IdeaWell

Project ideas from Hacker News discussions.

Not all elementary functions can be expressed with exp-minus-log

Original Article

Hacker News Discussion

📝 Discussion Summary (Click to expand)

Theme 1 – Disagreement over what counts as “elementary.”

"The quintic has no closed form solution ... but if we broaden our repertoire of functions, such as with the Bring radical." — reikonomusha

Theme 2 – Claims of a universal operator and the surrounding hype.

"If this is true, then this blog post debunking EML is going to up‑end all of mathematics for the next century." — renewiltord

Theme 3 – Technical limits: decidability and known theorems.

"You are correct, it is undecidable by Richardson’s theorem." — reikonomusha

🚀 Project Ideas

EML Explorer

Summary

  • A web sandbox that lets users define custom binary operators and test whether they can generate polynomial root solvers or other “elementary” functions.
  • Visual feedback shows tree depth, verification results, and comparison against Richardson’s theorem.

Details

Key Value
Target Audience Researchers and hobbyist mathematicians interested in symbolic regression and universal operators
Core Feature Interactive tree builder with real‑time verification of functional completeness
Tech Stack React + TypeScript front‑end, Flask API back‑end, SageMath for algebraic checks, Docker for reproducible environment
Difficulty Medium
Monetization Revenue-ready: SaaS subscription $15/mo per user

Notes

  • Users can import known functions (e.g., Bring radical) and see if they can be expressed with a single binary operator.
  • Includes export to Python scripts for offline experimentation, fostering community contributions.

BringRadical Builder

Summary

  • A CLI/Python library that transforms any implicitly defined root (e.g., quintic solution) into an “elementary” representation using a chosen universal operator.
  • Generates ready‑to‑use code snippets and visual tree diagrams for embedding in scientific workflows.

Details| Key | Value |

|-----|-------| | Target Audience | Computational mathematicians, educators, and developers building symbolic math tools | | Core Feature | Automatic conversion of implicit root definitions into EML‑style expressions with verification | | Tech Stack | Python 3.11, SymPy, NumPy, Graphviz for visualization, FastAPI for optional web service | | Difficulty | Low | | Monetization | Hobby |

Notes

  • Provides templates for common “cheat” functions like Bring radical, square root, and omega constant.
  • Includes unit tests that check algebraic properties, helping users validate their generated expressions quickly.

Elementary Function Clarifier#Summary

  • An AI‑driven chatbot and tutorial generator that explains concepts from the Hacker News discussion (e.g., elementary functions, EML, Bring radical) in plain language.
  • Offers interactive Q&A and visualizations to reduce confusion and encourage deeper engagement.

Details| Key | Value |

|-----|-------| | Target Audience | Math enthusiasts, undergraduate students, and interdisciplinary researchers seeking clarity | | Core Feature | Context‑aware explanations with diagrams, code examples, and links to source material | | Tech Stack | GPT‑4‑style language model (hosted locally), React UI, Markdown renderer, Mermaid for diagrams | | Difficulty | Low | | Monetization | Revenue-ready: Freemium model – free basic queries, $5/mo for advanced API access and custom branding |

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