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Built for collaborative mathematical research and theorem proving

Do serious mathematics.
Prove together, verify fast.

ProofMesh is a collaborative workspace for mathematical proofs: teams explore ideas in shared threads, challenge assumptions in context, and validate results with @Rho. Meanwhile, Idea2Story embeddings keep every suggestion grounded in the right theorem context.

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Collaborative LaTeX, built for proof teams

Write together, review in context, and keep every compiled revision aligned with formal reasoning.

Collaborative LaTeX Workspace

Shared editor + Rho critique + compile rigor

proof.texx
editingUTF-8 · LaTeX · Ln 15, Col 14
1% Infinitude of Primes
2\documentclass[12pt]{article}
3\usepackage{amsthm, amsmath}
4\newtheorem{theorem}{Theorem}
5
6\begin{document}
7
8\begin{theorem}
9 There are infinitely many prime numbers.
10\end{theorem}
11
12\begin{proof}
13 Assume p_1, p_2, ..., p_n are all primes.
14 Let N = p_1 * p_2 * ... * p_n + 1.
15
16\end{proof}
17\end{document}
proof.tex
Tighten the proof with explicit modular argument and rigorous finish.
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On the Infinitude of Prime Numbers

A. Lovelace

Theorem 1. There are infinitely many prime numbers.

Proof.

Assume p_1, ..., p_n are all prime numbers. Define

N = p_1 p_2 ... p_n + 1.

Draft output: the contradiction step is still missing, so this PDF has not yet been refreshed with the final argument.

1
Latexmk 4.86
Rc files read:
Watching for file changes...
Rho chat reasoningIdea2Story embeddings retrievalRigorous PDF previewAuto-recompile checks

Social workflow for mathematical proof teams

Shared feed, threaded critique, and branch history where Rho assistance and Idea2Story embedding retrieval keep exploration and formal rigor connected.

Live activity
Rho Hackathon
ER

Elena opened a rigor review on theorem node

2m ago

Boundary case k = 0 needs an explicit justification.

Rigor
SJ

Sofia merged exploration branch euclid-fix

5m ago

Lean verification passed and discussion resolved.

Merge+Verify
DM

David published a reusable lemma to shared KB

11m ago

Lemma `mod_one_not_divides` is now reusable by the team.

Knowledge
Proof review thread
Elena: Let's make the non-divisibility claim explicit before merging.
You: Added the missing step, linked the Lean check, and updated the branch summary.
Thread resolved after formal verification pass.
Verification snapshot

Active explorations

6

Resolved rigor checks

18

3 collaborators co-authoring this theorem right now

One workflow from conjecture to verified proof

Brainstorm, branch, critique, and verify in one auditable workspace for mathematics.

Real-time Co-Exploration

Collaborate live on the same proof graph, with shared intent and clear ownership of each step.

Exploration Branches

Test bold lines of attack in branches, compare alternatives, and merge only what survives verification.

Contextual Social Review

Debate assumptions directly on nodes and edges, resolve threads in context, and preserve the reasoning trail.

Rho Stack

Meet @Rho, your proof copilot

Ask for critique, formalization, or verification without breaking the flow of mathematical discussion.

@

What is Rho?

Rho is the orchestration layer that keeps mathematical context intact while helping your team think, formalize, and verify in one place.

plays skeptic on demandkeeps theorem context loadedbridges chat to formal checks

Technical routing behind Rho

Rho routes each request through the right model and toolchain, while Idea2Story embeddings supply grounding context from nodes, discussions, and library items before formal checks run.

ρ

How Rho works

Rho selects the right reasoning mode, retrieves relevant context, and balances Gemini 3 Flash and Gemini 3 Pro for speed or depth based on the task.

Mode
Router
Gemini 3 Flash/Pro
Embeddings + Lean

Fast modes (Gemini 3 Flash)

ExplorerCriticComputeSocratic

Deep modes (Gemini 3 Pro)

FormalizeVerifyStrategist
Personalities: You can explore new ideas, challenge your colleagues’ work, and get inspired. Rho assembles these roles dynamically for each step of the proof.
Social Peer Review

"A research conversation, not a file exchange."

We moved from scattered drafts to one shared proof graph. Every assumption, critique, and verification step is visible, discussable, and recoverable by the full team.

ER
Dr. Elena Rostova
Institute of Applied Mathematics
ER
ElenaThe exploration branch misses rigor on node 3. Can we justify the k=0 boundary case?
YouGreat catch. I opened a review branch, added the formal check, and linked the result.
Me

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