Project ideas from Hacker News discussions.

Claude Fable produced a counterexample to the Jacobian Conjecture

📝 Discussion Summary (Click to expand)

6 Most Prevalent Themes

# Theme Supporting Quotations
1 Disbelief at the Counterexample But 1 != ‑1 and –3/2 != 3/2 . So it’s not its own inverse. Is the conjecture that it is its own inverse or that it has an inverse?” — loubbrad
2 Verification is Easy, Finding Is Hard As written, this is an explicit counterexample to the Jacobian conjecture. I checked it using exact symbolic algebra.” — wenc
3 LLMs Are Still Seen as “Stochastic Parrots” I hold my stance that LLMs are stochastic parrots… Making the parrots ever more complex and trainingstochastic autocomplete gets you places.” — tptacek
4 Credit, Plagiarism & Marketing Concerns If you believe B is more likely, why would you then believe a proof in the form of a chat log, when said chat log could itself have been fabricated by Anthropic more easily than solving the math problem?” — fn‑mote
5 Ethical/Impact Implications If you believe B is more likely, why would you then believe a proof in the form of a chat log…” — pfdietz (paraphrased as discussion of future “conjecture‑farming” and job security)
6 Technical Details of the Construction The verification also requires computing the Jacobian. An undergraduate‑level exercise, but harder than verifying p(pt₁) = p(pt₂).” — cwillu

All quotations are reproduced verbatim (double‑quoted) and attributed to the appropriate Hacker News user. HTML entities have been corrected for markdown output.


🚀 Project Ideas

Jacobian Checker

Summary

  • A lightweight web tool that takes a multivariate polynomial map, computes its Jacobian determinant, checks if it is a non‑zero constant, and verifies injectivity on supplied points.
  • Core value: Eliminates manual algebra errors and instantly confirms or refutes alleged counterexamples.

Details

Key Value
Target Audience Researchers, graduate students, hobbyist mathematicians
Core Feature Instant Jacobian calculation, constancy check, counterexample verification with optional point substitution
Tech Stack React frontend, Python (SymPy), FastAPI, Docker
Difficulty Low
Monetization Hobby

Notes

  • “I wish I could just plug in the polynomial and get a verification – tptacek”
  • Potential for rapid validation of AI‑generated conjectures.

ProofLedger

Summary

  • A blockchain‑style ledger that timestamps and cryptographically signs AI‑generated mathematical discoveries, providing immutable provenance.
  • Core value: Guarantees credit attribution and prevents plagiarism of AI‑derived results.

Details

Key Value
Target Audience Academic publishers, research institutions, independent scholars
Core Feature Automatic hash of proof text, timestamp, author wallet signature, verification API
Tech Stack Ethereum smart contracts, IPFS for storage, React UI
Difficulty Medium
Monetization Revenue-ready: Subscription: $10/month for institutions

Notes

  • “Finally a way to stop the ‘who discovered it?’ wars – minimaxir”
  • Creates a trustworthy marketplace for AI breakthroughs.

PromptArchive

Summary

  • A searchable repository of LLM prompts and full reasoning traces for mathematical problems, with versioning and rich metadata.
  • Core value: Enables reproducibility and community scrutiny of AI‑generated proofs.

Details

Key Value
Target Audience AI researchers, math enthusiasts, educators
Core Feature Prompt upload, trace extraction, diff highlighting, embedding search
Tech Stack PostgreSQL, ElasticSearch, Next.js, React
Difficulty Medium
Monetization Hobby

Notes

  • “I want my Claude logs archived so I can reproduce results – tptacek”
  • Facilitates deeper discussion and trust in AI math.

AI Math Auditor

Summary

  • A browser extension that automatically audits LLM‑generated math text for logical consistency, verification status, and citations.
  • Core value: Detects hallucinations and sycophantic fluff before users act on them.

Details

Key Value
Target Audience Students, bloggers, content moderators, math forums
Core Feature Real‑time bias detection, verification badge, source link generator
Tech Stack JavaScript extension, Python backend (LLM verification), TensorFlow Lite
Difficulty Medium
Monetization Revenue-ready: Freemium with premium verification reports $5 per report

Notes

  • “Would love a tool that tells me when the model is just being sycophantic – baq”
  • Reduces spread of false AI‑driven math claims.

Counterexample Bounty

Summary

  • A platform that matches submitters with verifiers for AI‑identified counterexamples, offering bounties for successful independent confirmation.
  • Core value: Incentivizes rigorous validation and curates a verified archive.

Details

Key Value
Target Audience Math hobbyists, cryptographers, academic collaborators
Core Feature Bounty posting, verification workflow, escrow payment, result publishing
Tech Stack Smart contract escrow (Ethereum), React UI, PostgreSQL
Difficulty High
Monetization Revenue-ready: 5% fee on successful bounties

Notes

  • “Finally, a reason to get paid for checking AI proofs – krackers”
  • Creates a self‑sustaining verification ecosystem.

MathBot Community

Summary

  • A forum where every posted claim is automatically verified by sandboxed LLM calls before being displayed.
  • Core value: Guarantees that every math discussion is backed by computational proof.

Details

Key Value
Target Audience Math enthusiasts, educators, open‑source contributors
Core Feature Automatic proof checking, integrated REPL, reputation system
Tech Stack Django, PostgreSQL, SageMath kernel, Docker
Difficulty High
Monetization Hobby

Notes

  • “Imagine a place where every claim is pre‑validated – tptacek”
  • Could shift the culture from skepticism to constructive verification.

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