Project ideas from Hacker News discussions.

“Erdos problem #728 was solved more or less autonomously by AI”

📝 Discussion Summary (Click to expand)

1. AI Accelerates Proof Reconfiguration and Formalization

AI excels at tedious tasks like refactoring proofs or translating informal ideas to Lean, unlocking new insights.
"Reconfiguring existing proofs in ways that have been tedious or obscured from humans... will be done at superhuman speeds" (observationist).
"the more interesting capability... is the ability to rapidly write and rewrite new versions of a text as needed" (pfdietz quoting Tao).

2. Formal Verification Ensures Trustworthy Proofs

Tools like Lean eliminate hallucinations via machine-checked proofs, even if opaque.
"We know they are correct because they check in Lean" (roadside_picnic).
"Once a proof is formalized into Lean... there is no doubt that the proof is correct" (maxwells-daemon).

3. AI Solves Erdos Problems via Remixing, Not Pure Novelty

Impressive for Erdos #728, but relies on existing methods and training data patterns.
"solved more or less autonomously by AI (after some feedback from an initial attempt)" (Tao, via OP).
"this was exactly a 'remix' of similar proofs that most likely were in the training data" (zozbot234).

4. Human Expertise Remains Essential

AI mirrors user skill; experts like Tao drive breakthroughs through guidance.
"they mirror the intellect of the user but give you big dopamine hits that'll lead you astray" (MyFirstSass).
"human augmented AI here or AI augmented human" (jacquesm).

5. Narrow AI "Cleverness," Not AGI

Valuable for math but far from general intelligence; debates on goalposts.
"I doubt that anything resembling genuine 'artificial general intelligence' is within reach... [but] 'artificial general cleverness' is becoming a reality" (pfdietz quoting Tao).
"This is very narrow AI, in a subdomain where results can be automatically verified" (mkl).


🚀 Project Ideas

Proof Refactorer

Summary

  • AI-powered tool that automates global symbol/constant replacement in LaTeX proofs (e.g., pi to tau, Gamma to factorial) and simplifies expressions while preserving validity.
  • Core value: Saves tedious manual refactoring, uncovers novel perspectives as discussed by malux85 and observationist.

Details

Key Value
Target Audience Mathematicians, researchers using LaTeX/Lean
Core Feature Upload LaTeX, select refactor (e.g., tau=2pi), auto-rewrite + SymPy/Lean verification
Tech Stack SymPy, Lean 4, LangChain + GPT-4o for parsing, Streamlit webapp
Difficulty Medium
Monetization Revenue-ready: Freemium ($10/mo pro)

Notes

  • "What happens if we use Tao instead of Pi everywhere" (malux85); "rewrite every formula featuring the Gamma function" (ogogmad) – HN would love instant experiments.
  • High utility for "scientific refactoring"; sparks discussions on new proofs.

MathLit Insight Miner

Summary

  • Agentic tool that ingests PDFs (arXiv, scans old papers via OCR), extracts theorems/proofs, finds cross-paper correlations/latent knowledge missed by humans.
  • Core value: Surfaces hidden insights from vast, unsearchable literature, addressing kridsdale3 and zozbot234's frustrations.

Details

Key Value
Target Audience Researchers, academics in math/science
Core Feature PDF upload/batch from Scholar, LLM extraction + embedding search for novel links
Tech Stack Llama3.1, Unstructured.io OCR, FAISS vector DB, FastAPI backend
Difficulty High
Monetization Revenue-ready: Subscription ($20/mo unlimited scans)

Notes

  • "agents scanning the vastness of PDFs to find correlations" (kridsdale3); old scholarship ignored (zozbot234) – perfect for HN's meta-analysis love.
  • Practical for lit reviews; potential viral threads on discoveries.

LeanProof Assistant

Summary

  • Web-based IDE that translates informal English proofs to Lean code, generates/verifies proofs via Aristotle-like integration, iterates on feedback.
  • Core value: Bridges natural language to formal math, reducing tedious confirmation as per roadside_picnic and sublinear.

Details

Key Value
Target Audience Math students, researchers new to proof assistants
Core Feature NL input → Lean gen + verify; chat for refinements; export to Mathlib
Tech Stack Lean 4 + Aristotle API, o1-preview for NL→Lean, VS Code extension
Difficulty Medium
Monetization Hobby

Notes

  • "assisting in the creation of Lean proofs is a huge area" (roadside_picnic); "tedious to confirm what the LLMs say" (sublinear) – HN theorem-provers excited.
  • Utility for Erdos problems; fosters collaborative formalization.

ErdosAI Benchmark Hub

Summary

  • Collaborative platform for running AI tools (GPT, Aristotle) on Erdos/Millennium problems; auto-formalizes statements, tracks solves, verifies proofs.
  • Core value: Standardized benchmarking of AI math progress, building on svat/Tao's wiki.

Details

Key Value
Target Audience AI/math researchers, hobbyists
Core Feature Problem DB, one-click AI runs, Lean verification leaderboard
Tech Stack Lean 4, Dockerized AIs (o1, Claude), Supabase DB, Next.js frontend
Difficulty High
Monetization Revenue-ready: Sponsorships + API ($0.01/query)

Notes

  • Tao's "AI contributions to Erdős problems" wiki; MPPbench excitement (kelseyfrog) – HN loves benchmarks.
  • Sparks debates/utility on AI capabilities.

FormalVerifier Chat

Summary

  • Chatbot specialized in verifying AI-generated math/code proofs; cross-checks with Lean/Z3, explains gaps, suggests fixes.
  • Core value: Automates tedious human verification of LLM outputs, as lamented by sublinear and jacquesm.

Details

Key Value
Target Audience Developers, mathematicians using LLMs for proofs/code
Core Feature Paste LLM proof → verify/explain; multi-tool (Lean, Coq, Z3) integration
Tech Stack LangGraph agents, Lean/SMT solvers, GPT-4o-mini, Telegram/Discord bot
Difficulty Medium
Monetization Revenue-ready: Freemium ($5/mo unlimited)

Notes

  • "still likely very tedious to confirm what the LLMs say" (sublinear); AI as "rubber duck" but needs checks (jacquesm) – addresses core HN skepticism.
  • Practical for daily research; high discussion potential.

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