IdeaWell

Project ideas from Hacker News discussions.

Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

Original Article

Hacker News Discussion

📝 Discussion Summary (Click to expand)

1. LLMs as collaborative partners for experts

“To me, this shows that extremely talented and qualified mathematicians (can) use frontier‑level LLMs to automate their personal grind‑y workloads.” – arm32

2. Dense mathematical notation creates a communication barrier

“Mathematics would be much more approachable if it just used plain English like sum(0, Infinity, my_func) instead of a big Greek sigma.” – chongli

3. Brute‑force search is computationally impossible

“If you searched for coefficients from -12 to 12, this would be 25^360 = 2 × 10^503 different possibilities.” – traes

4. Hallucinations and trust concerns when evaluating AI output

“You absolutely can hallucinate a working lean proof.” – tempfile

5. Iterative “keep‑going” prompting can unlock breakthroughs

“Keep going is exactly how many mathematicians achieved success.” – hyperhello

6. Skepticism about labeling AI output as “intelligence”

“at this point, for me, any comment about LLMs that begins with “it’s just …” is hard to take seriously.” – slidehero

🚀 Project Ideas

MathPrompt Lab

Summary

  • Platform to design, store, and iterate expert-level prompts for deep‑math problems like Jacobian conjecture counterexamples.
  • Core value: turns vague intuition into reproducible, testable interactions with LLMs, accelerating breakthroughs.
  • Enables systematic exploration of “right questions” that HN users repeatedly ask.

Details

Key Value
Target Audience Mathematicians, research students, AI‑assisted proof explorers
Core Feature Structured prompt editor with versioning and collaborative sharing
Tech Stack React front‑end, Node.js backend, PostgreSQL storage
Difficulty Medium
Monetization Revenue-ready: Subscription tiered by stored prompts and API calls

Notes

  • HN users have repeatedly asked “how to ask the right question” – they'd love a tool that systematizes that.
  • Could spawn discussions on prompt‑engineering best practices and open‑source prompt libraries.

ProofValidator Cloud

Summary

  • Automated verification service that checks AI‑generated mathematical proofs against formal systems (Lean/Coq) and flags inconsistencies.
  • Core value: safeguards against hallucinated proofs, giving researchers confidence to build on AI output.
  • Bridges gap between AI output and formal verification.

Details

Key Value
Target Audience Math researchers, graduate students, theorem‑proving hobbyists
Core Feature Upload proof script → run through Lean/Coq extraction and consistency checker
Tech Stack Python micro‑services, Lean 4 kernel, Docker orchestration
Difficulty High
Monetization Revenue-ready: Pay‑per‑verification token bundle

Notes

  • Comments like “I can’t evaluate AI outputs without domain knowledge” show demand for reliable verification.
  • Potential to integrate with Lean’s community and become a de‑facto verification hub.

MathTranslatR

Summary

  • AI tool that converts dense mathematical notation, jargon, and proofs into plain‑language explanations tailored to user’s expertise level.
  • Core value: bridges the gap between expert discourse and newcomers, reducing the “language barrier” in math.
  • Tailors explanations to varying expertise levels.

Details

Key Value
Target Audience Undergrad math students, enthusiasts, non‑technical analysts
Core Feature Input equation/journal excerpt → output simplified narrative with optional step‑by‑step walkthrough
Tech Stack GPT‑4‑style model fine‑tuned on LaTeX → plain‑text, React UI for interactive exploration
Difficulty Low
Monetization Revenue-ready: Freemium (basic explanations free; premium detailed walkthroughs)

Notes

  • HN threads repeatedly lament “impenetrable math notation”; users would pay for instant translation.
  • Could fuel discussion on educational tech and accessibility of advanced topics.

ExpertSwap

Summary

  • Marketplace connecting domain experts with AI users to review, critique, and refine AI‑generated insights in real time.
  • Core value: mitigates trust gaps and ensures that breakthrough ideas are vetted by knowledgeable humans.
  • Enables real‑time expert critique of AI insights.

Details

Key Value
Target Audience AI researchers, startup founders, collaborative research teams
Core Feature Live chat sessions where experts query and challenge AI outputs, feeding back improvements
Tech Stack WebSocket real‑time backend, Node.js, MongoDB for session logs
Difficulty Medium
Monetization Revenue-ready: Hourly expert rates + platform commission

Notes

  • Conversations show frustration with “I can’t evaluate responses” – a paid review service would be valuable.
  • Sparks dialogue on expert compensation and collaboration workflows.

LeanCoach

Summary

  • Interactive tutoring environment that guides users through constructing formal proofs step‑by‑step, encouraging Socratic questioning of the AI.
  • Core value: builds genuine understanding rather than passive consumption of AI answers.
  • Promotes active learning through guided questioning.

Details

Key Value
Target Audience Math students, self‑learners, hobbyist theorem provers
Core Feature Conversational coach that asks probing questions, validates each proof step, and suggests next moves
Tech Stack Lean 4 integration, TypeScript front‑end, Firebase for state persistence
Difficulty Medium
Monetization Revenue-ready: Subscription for premium proof libraries

Notes

  • HN users discussed “being able to ask the right question” – LeanCoach makes that iterative process explicit.
  • Could inspire community‑driven proof libraries and foster deeper learning.

Counterexample Miner

Summary

  • Automated search engine that uses guided prompting and feasibility filters to discover structured counterexamples for open conjectures like the Jacobian problem.
  • Core value: democratizes discovery of mathematically significant counterexamples without requiring massive compute clusters.
  • Includes built-in verification to reduce false positives.

Details

Key Value
Target Audience Math grad students, open‑problem enthusiasts, AI‑driven research groups
Core Feature Prompt generator + constraint engine to prune search space, returns candidate polynomials with verification scripts
Tech Stack Python backend, PyTorch for guided search, Lean for post‑verification
Difficulty High
Monetization Revenue-ready: Tiered access based on compute credits and exportable result packs

Notes

  • Community repeatedly highlighted the difficulty of brute‑forcing massive coefficient spaces; this tool directly addresses that pain point.
  • Opens avenues for discussion on AI‑assisted combinatorial search and sharing discovered counterexamples.

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