# An AI assistant for mathematics

Work on mathematics with Prismo, an AI assistant that reads your definitions, cites your sources, proposes proof edits and runs Python checks.

## It reads before it answers

The assistant in Manifield is called **Prismo**. It works from your project rather than from memory: it searches your library, reads the items it needs, and cites them by id. When you ask about "the closed graph theorem", it opens your item `thm-closed-graph`, with your definitions and your notation, before it says anything.

It always has your **notation file** and your **research memory** (`memory.md`, the project's notes on goals, what was tried and what failed) in view, and it keeps the memory up to date as you work.

## Every mention is a link

When Prismo mentions an item, the id becomes a link. Click it and the item opens beside the conversation, rendered as in the library, so you can check a statement without losing your place. Items from an attached book or paper are linked the same way, as `source:item-id`.

## You decide what gets written

The composer has four modes:

| Mode | What Prismo may do |
| --- | --- |
| **Ask** | Read and discuss. No changes |
| **Plan** | Draft a research target for [research mode](/research/) |
| **Propose** (the default) | Everything, but every change to the library comes to you as a proposal you accept or reject |
| **Auto** | Write to the library directly. Manifield asks you to confirm before switching it on |

Statuses have a hard limit in every mode: an agent can raise a result as far as **Review found no errors**. *Human approved*, *Cited literature* and *Formally verified* are set only by you.

## It can compute

Ask Prismo to check a conjecture and it writes a Python script, using networkx, sympy or numpy, and runs it in a sandbox on your Mac:

- **No network, confined writes and a hard time limit,** enforced by a macOS sandbox profile.
- **Every run is kept.** A folder under `artifacts/` holds the script, its output, its errors and a record of the run: the evidence behind any "I checked every graph up to seven vertices" claim. The chat's *Artifacts* button opens it.
- **Results attach to items as evidence.** A clean run can move a conjecture to *Tested*; a counterexample sends it back to *Conjecture*. Like every write, this is a proposal by default.

It can also look integer sequences up in the [OEIS](https://oeis.org).

## It can draw

Prismo can render a picture with Python, and keep it: a saved figure becomes an item in your library, with its caption, what it illustrates, and the script that drew it. Agents cannot see images, so a figure's caption is the only description any of them gets. Manifield insists on one.

## It can use your sources

If you have attached books or papers to the project ([sources](/sources/)), Prismo searches them and cites their own statements. It reads a full text only with your permission: it asks in the chat (Allow or Deny), or you switch on standing access in the composer. The same holds for documents kept in the project.

## What it does not do

- **It does not browse the web.** The chat can query the OEIS. Research mode can search arXiv for titles and abstracts while it plans.
- **It does not prove things "correct".** The best outcome of an AI review is *Review found no errors*. Manifield records what evidence exists, never more.
- **It does not run on your Mac.** Models run at the provider you choose; the context sent to them (the items Prismo reads, your notation, your question) goes to that provider.

## Other agents in the app

- **The Organizer** turns an imported `.tex` file or PDF into proposed items.
- **The Explorer** suggests new conjectures and connections from the library and graph toolbars. It is the least tested agent in the app.
- **The Prover and the Reviewer** draft proofs and hunt for flaws in them, inside [research mode](/research/).

Each can run on its own model: **Settings → Roles**.

## Try it on a proof draft

The included Baire notes contain an unfinished step in the closed graph theorem. The [worked example](/baire-example/) follows the definitions, dependencies and norm estimate you can check. For a broader workflow, see [studying advanced mathematics with AI](/studying-mathematics/).