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Project ideas from Hacker News discussions.

Palomar: A registry of Lean verified mathematics

Original Article

Hacker News Discussion

📝 Discussion Summary (Click to expand)

3 Prevalent Themes

1. Incentive to contribute

"Same reason why you would use arxiv instead of posting the result to X." — mlpoknbji
"Why publish research articles? Why contribute to the Linux kernel? ..." — teiferer

2. Vision of a unified, searchable formalization of mathematics

"Turning the entire field of mathematics into a formalized and connected system... All fields will undergo this change!!!" — seeknotfind

3. Platform dependence & verification difficulty

"However, checking that a given Lean repository actually proves the claimed statement is somewhat non‑trivial, especially for an audience which is not expert in the use of Lean." — demibabs
"It only works for GitHub;" — fuglede_

🚀 Project Ideas

ProofPulse: Incentivized Formal Proof Submission Platform

Summary

  • A community platform that rewards mathematicians and formalizers with reputation points and token incentives for submitting verified Lean proofs.
  • Solves the contribution incentive problem highlighted in the HN discussion.

Details

Key Value
Target Audience Mathematicians, graduate students, formal methods hobbyists
Core Feature Earn reputation and token rewards for verified Lean proof submissions; community voting and bounty system
Tech Stack Node.js backend, React frontend, PostgreSQL, smart‑contract‑style incentive engine
Difficulty Medium
Monetization Revenue-ready: tiered subscription ($5/mo basic, $20/mo premium)

Notes

  • Directly answers the recurring HN question “what’s the incentive to contribute?”
  • Gamified contribution could increase the volume and quality of formalized mathematics.

LeanCheck: Automated Verification & Discovery Service for Lean Formalizations

Summary

  • An online service that automatically checks Lean repositories for correctness, consistency, and completeness, reducing manual verification overhead.
  • Directly tackles the comment about “checking that a given Lean repository actually proves the claimed statement is non‑trivial”.

Details

Key Value
Target Audience Lean maintainers, repository curators, research students
Core Feature Upload a Lean repo; service runs automated proof checking, flags mismatches, suggests improvements
Tech Stack Python backend, Lean 4 engine, Docker, Elasticsearch for indexing
Difficulty Medium
Monetization Revenue-ready: pay‑per‑verification ($0.01 per check)

Notes

  • Addresses the “recursive problem” concern by providing a lightweight verification layer.
  • Would be highly valued by the community seeking reliable, searchable proof verification.

MathIndex: Searchable Structured Index of Formalized Mathematics

Summary

  • A centralized, searchable index that links and cross‑references formalized theorems across Lean, Isabelle, and Coq repositories, creating a “cipher key” to mathematical knowledge.
  • Mirrors the desire expressed for “an index of mathematical understanding” that is manually vetted yet searchable.

Details

Key Value
Target Audience Researchers, educators, mathematics students
Core Feature Unified search interface; auto‑generates cross-references and relation graphs between formalizations
Tech Stack Python, Neo4j graph database, Elasticsearch, Docker
Difficulty High
Monetization Hobby

Notes

  • Directly responds to comments about “turning the entire field of mathematics into a formalized and connected system”.
  • Potential for academic citation tools and educational platforms to built upon the index.

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