Why we built this
Serious math usually happens in a few specific places: universities, journals, research groups. To be taken seriously you generally need the right degree, the right institution, or a finished proof with clean citations, and plenty of good ideas never make it past that.
But you don't need anyone's permission to think about a problem. People have done real mathematics with none of those credentials: noticing a pattern, following a question no one else had bothered to ask.
So we built a place where you can just start. Post a rough idea and let other people help sharpen it. Nobody checks your background at the door.
What we believe
Anyone can do math.
You don't need a degree or a title. A good question and the patience to follow it are enough. Some of the most important ideas in math came from people the world overlooked.
Unfinished ideas are welcome.
You don't have to show up with a proof. A partial argument, a pattern you noticed, a question you can't answer yet. All of it has somewhere to go here.
Rough is fine.
Strange conjectures and half-formed guesses are how math actually gets made. Rigor matters, but it's something you work toward, not a test you have to pass before you're allowed to speak.
Math is something people do together.
It grows out of conversations, arguments, and shared notebooks. That's why the site is built so other people can see what you're working on and join in.
If you’ve ever had a mathematical idea and nowhere to take it, this is that place.
Start with whatever you’ve got:
a question, a sketch, a half-finished proof. You can share it before it’s finished.
Everything on UnboundedFigures
Every page and feature on the site, with live demos. Use the menu to jump around, and open any feature to see how it works.
The Sketch
The Sketch is the public wall. Anyone can post a math idea at any stage: a rough idea, a partial conjecture, or a finished argument.
You can flag a post as Looking for rigorous feedback when you want help making it rigorous, and the editor renders math as you type.
Posting a sketchTitle, body, topic tags, and the thinking behind it, from the “+ Post a Sketch” button.
Open The Sketch and click + Post a Sketch to write your idea.
Title: A one-line summary of the idea. This is what shows on the wall.
Body: The idea itself, written in the rich editor with live math. Long posts collapse behind a Read more on the wall.
Looking for rigorous feedback: An optional flag (below) that tells people you want help making the idea rigorous. Leave it off for everything else.
Topic tags: Optional tags like #combinatorics. They make your sketch easier to find and feed trending topics and recommendations.
Looking for rigorous feedbackOne optional flag that signals you want help making an idea rigorous.
The author is asking for help turning this into rigorous mathematics.
Most sketches are early ideas, so there’s no need to say how finished something is. The one thing worth flagging is when you want help.
Looking for rigorous feedback: Tells people you want help turning your idea into rigorous math. Leave it off for everything else.
Writing mathCtrl+M (⌘M on a Mac) puts math in a line. Add Shift for an equation on its own line. It renders as you type, with no dollar signs.
For every prime
Writing a sentence? Press Ctrl+M (⌘M on a Mac) to put a formula right into the line. No $ … $ needed.
Illustrated example. The names and activity are made up.
The same editor is used everywhere you write on the site: sketches, comments, Network requests, and papers. It renders your notation as you type.
⌘M / Ctrl+M: Drop an inline formula into the middle of a sentence.
⌘⇧M / Ctrl+Shift+M: Give an equation its own centered display line.
No delimiters: There are no $…$ to balance. Click a rendered formula and it reopens as LaTeX to edit.
The full sketch: intuition & contextFields for the thinking behind the idea. Intuition is required. The rest are optional.
Intuition
“It feels like the peaks line up with something combinatorial…”
Open any sketch to see the whole picture. Beyond the body, a sketch can include context that helps other people understand an early idea:
Intuition: How you got to the idea. It's the one required field, and it shows on the sketch's card.
Related ideas: Related results or techniques you’ve seen before.
Self-critique: Where you think it might break. Saying so up front gets you better help.
Hypotheses: What has to be true for the idea to work.
Browsing & filtering the wallNew / Top sorting, a Seeking-rigor filter, tag filters, and follow-a-topic.
New vs. Top: Toggle between the newest sketches and the most upvoted.
Seeking-rigor filter: Narrow the wall to only sketches whose author is asking for help making them rigorous.
Tag filter: Click any #tag to see only sketches on that topic.
Follow a topic: The + beside a tag follows it, so it starts shaping your Feed. A ✓ means you already follow it.
Load more: Click Load more at the bottom to see more sketches.
Reacting & discussingUpvote a sketch, reply in its comments, or open the full page.
Upvote: One tap signals that a sketch is worth attention. Upvotes drive the Top sort and trending.
Comments: Every sketch has a discussion thread with the same live-math editor, so feedback can itself contain real notation.
Read sketch: Opens the full page with intuition, context, comments, and the option to open it to The Network.
The Network
The Network connects people who have a mathematical idea with people who can make it rigorous. You post a request describing your idea. Once it's open, other people reply with a response: a formal version, a supporting result, a reference, a counterexample, or a question. Every response shows the name of the person who wrote it.
You don't need to be a professional mathematician to post an idea or to answer one.
Asking the NetworkChoose a new idea or existing work, then say what you want help with.
Click ⌬ Ask the Network at the top of The Network. On the page that opens, choose A new idea and write it out there, or choose Existing work and search for it, then describe what you want help with. The description uses the live-math editor, so it can contain real notation.
Existing work: One search covers public sketches, finished public papers and Open Problem attempts, by title or tag. Before you search, the list shows your own work. Search to find someone else's.
Focus area: One line on what kind of help you want.
Category & tags: Route the request to the people who work in that area.
Someone else's work: Pick it under Existing work, or go to their sketch, finished paper or Open Problem attempt and click ⌬ Ask the Network about this. You then click Send for approval, and the request opens once its author approves.
Reading the badges: types & lifecycleEvery card shows where a request came from and whether it's open yet.
Where it came from
Lifecycle
New idea: Posted on its own, not about a sketch, paper or attempt.
From a sketch: Asks about a sketch.
From a paper: Asks about a finished paper.
From an Open Problem attempt: Asks about an attempt on an Open Problem.
A request is in one of three states:
Waiting for approval: A request on someone else's work, waiting for the author to approve it.
Open: Other people can respond. There's no “claimed” or “completed” step. A request keeps taking responses for as long as people have something to add.
Declined: The author chose not to approve it. The request isn't listed in The Network and is closed to responses and comments, but its link still shows what was asked.
How an idea growsAsk about your work (or someone else's, once they approve) → others respond → it branches into a map of responses.
- 1
Ask about your own work
Click ⌬ Ask the Network on the Network page.
- 2
Ask about someone else's work
From their sketch, paper or attempt. It opens once they approve.
- 3
People respond
You can reply to their responses.
- 4
It grows into a map
Open any request to see it with its map of responses.
Ask: Click ⌬ Ask the Network on the Network page 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.
Approve: Your own work opens right away. If you ask about someone else's sketch, paper or attempt, the author is notified and it opens only if they approve it.
Respond: Anyone other than the person who asked can respond, with a written proof, an uploaded document, or a finished Project Lab paper. Nothing needs to be claimed first. The person who asked takes part by replying to those responses.
Branch: A response can reply to the original request or to another response, so one idea can grow into a whole tree of responses.
What a response can beTitle your response and, if you like, give it one of the labels below.
Every response has a title you write. A label is optional.
Formal version: The idea rewritten in formal language.
Supporting result: A precise statement that comes out of the idea and can be proved or disproved.
Reference: This already exists somewhere. Here's where to find it.
Counterexample: An example showing the idea is false.
Open question: A question of your own, which a later response can answer.
No label: Anything that moves the idea forward and doesn't fit a label.
Finding requestsFilter by request type and search tags to find open requests.
Type pills: Show one kind of request: new ideas, or those about a sketch, a paper or an attempt.
Tag search: Type to narrow to a topic. Matching tags appear as clickable chips.
Open requests: The board lists every open request, each with a live count of how many responses it has drawn so far.
The NetworkSee an idea's whole history as one map: the original request and every response.
Illustrated example. The names and activity are made up.
An idea rarely stays a single request. The original request draws responses, each response can draw further responses, and a question can be answered by another response. The Network draws all of that as one map.
Opening it: Click any request in The Network. The request sits at the top of its page, with the map below it.
Nodes: The original request (the root, with a badge saying where it came from) and the responses. Each response shows its title and, beneath it, an optional label. Open questions are drawn with a dashed outline.
Edges: An arrow points from a response to the response (or request) it replies to.
Start here: New to a request? ▸ Start here walks you through it in reading order: the original request first, then each branch in turn. The map glides and rings each node as you step through with ◀ / ▶.
People & responses: The header shows a live count of the people taking part and the responses posted so far.
To have the map explained in words, use Zakhira.
Zakhira, the AI historianTells the history of a request, explains responses, and draws connections. It never does the math.
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.
Zakhira is the one place AI is used on the platform, in a deliberately narrow role. It is a historian for The Network: it tells the history of a request's map, explains responses, and draws connections between them. Everything it writes is AI-generated and labelled as such.
On a response: Hover a node on the map and press ✦ Zakhira for a bulleted summary of that response plus a few suggested connections.
History: ✦ Read the history tells how the request grew, in short points, and where it stands now. If no one has responded yet, it says so.
Following a connection: Zakhira surfaces connections between responses to a request. Clicking one moves the map to it and draws a dashed arc between the two responses.
Across requests: ✦ Explore connections → Other requests finds related requests. Opening one shows both side by side, with lines drawn between the responses that connect them.
What it won't do: It never does, checks, judges, or suggests mathematics. That stays with the community.
The name: Zakhīra (ذَخِيرَة) is Arabic for a treasury: something valuable set aside for those who come after.
The spirit of The NetworkThe ground rules for responding.
- ⌬ Be respectful of the original work.
- ∀ Counterexamples are welcome.
- 🔗 Your responses stay on the record under your name.
- 📐 Responses that are vague or dismissive and don't add any math will be removed.
The same rules are posted on The Network page. Build on a request or make it clearer, and keep in mind that anything you post stays on the record under your name.
Counterexamples count as real contributions. Responses that are vague or dismissive and don't add any math will be removed.
The Feed
The Feed shows what's happening across the site: new sketches, active projects, and open requests on the Network. The main column is sorted around your interests.
The sidebar shows trending topics and posts, open Network requests, active projects, and people to follow.
For You & FollowingTwo views: a ranked mix tuned to your interests, or only people you follow.
A tiling identity for Collatz orbits
For you: A ranked mix from everyone on the site. It's the default, and it's what visitors see before signing in.
Following: Only sketches from the figures you follow, newest first. Appears once you’re signed in.
Each card shows the author, the title, a comment count, and a link straight into the full sketch.
Why you’re seeing somethingSmall badges explain the ranking: views, interests, active discussion, or follows.
Every card that gets boosted in “For you” says why it’s there.
Recently viewed: Ideas near things you just looked at, with a time-decayed boost.
Matches your interests: Built from the categories and tags you engage with and follow.
Active discussion: Sketches with live comment threads get surfaced.
From people you follow: People you follow get a boost.
The ranking also mixes up authors, so one very active poster can’t take over your feed.
Figures
Figures is the directory of people on the platform. Use it to find collaborators and follow people whose work you want to keep seeing.
The directory lists only people with activity (a post, a project, a filled-out profile, or an open-to-collaborate flag), so empty accounts stay hidden.
Searching the directoryLive search with keyboard navigation and your recent searches.
Recent searches
Live results: Matches appear as you type, across username, display name, and bio.
Keyboard navigation: Use ↑ / ↓ to move through results and Enter to jump to a profile.
Recent searches: Your past searches are saved as quick chips. Click one to run it again.
Recommended figuresPersonalized suggestions with a reason for each match.
Riya Nair
@riya
Works on topics you follow
When you’re signed in, the top of the page shows a handful of recommended figures chosen from real signals: people whose sketches you’ve viewed or commented on, active posters in your topics, and matches to your interests. Each card explains why it’s suggested. Signed-out visitors see the most-followed figures instead.
Figure cardsBio, follower count, an “Open to collaborate” flag, and a one-click follow.
Maya Okonkwo
@maya
Number theory & dynamical systems. Chasing the Collatz map.
Open to collaborateBio & handle: A short description and link straight to the full public profile.
Followers: How many people follow this figure.
Open to collaborate: A flag people turn on to say they’re looking for projects to join.
Follow: One click follows a figure so their sketches flow into your Following feed.
The Project Lab
The Project Lab is where projects are built. A project has a shared paper, a research log, live co-editing, version history, roles, and a dependency map of its results.
Projects are public by default, so anyone can see the work, and who is editing it, while it happens.
A project can have just one person. Everything works the same whether you're alone or with a team.
Browsing projectsSearch, status tabs, sorts, “My projects”, “Open to join”, and rich project cards.
Collatz Triangles
Search + autocomplete: Type to jump straight to a project by name.
Status tabs: Filter by Active, Paused, or Completed.
Sort: Newest, Recently active, or Most members.
My projects / Open to join: Scope to your own memberships, or only projects actively seeking contributors.
Topic tags: Click a card’s tag to filter the directory to that subject.
Card signals: Every card shows the lead, member count, last-active time, a live “here now” badge, status and privacy, an AI-Assisted flag when relevant, and its latest research-log updates.
Private teasers: Private projects still show up in the list, marked “🔒 invite only.” Their card shows the title, summary, mission, tags, lead, and member count. Only members can open the workspace.
Starting a projectTitle, mission, background, topics, visibility, and whether you're recruiting.
Start a project from the Project Lab. You set:
Mission: One sentence on what the project is trying to prove or find. It shows on the project card.
Background: What someone should know before joining: related results, what’s been tried.
Existing work: Paste in notes or a draft and it becomes the project’s Paper.
Topics: Tags that help people find the project.
Visibility: Public (the default) or private and invite-only.
Seeking contributors: Lets people know you’re recruiting.
Live collaboration & presenceEdit the same paper at once with live cursors. See who’s “here now” and who’s viewing.
Let Amarax₀ be any periodic point.
Each step multiplies the gap by 1/φ, so the orbit contracts by 1/φ.Toma
Everyone edits the same paper at once. You see collaborators' cursors and names as they type.
Illustrated example. The names and activity are made up.
Real-time editing: Members edit the shared paper at the same time. You see each person’s cursor and name move through the text. There are no merge conflicts or version emails.
Here now: Members currently in the project appear with a green presence badge.
Viewing now: Anyone can read a public project's paper while it's being edited. Signed-in viewers who aren't project members appear in the “viewing now” count and can't edit.
The shared PaperA structured, section-by-section paper every member co-writes.
Every project has one collaborative paper, organized into standard sections: Abstract, Introduction, Body, Proofs, and Conclusion. Members edit it live, using the same live-math editor (⌘M) throughout.
Section-by-section editing: The paper is edited section by section, which keeps large collaborations from stepping on each other.
Code & images: The </> toolbar button inserts a syntax-highlighted code block, and the image button embeds a figure next to your prose and math.
Download as PDF: Members can export the paper with ⤓ Download PDF. You get the full paper, math and all, as a PDF.
Structured proofs & the Result MapWrap results in proof blocks, cite dependencies, and get an automatic dependency graph.
Put any result (a theorem, lemma, or definition) in a collapsible block.
Illustrated example. The names and activity are made up.
Results in a paper often depend on one another. Proof blocks and references make those dependencies explicit, and the Result Map draws them. Both are inserted from buttons on the paper editor’s toolbar.
Proof blocks (∎): The ∎ toolbar button wraps a result in a collapsible, titled container for a theorem, lemma, or definition, with the statement in real notation. Skim the claims, expand the ones you want.
References (↪): The ↪ button cites one result from another, anywhere in the paper, through a cross-section picker.
Result Map: Every citation becomes an edge in a live dependency graph at /projects/…/map. Click any result to trace everything that rests on it. If a lemma changes, you can see what it affects.
The Research LogA running feed of updates and experiments. Anything worth keeping can go straight into the paper.
Tried the trace formula. Side ratios converge
2h ago
The Research Log is a running log where collaborators post updates, ideas, dead ends, and experiments, with live math and images.
Add to paper: A log entry that turns out to matter can be added straight to a paper section (appended or prepended). That way good scratch work ends up in the paper.
On the cards: The two latest log entries preview on the project’s directory card.
Project tabs & version historyResearch Log, Paper, Result Map, History, and Documents.
Research Log: The project’s home: the running log, members, who’s here, and settings.
Paper: The shared paper, with each section’s version history.
Result Map: The dependency graph of the paper’s results.
History: Milestones and progress summaries the team posts along the way.
Documents: Files and papers attached to the project.
Roles & membershipLead Figure, Member, and Contributor, plus invites, join requests, and handing off the lead.
Lead Figure: Starts the project, sets direction, manages members, and controls settings.
Member: Co-edits the Paper live and takes part in everything.
Contributor: Joins the Research Log and discussion.
Invites: Leads can invite by shareable link or by email straight from the project.
Request to join: On recruiting projects, anyone can request to join. The lead approves and assigns a role.
Promote / demote / transfer: Leads can change a member’s role, and even transfer the Lead Figure title to someone else.
Following & finishing a projectWatch a project, recruit, and mark it complete to enter the Archive.
Watch: Follow a project you’re not in to get notified about updates.
Seeking contributors: A toggle that lists the project under “Open to join” and shows the recruiting badge.
Mark complete: When the work reaches its conclusion, the lead marks it complete and it can enter The Archive, the record of finished mathematical work. Open it from the sidebar, or from the menu on a phone.
Open Problems
Open Problems is a board of well-known unsolved problems. You can submit work on any of them.
A submission records an attempt, not a claimed solution. Each one asks what you tried and where it broke down, so partial progress is useful to others.
The boardProblems grouped by field, with difficulty, prize, age, and a live submission count.
Number Theory
The Riemann Hypothesis
7
submissions
By category: Problems are organized by field: number theory, geometry, and more.
Background: The badge describes how much background you need to understand the question. All these problems remain unsolved.
Prize: Millennium and other prize problems are flagged.
Since: How long the problem has stood open.
Submission count: How many community attempts each problem has drawn.
How submitting worksExplain your approach and be honest about its weaknesses.
Your attempt
Your approach, how far it got, and where it’s weak.
Argument / proof (optional)
The full argument or a partial proof, in live math.
Open a problem to read other people’s attempts and add your own.
Your attempt: Your approach, written in live math. Partial progress is welcome. Be honest about its weak points: the case that resists, the step you couldn’t close. That is what lets someone else pick up the thread.
Argument / proof: Optional. Your full argument, notes, or a partial proof. You can also upload a document.
Search
Search covers the whole platform: Figures, projects, sketches, and topics. Results appear as you type, grouped by type.
Two ways to searchSearch in the sidebar, or the full search page.
Sidebar search: Search in the sidebar (or Ctrl K) opens a quick search from anywhere. Press Enter to go to the full results page.
Search page: /search is the full experience, with live results and topic follow controls. It needs at least two characters to run.
Grouped resultsTopics, Figures, projects, and sketches. You can follow a topic right from the results.
Topics
Projects
Topics: Matching tags with a count. Follow one right from the results.
Figures: People whose handle, name, or bio matches.
Projects: Public projects, each tagged with its status.
Submissions: Sketches matching by title or content, with their topic tags.
Follow inline: Any tag in the results can be followed on the spot, feeding your Feed.
Notifications
Notifications tell you when someone engages with your work: your sketches, projects, or requests. When you’re signed in, open Notifications in the sidebar. On a phone, open the menu first.
The bell & unread badgeA quiet amber dot appears the moment something needs your attention.
Unread dot: An amber dot on the bell next to Notifications means you have unread notifications.
Always present: Notifications is in the sidebar on every page once you’re signed in.
The notifications panelOpen it to read, jump straight to the source, and clear unread.
Riya responded to your request
“A tiling identity for Collatz orbits”
Maya requested to join
Collatz Triangles
Clicking Notifications opens a panel of recent notifications, newest first. Unread items are tinted. The ones you see there are marked read; Show older loads earlier ones. The dot stays while anything is unread.
Deep links: Most notifications link straight to the thing they’re about: the sketch, the request, or the project.
What triggers them: New comments on your work, new followers, messages on your profile board, requests to ask the Network about your work, join requests and approvals, invites, and new work on projects you watch.
The Dashboard
The Dashboard is your account home. It collects your sketches, comments, projects, and following, plus the settings for your public profile and account.
At a glanceStat cards for sketches, comments, and projects, plus your recent activity.
14
Sketches
39
Comments
3
Projects
New sketch: A tiling identity…
Stat cards: Totals for your sketches, comments, and projects, with a shortcut to your public profile.
Your projects: The projects you’re in, each tagged with your role and its status.
Recent activity: A timeline of your latest sketches and comments, newest first.
Your public profileEverything above rolls up into the page other figures see.
Maya Okonkwo
Number theory & dynamical systems.
Your dashboard settings control your public profile: the page linked from your sketches, comments, and projects. It shows your work, your collaboration board, and whether you’re open to new projects.
Who is this for?
The absolute beginner
You've never written a proof, but you noticed something interesting. That is enough to start here.
The graduate student
You have ideas you're not ready to show your advisor yet. You can post them here while they're still rough.
The formal mathematician
You can formalize things quickly. The Network is where people ask for rigorous help. That's what you're good at.
The curious mind
You're not a mathematician by training, but you think mathematically. That's enough to start here.
Start with a thought.
No theorem or proof needed. One idea you're willing to share is enough.