The Network
A place to get help with a math idea, or to help someone else with theirs. You don't need to be a professional mathematician to take part.
Reading is open to everyone. You only need an account to post.
Maybe you have a conjecture you can't prove, or an argument with a gap you can't close.
Post it here, and other people can work on it with you.
How The Network worksThe steps, Zakhira, the house rules, and what the badges mean
How it works
Ask about your own work
Click ⌬ Ask the Network above and describe what you need help with. It can be a new idea or existing work: a sketch, a finished paper or an Open Problem attempt.
Ask about someone else's work
Pick it under Existing work, or go to their sketch, finished paper or attempt and click ⌬ Ask the Network about this. It opens once they approve.
People respond
Others respond with a formal version, a supporting result, a reference, a counterexample, or a question. You can reply to their responses.
It grows into a map
Click any request in the list below. Its page shows the request at the top and all of its responses as boxes on a map, with lines showing what each response is replying to. Hover over a box to read it or reply to it.
ذَخِيرَة
✦ Zakhira
Zakhira, an AI historian
Zakhira is an AI historian for The Network. It tells the history of the map, explains responses, and draws connections, including between two responses that never replied to each other. It doesn't solve or check any math.
The name comes from the Arabic word zakhīra (ذَخِيرَة), meaning a store of something valuable. Medieval Islamic scholars used the plural, zakhā'ir, for large collections of knowledge. Here, Zakhira keeps a history of how each request developed.
Everything it writes is AI-generated. On a request's page, click Read the history, or hover over a box on the map and click ✦ Zakhira.
The spirit of The Network
Be respectful of the original work. Someone chose to share their idea. Try to build on it or make it clearer.
Counterexamples are welcome. Showing a conjecture is false is real progress. Just explain it kindly.
Your responses stay on the record with your name on them, so post something you'd be glad to have there.
Responses that are vague or dismissive and don't add any math will be removed.
Reading the badges
Request type
Lifecycle
Open requests
2Proving the Collatz-triangle side ratios → √5, √5/2, ½ (so (D₂+D₃)/D₁ → φ), and connecting it to the golden-mean shift of the 3x+1 itineraries.
Turning the numerical φ-appearances in the golden map's periodic points into a proof, starting with the 2-cycle segment length → φ².