Math Atlas Problem

Math Atlas Problem Optimization

End-to-end workflow for creating or optimizing an interactive math problem page with verified formulas, accurate history, contributor avatars + profile links, and a high-quality Canvas visualization.

When to use

• User asks to optimize/fix/create a problem page at /problems/<slug>
• User reports incorrect formulas, bad visualization, or missing references
• User wants to add a new mathematical problem to the atlas

Architecture (read this first)

Each problem is one self-contained file under src/content/problems/<slug>.ts that calls defineProblem({...}). There is no central problems.ts data array and no separate coreFormulas record — formulas, videos, authors, timeline all live inline in that object.

A new/edited problem touches up to four places:

1. src/content/problems/<slug>.ts — the defineProblem(...) object (data, formulas, videos, authors, timeline)
2. src/content/problems/index.ts — import the export and add it to the configuredProblems array
3. src/components/viz/classic-viz.tsx — the draw<Name> function + <Name>Viz wrapper
4. Two viz registries — src/components/viz/viz-loader.tsx and src/components/ui/problem-card.tsx

Types live in src/lib/problem-types.ts. Helpers (defineProblem, scholarSearch) in src/lib/problem-template.ts.

Workflow

Phase 1 — Audit

1. Navigate to the page in the browser (npx next dev) and take a full-page screenshot
2. Read the problem file src/content/problems/<slug>.ts
3. Read the draw<Name> function in src/components/viz/classic-viz.tsx
4. Note issues: vague descriptions, missing/weak authors, no avatars, weak references, flat visualization, media-hype framing

Phase 2 — Research

Spawn a research agent to gather verified data. See references/research-checklist.md:

• Precise formal statement with LaTeX, plus 1-2 equivalent formulations
• Verified historical timeline with exact paper citations
• Key contributors (provers, verifiers, generalisers) with institutions
• For each person: homepage / Google Scholar / X(Twitter) / LinkedIn (verify identity!)
• Avatar source per contributor (personal photo for people, logo for orgs)
• DOI / arXiv links for all papers
• 2-3 relevant YouTube videos (verify each videoId exists)

Be skeptical of recent (current-year) AI/math news — distinguish the exact result from media conflation, and lean on primary sources (arXiv, the proof PDF, the problem's own catalogue).

Phase 3 — Write/update the problem file

Edit src/content/problems/<slug>.ts. See references/data-schema.md for the field-by-field guide. Key fields: status, field, year, shortDescription, longDescription, vizComponent, collections, coordinates, connections, authors, papers, timeline, formulas, videos.

For a new problem, also register it in src/content/problems/index.ts (import + array entry).

Phase 4 — Formulas

Set the inline formulas: ProblemFormula[] array (2-4 entries), each { label, latex, description }:

1. Main statement — the theorem / problem definition
2. Key mechanism — the underlying quantity or bound that drives the result
3. Classification / structure — a structural quantity, or the contrasting bound (e.g. the conjecture vs. the disproof)

Use String.raw for LaTeX; keep descriptions ≤120 chars.

Phase 5 — Authors: avatars + profile links

See references/data-schema.md "Authors" section.

• Avatars (avatarUrl): for a person, use a personal photo; for a company/institution entity author, use the org logo. Download assets into public/people/<name>.<ext> (photos) or public/orgs/<name>.<ext> (logos) and reference "/people/..." / "/orgs/...". Local assets avoid the next.config.ts remotePatterns allowlist (only upload.wikimedia.org + scholar.googleusercontent.com) and never expire (LinkedIn/Twitter CDN URLs are signed and expire).
• Links: prefer Google Scholar; the Homepage slot falls back personal-site → Scholar → Twitter/LinkedIn. Rendered as brand logos by src/components/ui/author-card.tsx via src/components/ui/brand-icons.tsx (Google Scholar, X, LinkedIn, Wikipedia). Fields: homepageUrl, scholarUrl, twitterUrl, linkedinUrl, wikipediaUrl.
• Order: put the result's main contributors first, historical figures last.

Phase 6 — Visualization

Add a draw<Name> function + <Name>Viz wrapper at the end of classic-viz.tsx, then register the PascalCase name in both viz-loader.tsx and problem-card.tsx. See references/viz-patterns.md:

• Show the actual mathematical objects (point sets, vector fields, mappings), not abstract decoration
• Add pointer interactivity (mouse controls a meaningful parameter; gentle time animation when idle)
• Mark key features (fixed points, singularities, the active element) with blue glow + label
• Style: dark bg (#050505), white strokes, blue (#60a5fa) highlights; degrade gracefully on card previews

Phase 7 — Verify

1. Reload the page in the browser, take a screenshot
2. Check formulas render (no KaTeX errors) and the visualization animates + responds to the pointer
3. Confirm every avatar serves (200) and each profile link / video resolves
4. Run npx next build — must pass TypeScript and static generation with no errors
5. Verify all DOI/arXiv/homepage URLs are valid (curl 200) and videoIds exist (YouTube oEmbed)

File map

References

• references/research-checklist.md — what to verify during research
• references/data-schema.md — field-by-field guide for the problem file
• references/viz-patterns.md — Canvas visualization conventions and patterns