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Project ideas from Hacker News discussions.

Erdos 281 solved with ChatGPT 5.2 Pro

Original Article

Hacker News Discussion

📝 Discussion Summary (Click to expand)

4 Prevalent Themes in the Discussion

1. Validation & Scrutiny of LLM Math Proofs

Many commenters emphasize the need for rigorous human verification, highlighting concerns about LLMs confidently producing incorrect solutions and the discovery of prior solutions in literature. - skepticism about verification: "I've 'solved' many math problems with LLMs, with LLMs giving full confidence in subtly or significantly incorrect solutions." (redbluered) - discovery of prior solutions: "On following the references, it seems that the result in fact follows... from a 1936 paper of Davenport and Erdos (!), which proves the second result you mention." (pessimist, quoting forum post)

2. The Pace & Impact of AI on Mathematical Research

Discussion centers on how LLMs are accelerating progress in mathematics, particularly for lower-tier problems, and the implications for the field's speed of advancement. - Tao's endorsement and cautious optimism: "Very nice! ... actually the thing that impresses me more than the proof method is the avoidance of errors... Previous generations of LLMs would almost certainly have fumbled these delicate issues." (pessimist, quoting Terry Tao) - acceleration of minor results: "Many minor theorems will fall. Next major milestone: Can LLMs generate useful abstractions?" (pessimist, quoting Terry Tao)

3. LLMs as Pattern Matchers vs. True Intelligence

Debate persists over whether LLMs' capabilities stem from sophisticated pattern matching or genuine reasoning, with arguments comparing human and machine cognition. - pattern matching perspective: "My take is a huge part of human intelligence is pattern matching. We just didn’t understand how much multidimensional geometry influenced our matches" (qudat) - world model perspective: "Prediction is the mechanism they use to ingest and output information, and they end up with a (relatively) deep model of the world under the hood." (sdwr) - alien intelligence concept: "I don't think they will ever have human intelligence. It will always be an alien intelligence." (threethirtytwo)

4. Hype vs. Practical Utility in Software & Math

A strong divide exists between those who see LLMs as transformative and those who view current capabilities as overhyped, with skepticism about reliability in real-world applications. - optimistic view of impact: "I have 15 years of software engineering experience... I truly believe that ai will far surpass human beings at coding... We are very close." (mikert89) - skepticism about practical reliability: "Holding out with the vague 'I tried it and it came up with crap'. Isn't that a perfectly reasonable metric? The topic has been dominated by hype... it's natural to try for yourself, observe a poor result, and report back 'nope, just more BS as usual'." (fc417fc802) - practical utility in cleaning up backlogs: "There is still enormous value in cleaning up the long tail of somewhat important stuff. One of the great benefits of Claude Code to me is that smaller issues no longer rot in backlogs." (MattGaiser)

🚀 Project Ideas

Proof Verification Platform for Erdős Problems

Summary

  • [A web platform that provides a centralized, verified repository for solutions to Erdős problems, preventing "rediscovery" of existing proofs.]
  • [Core value proposition: Saves mathematicians and AI researchers time by immediately flagging when a "new" solution is actually a rediscovery of old work.]

Details

Key Value
Target Audience Mathematicians, AI researchers, and students studying Erdős problems.
Core Feature Searchable database of problems with links to prior solutions, automatic literature cross-referencing, and user-submitted proofs with verification status.
Tech Stack Next.js (frontend), Python/FastAPI (backend), PostgreSQL, Elasticsearch, OAuth (for user accounts).
Difficulty Medium
Monetization Hobby (free access, potentially grant-funded for academic research).

Notes

  • [Directly addresses the pain point highlighted by xeeeeeeeeenu: "> no prior solutions found. This is no longer true, a prior solution has just been found." This platform would make such discoveries immediate rather than reactive.]
  • [High practical utility for the AI/math community; reduces wasted effort and hype cycles around "new" solutions to old problems.]

AI Code Review & Architecture Analysis Tool

Summary

  • [A tool that uses LLMs to analyze codebases for architectural flaws, maintainability issues, and "common sense" problems that pure syntax checkers miss.]
  • [Core value proposition: Complements coding agents by providing the "common sense" layer of software engineering that daxfohl notes LLMs currently lack, acting as a senior engineer consultant.]

Details

Key Value
Target Audience Senior software engineers, tech leads, and teams using AI coding assistants.
Core Feature Scans a codebase (local or GitHub) to identify architectural smells, security vulnerabilities, maintainability debt, and design pattern misapplications.
Tech Stack Python (AST parsing, code analysis), LLM API integration (e.g., OpenAI, Anthropic), React (frontend), Docker (deployment).
Difficulty Medium
Monetization Revenue-ready: Freemium model (limited scans) or subscription for teams ($20-50/user/month).

Notes

  • [Addresses the frustration from daxfohl: "They already do [surpass humans at coding]. What they suck at is common sense. Unfortunately good software requires both."]
  • [Positions the AI not as a replacement but as a tool that helps "inexperienced" developers ship better software, aligning with anonzzzies' observation about shipping apps with fewer people.]

Math Proof Formalization & Literature Search Service

Summary

  • [A service that takes an LLM-generated proof (or human proof), formalizes it in Lean, and automatically searches mathematical literature to verify novelty.]
  • [Core value proposition: Automates the rigorous verification process that Terence Tao and others perform manually, turning the "discovery" phase into a formal workflow.]

Details

Key Value
Target Audience Professional mathematicians, math PhD students, and AI research labs.
Core Feature 1. Formalize natural language proofs into Lean/Rocq code. 2. Run literature search queries against arXiv, MathSciNet, and historical texts. 3. Generate a report on novelty and correctness.
Tech Stack LLMs fine-tuned on math (e.g., GPT-5.2, specialized math models), Lean 4 compiler API, Python (scraping/connectors), vector database (Pinecone/Weaviate).
Difficulty High
Monetization Revenue-ready: Pay-per-proof verification or institutional subscriptions for universities/research labs.

Notes

  • [Directly addresses the core workflow seen in the discussion: Tao manually checking literature after the "breakthrough." This tool would scale that verification step.]
  • [Exploits the pain point of obscure literature (e.g., Rogers' Theorem) that even experts like Tao or Erdős missed, making AI a powerful research assistant.]

LLM "Hallucination" & Accuracy Benchmark Platform

Summary

  • [A platform where users test LLMs on logic/math tasks and crowdsource verification of results, creating a leaderboard based on "Verified Correctness" rather than just benchmarks.]
  • [Core value proposition: Solves the trust issue ("I've 'solved' many math problems with LLMs... giving full confidence in subtly or significantly incorrect solutions") by shifting to a community-verified model.]

Details

Key Value
Target Audience AI researchers, developers, and power users comparing model capabilities.
Core Feature Users submit problems; the platform routes them to multiple LLMs. Results are peer-reviewed by human experts and other LLMs (e.g., using Opus to verify GPT).
Tech Stack Frontend (React/Next.js), Backend (Node.js/Python), Multiple LLM APIs, User authentication, Reputation system.
Difficulty Low-Medium
Monetization Hobby (open source/community driven) or ad-supported.

Notes

  • [Addresses the skepticism from redbluered: "Has anyone verified this? I've 'solved' many math problems with LLMs, with LLMs giving full confidence in subtly or significantly incorrect solutions."]
  • [Creates a trusted environment for evaluating AI progress, moving beyond hype to demonstrable, verified results.]

AI-Assisted "Vibe Coding" Architecture Scaffolder

Summary

  • [A tool that takes high-level feature descriptions and generates not just code, but a full system architecture diagram, data model, and API contracts before writing a single line of code.]
  • [Core value proposition: Solves the "common sense" and architecture gap by forcing the AI to plan the "hard part" (architecture) before the "easy part" (coding), as mentioned by pelorat.]

Details

Key Value
Target Audience Solo developers, startups, and product managers validating ideas.
Core Feature Input a product requirement; output a Mermaid/PlantUML diagram, database schema, API specs (OpenAPI), and a scaffolded codebase in the chosen language.
Tech Stack LLM for planning, React/D3.js for visualization, Code generation templates, Docker for environment setup.
Difficulty Medium
Monetization Revenue-ready: SaaS subscription for teams ($15/month) or one-time purchase for individuals.

Notes

  • [Addresses pelorat's insight: "Getting the architecture mostly right... is the hard part, but I find that this is where AI shines."]
  • [Aligns with anonzzzies' claim of shipping software without touching much code, providing a structured "no-code" layer that respects software engineering principles.]

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