Mathematical research
Explore conjectures, discover useful lemmas, and develop machine-checked proofs.
Mathematicians & formalizersA Lean-native coding agent for
mathematics and theoretical sciences.
Explore the unknown. Formalize your thinking.
Build on results you can verify.
CORE DOMAINS / WHO IT’S FOR
For researchers, builders, and teams
working at the edge of what we know.
Explore conjectures, discover useful lemmas, and develop machine-checked proofs.
Mathematicians & formalizersConnect mathematical structures, formal reasoning, and computational experiments.
Physicists & research groupsReason about algorithms, formal methods, and the foundations of computation.
Theorists & verification teamsInvestigate learning theory, test hypotheses, and build reproducible research loops.
AI & machine learning researchersDevelop mathematical models and evaluate the assumptions behind quantitative strategies.
Quants & quantitative researchers01 / THE RESEARCH TOOLKIT
An agent that speaks mathematics.
A workflow that checks its work.
Your toolchain is part of the agent. Work with Lean, Lake, and Mathlib, with real compiler feedback at every step.
NATIVE TOOLCHAINTurn informal mathematics into formal statements. Let the agent propose, check, and refine proofs in a Lean-driven loop.
AUTOFORMALIZATION & PROOF LOOPSExplore the literature, connect relevant results, and bring the mathematical context back into your research workflow.
LITERATURE SEARCHBuilt-in Mathlib search engines and Lean language-server integration put existing definitions and useful lemmas within reach.
MATHLIB SEARCH & LSPRun integrated Lean mathematical benchmarks. Compare proof outcomes and research workflows in reproducible environments.
MATHEMATICAL BENCHMARKSFollow long-running work and interact with supported research workflows from your phone through the Telegram connector.
TELEGRAM CONNECTORWork with local models on your own hardware. Keep model inference close to your research and choose the setup that fits your workflow.
LOCAL MODEL SUPPORTNative integration with HPC resources connects your research to SLURM-managed systems and Ray compute clusters. Scale experiments and compute-intensive workflows on your own infrastructure.
HPC & DISTRIBUTED COMPUTESHARED WORKSPACES / THEORIA-IDE
Bring your team into the same research workspace. Connect projects, conversations, and results—with shared context from the first question to the final proof.
02 / FROM INTUITION TO VERIFICATION
You bring the question.
Theoria helps you work through it.
A conjecture, a paper, an informal argument. Give your research a direction.
Search for useful results and turn your mathematical intent into Lean.
Propose a proof. Read Lean’s feedback. Refine until the statement checks.
# Every discovery starts somewhere.
❯ Prove that the sum of two even
natural numbers is even.
Let’s make that precise.
import Mathlib
theorem even_add
(a b : ℕ)
(ha : Even a) (hb : Even b) :
Even (a + b) := by
exact ha.add hbILLUSTRATIVE WORKFLOW / LEAN 4 + MATHLIB
/formalize/prove/benchmark03 / A HOME FOR YOUR RESEARCH
The terminal is just the beginning. Theoria-IDE connects your research in a graphical workspace built for deep, collaborative work.
04 / YOUR NEXT QUESTION STARTS HERE
A familiar terminal.
An entirely new research companion.
The Lean-native research agent, right where you work. Formalize statements, discover lemmas, and iterate on proofs with feedback from Lean.
curl -fsSL https://<your-domain>/install/cli.sh | bashCurrent source requires Node.js 22.19+. Public installer coming soon.
Public downloads will appear here when releases are ready.