`.
Filters out archival "YYYY Month changes" pages.

### 3. OEIS

Online Encyclopedia of Integer Sequences — only relevant when an integer sequence appears.

```bash
wolframscript -f "${PLUGIN_ROOT}/scripts/search_oeis.wls" <keyword1> <keyword2> ...
```

Returns JSON array of `{anum, name, sequence, url}`.
`anum` is the A-number (e.g. `A000045`).
`sequence` is the first ~120 chars of the data row.

You can also query by **first terms**:

```bash
wolframscript -f "${PLUGIN_ROOT}/scripts/search_oeis.wls" 1 1 2 3 5 8 13 21
```

### 4. DLMF

NIST Digital Library of Mathematical Functions — authoritative for special functions, asymptotics, identities.

```bash
wolframscript -f "${PLUGIN_ROOT}/scripts/search_dlmf.wls" <keyword1> <keyword2> ...
```

Returns JSON array of `{name, url, location}`.
`location` is the DLMF locator (e.g. `10.2#E5` is chapter 10, section 2, equation 5).

### 5. Wikipedia math

Filtered Wikipedia search — uses the MediaWiki search API and ranks results by math-keyword overlap and presence of LaTeX markers in snippets.

```bash
wolframscript -f "${PLUGIN_ROOT}/scripts/search_wikipedia_math.wls" <keyword1> <keyword2> ...
```

Returns JSON array of `{title, url, snippet}`.

## After searching

Present a single combined summary, grouped by source:

```
Math Resource Search: <topic>

MathWorld:   <n> entries
- <name> — <url>

nLab:        <n> entries
- <name> — <url>

OEIS:        <n> sequences
- A000045 — Fibonacci numbers — <url>

DLMF:        <n> formulas
- 10.2#E5 — <url>

Wikipedia:   <n> articles
- <title> — <url>
```

Then ask the user **which to keep**.
For each kept result:

1. If `Wiki/` exists: invoke [wiki-add-resource](../wiki-add-resource/SKILL.md) with the URL — wiki-add-resource will recognise the URL pattern and create the right kind of wiki article (MathWorld / nLab / OEIS / DLMF / Wikipedia).
2. If no `Wiki/`: just print the URLs as references the user can keep.

## Integration with other skills

- Pair with [wiki-search-wolfram](../wiki-search-wolfram/SKILL.md) when the project also touches Wolfram-ecosystem material.
- Pair with [paper-cite](../paper-cite/SKILL.md) to immediately produce a BibTeX entry for any DOI/arXiv ID surfaced (e.g. references inside a MathWorld or Wikipedia article).
- Pair with [wiki-add-resource](../wiki-add-resource/SKILL.md) to commit kept results to `Wiki/Resources/`.

## When NOT to use

- Pure Wolfram-ecosystem questions → use [wiki-search-wolfram](../wiki-search-wolfram/SKILL.md).
- Looking for a specific paper (arXiv / DOI / title) → use the existing arXiv MCP and [paper-cite](../paper-cite/SKILL.md).
- Reading an already-added paper → use `mcp__arxiv-latex-mcp` or `mcp__arxiv__read_paper`.