Hit + Post a Sketch on the wall (or the gold CTA anywhere on the site) to open the composer.

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.

Seeking rigorous insight — An optional flag (below) that tells people you want help making the idea rigorous. Leave it off for everything else.

Category & topic tags — Optional labels like Number Theory or #combinatorics. They make your sketch findable and feed the trending-topics and recommendation engines.

Most sketches are early ideas — that’s the whole point, so there’s no need to grade how finished something is. The one flag worth raising is when you’re explicitly asking for help.

Seeking rigorous insight — An explicit call to have your intuition translated into formal mathematics — the doorway to the Exchange. Leave it off for everything else.

The same rich editor powers every place you write on the platform — sketches, comments, bridge requests, and papers — and 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. A formula is a first-class object — click a rendered one and it reopens as LaTeX to edit.

Open any sketch to see the whole picture. Beyond the body, a sketch can carry structured context that makes early ideas legible to collaborators:

Intuition (“feeling”) — The gut sense behind the idea, shown in a distinct dark panel at the bottom of the card.

Analogies — What this reminds you of — the mental image you’re working from.

Self-critique — Where you already suspect it’s weak. Honesty invites better help.

Conditions — The assumptions or special cases under which you think it holds.

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 — The wall pages in as you scroll to the bottom.

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 request a Bridge.

Click ⌬ Open a request at the top of The Network. The description uses the live-math editor, so a request can contain real notation.

Focus area — One line on what kind of help you want — a proof, a translation, a connection.

Category & tags — Route the request to the people who work in that area.

Three ways in — Open a request directly here, or open a specific sketch — or a completed project paper — to the Network.

Open Request — Opened directly — no sketch or paper attached.

Sketch-linked — Tied to a specific sketch on the platform.

Paper-linked — Tied to a Project Lab paper.

A request has just two states:

Awaiting consent — A request on someone else's work, waiting for the author to open it.

Open — Approved and open to the community. From here it grows through responses — there's no “claimed” or “completed” step; a live idea keeps accepting responses.

Open — Hit Open a request and describe the gap. Add category and tags so the right people find it.

Approve — If it's tied to someone else's work, the owner opens it. Your own opens immediately. That approval is a one-time gate — responses after it never need approval.

Respond — Any member posts a response — a written proof, an uploaded document, or a full Project Lab paper. No claiming and no queue: you respond to whatever you want, whenever you want.

Branch — A response can reply to the original request or to another response, so one idea grows into an expanding tree of contributions.

Every response has a title you write. A label is optional — not everything needs one.

Translation — The rough idea rewritten in formal language; the insight stays.

Formal Lemma — A precise statement built from the idea — provable or disprovable.

Literature Pointer — This already exists somewhere; here's where to find it.

Counterexample — The idea is false — and here's why. A gift, not an attack.

Open Question — A question of your own — answerable by any later response.

No label — A response that simply advances the idea, no category needed.

Type pills — Show only open requests, sketch-linked, or paper-linked.

Tag search — Type to narrow to a topic; matching tags appear as clickable chips.

Open to the community — The board lists every idea that's been opened, each with a live count of how many responses it has drawn so far.

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 — The ⌬ Network link on any request card, or the “Go to network” button on a request page.

Nodes — The original request (the root, with a sketch/paper badge), and responses — each showing 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 network? ▸ 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 is the one place AI is used on the platform, in a deliberately narrow role. It is a historian for The Network: it reads a network of requests and responses and explains, in plain language, how the line of inquiry came together. Its narrations are 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 — The History button narrates the whole network's arc, in short segments, and where it currently stands.

Following a connection — Zakhira surfaces connections between responses in a network. Clicking one moves the map to it and draws a dashed arc between the two responses.

Across networks — ✦ Explore connections → Other networks finds related networks; 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 Network page states the norms it runs on: engage with a request to extend or clarify it, not to dismiss it. Once you contribute, your name stays on that idea's record.

A counterexample counts as a contribution, not an attack. Responses that add no mathematical value are removed.

For you — A ranked blend of the whole community — the default, and 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.

The “For you” ranking is transparent — every promoted card tells you 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 — Your follow graph feeds directly into the mix.

The engine also spreads authorship, so a single prolific poster can’t dominate your feed.

Trending in your interests — Hot tags filtered to the subjects you follow.

Trending topics — The tags moving across the whole platform right now.

Trending now — The submissions gathering the most momentum this window.

Open bridge requests — Live from the Exchange, ranked toward your interests.

Active projects — Recently active Project Lab work, with a green “here now” badge when people are editing live.

Discover figures — Suggested people to follow, each with an inline follow button.

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.

When you’re signed in, the top of the page shows a handful of recommended figures chosen from real signals — people whose submissions 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.

Bio & handle — A short description and link straight to the full public profile.

Followers — How many people follow this figure.

Open to collaborate — An amber flag people set on themselves to say they’re looking for projects — a fast way to find willing partners.

Follow — One click follows a figure so their sketches flow into your Following feed.

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 appear as mission-only teasers (“🔒 invite only”) so the work is discoverable even when the interior is gated.

Start a project from the Lab or the gold CTA. You set:

Title & description — What the project is and why it matters.

Goal — A one-line north star, shown on the card and overview.

Tags — Topics that make the project discoverable.

Visibility — Public (default) or private/invite-only.

Seeking contributors & max members — Signal that you’re recruiting, and cap the team size.

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.

Watching — On a public project, anyone can watch the paper being edited. Spectators show as an “N watching” count and can’t edit.

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-aware — 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 — alongside prose and math.

Download as PDF — Members can export the paper with ⤓ Download PDF — the full paper, math and all, saved to a PDF.

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 — so if a lemma improves, you see what it affects.

The Research Log is a running log where collaborators post updates, ideas, dead ends, and experiments, with live math and images.

Promote to paper — A log entry that turns out to matter can be promoted straight into a paper section (appended or prepended) — so good scratch work graduates into the result.

On the cards — The two latest log entries preview on the project’s directory card.

Overview — The paper, members, presence, goals, and project settings.

Research Log — The full running log of updates.

Result Map — The dependency graph of the paper’s results.

History — A version timeline of how the work evolved.

Documents — Files and papers attached to the project.

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.

Watch — Follow a project you’re not in to get notified about updates — presence without joining.

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 — a permanent record of finished community mathematics, reachable from the top nav.

By category — Problems are organized by field — number theory, geometry, and more.

Difficulty — A badge signals how brutal each one is.

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.

Open a problem to read other people’s attempts and add your own.

What you tried — The real approach, written in live math. Partial progress is welcome.

Where it breaks down — The honest failure point — the case that resists, the step you couldn’t close. This is what lets someone else pick up the thread.

Serious engagement only — The board is deliberately not a place for glib “solutions.” Structure and honesty are the standard.

Navbar search — The ⌕ icon in the top bar opens an inline box from anywhere — hit 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.

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.

Unread dot — An amber dot on the bell means you have unread notifications.

Always present — The bell is part of the navbar on every page once you’re signed in.

Clicking the bell opens a panel of recent notifications, newest first. Unread items are tinted; opening the panel marks everything read and clears the dot.

Deep links — Most notifications link straight to the thing they’re about — the sketch, the bridge, or the project.

What triggers them — New comments on your work, new followers, bridge activity (approvals and claims), project join requests and approvals, and invites.

Stat cards — Totals for your submissions, 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 submissions and comments, newest first.

My submissions / comments — Full lists of everything you’ve posted, to revisit or manage.

My projects — All your Project Lab memberships in one place.

Following & Followers — Manage your connections — who you follow, and who follows you.

Profile & settings — Edit your public profile (name, bio, avatar, the “open to collaborate” flag), notification preferences, and account/security — including data export and deletion.

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.