mathlas

An airtight-math tool an AI uses — no LLM, no API key, free. Plug it into Claude Code, Cursor, or any MCP client. The AI is the brain; mathlas is the hands — it gives the AI the capabilities it lacks and returns data (candidates, verdicts, checklists, scaffolds) for the AI to reason over. Apache-2.0. The code is free for any use; published corpus/index artifacts carry their own per-source terms (CC-BY/CC0).

Is this for you?

• You use Claude Code / Cursor and want your AI to stop hallucinating math — search_existing_math finds the real theorem from a 3.68M-doc index; verify_numeric and verify_formal check claims with zero hallucination risk.

• You have a numeric constant or integer sequence you can't identify — identify_constant runs PSLQ + closed-form matching (50-digit precision); identify_sequence does an exact OEIS term-match.

• You need the formal (Lean/mathlib) name of a result — search_formal_math proxies the public Loogle + LeanSearch services and returns declaration names + types, provenance-labeled.

• You're building an agent pipeline that needs airtight math in the loop — all 12 tools are pure data-returning MCP tools, no LLM inside, composable with any framework.

Related MCP server: oraclaw-mcp-server

Install & register with Claude Code (no API key)

One line, nothing to install first (needs uv):

claude mcp add mathlas -- uvx mathlas-mcp

uvx mathlas-mcp fetches + runs the server in an isolated env on first use. Prefer pip?

pip install mathlas-mcp              # core: numeric + retrieval + verify + scaffolds
pip install 'mathlas-mcp[mcp]'       # + official MCP SDK
pip install 'mathlas-mcp[retrieve]'  # + pyarrow, to read the real index
pip install 'mathlas-mcp[embed]'     # + sentence-transformers/torch, for the Qwen3 embedder

claude mcp add mathlas -- python -m mathlas.server

mathlas now appears as twelve tools the agent can call. The server prefers the official mcp SDK and falls back to a dependency-free stdio JSON-RPC server if mcp isn't installed — it always runs. (Cursor / any MCP client: point it at the same uvx mathlas-mcp or python -m mathlas.server stdio command.)

Optional local data (degrades honestly): identify_sequence wants a local OEIS copy; verify_formal wants a Lean toolchain. Without them the tools return a clear "data/toolchain not available" — never a fake answer. See RESULTS.md for the one-line setup of each.

A worked example — an AI using the tools

User:  "Does x = cos(x) have a unique solution I can reach by iterating?"

AI →   search_existing_math("contraction mapping unique fixed point complete metric space")
       ← [{name:"Banach Fixed-Point Theorem", statement:"Let (X,d) be a complete metric
            space and T a contraction. Then T has a unique fixed point ...", ...}, ...]
AI →   applicability_checklist(banach.statement)
       ← preconditions: ["(X,d) is a complete metric space", "T: X→X is a contraction"]
          conclusion:    "T has a unique fixed point"
AI  (reasons): [0,1] is complete; cos is a contraction there (|cos'|=|sin|≤sin 1<1).
       Every precondition holds ⇒ Banach applies ⇒ unique fixed point, reachable by iteration.
AI →   verify_numeric("0.7390851332151607", "<the Dottie-number closed form, if claimed>")

mathlas supplied the search, the checklist, and the airtight numeric check. The AI did the judging. No LLM was called inside mathlas.

Results

The discipline is airtight-or-nothing: a result is an independently-checkable fact or an honest "nothing." The false-positive rate is 0 across every tier (full tables + commands in RESULTS.md):

The 3.68M-doc index. search_existing_math is served from a 3,683,428-document dense index (Qwen3-Embedding-8B, 4096-d): the 1.34M permissive CC-BY/CC0 TheoremSearch subset + 2.34M slogan-embedded arXiv-math documents from Dolma, dense + Okapi-BM25 + RRF. Honest headline recall at full 3.68M scale: R@1 0.614 / R@10 0.832 querying by a document's raw body against its slogan-embedded entry — the hard cross-representation self-recall regime. (At the earlier 1.635M build, the easier same-representation slogan→slogan self-recall was R@1 0.977 / R@10 0.998 on its 81,833-doc held-out split.)

The self-augmenting loop — beating TheoremSearch

On TheoremSearch's own 110 human-written queries, baseline mathlas hits a coverage floor — TheoremSearch withheld 85% of their private 9.2M corpus, so 95 target papers are unreachable for any open system. The AI then runs the loop: for each missing theorem it web-finds the real statement, embeds it with the same Qwen3-Embedding-8B, and add_finding(dense_vec=…) fuses it through the dense channel at runtime:

The 10.0% floor exists because TheoremSearch withheld 85% of their corpus — the loop repairs that coverage gap. Reproduce with benchmarks/webaug_110_bench.py.

The 12 tools

search_existing_math ─▶ mapping_scaffold + applicability_checklist ─▶ (AI judges) ─▶ verify_numeric / verify_formal
   (own index)            (needs↔guarantees, no LLM)                                  (airtight)

Core four — what most agents use:

Full toolkit:

All tools return data. No tool calls an LLM. search_formal_math is the one tool that itself makes a web call (to the public Loogle/LeanSearch services); everything else is fully local.

CLI / Python

mathlas 1.6449340668482264364724151666460251892   # -> pi**2/6  [verified 51 digits]
mathlas 1,1,2,3,5,8,13,21                          # -> A000045 Fibonacci  https://oeis.org/A000045
mathlas "a bounded sequence has a convergent subsequence" --k 5   # search + scaffold
mathlas mcp                                                        # run the MCP server

import mpmath
from mathlas import identify, identify_sequence, mapping_scaffold, applicability_checklist
print(identify(mpmath.zeta(2)))            # -> pi**2/6 [verified 51 digits]
print(identify_sequence([1,1,2,3,5,8,13,21]).matches[1].a_number)  # -> 'A000045'

Docs

• RESULTS.md — every tool's validation, reproduced, with commands.

• docs/methods.md — architecture, design decisions, citations.

• docs/05_open_dataset.md — the open dataset & the index.

• docs/02_eval_vs_theoremsearch.md — the retrieval head-to-head.

• docs/REGISTRY_PUBLISH.md — publishing to the official MCP registry.

Positioning — retrieval is table stakes; verification is the moat

Credit where due: the closest system, TheoremSearch (UW Math AI Lab), now ships a production REST API and its own MCP endpoint (api.theoremsearch.com/mcp) over a 9.2M-document corpus — on raw recall over math literature it is the system to beat, and "we're MCP-native, they're a lab tool" is no longer a differentiator. We reuse only their openly-licensed (CC-BY/CC0) dataset subset as raw data for our own index — not their API, MCP, index, or code.

What no competitor has is everything that happens after retrieval:

• Verification tiers — verify_numeric (independent 50-digit re-evaluation) and verify_formal (a real Lean kernel typecheck, or an honest UNDETERMINED). Retrieval hands you a candidate; mathlas can also check the claim.

• applicability_checklist — decomposes a candidate theorem into atomic preconditions the AI verifies one by one, catching misapplications (open vs closed interval, infinite vs finite group). No competitor has one.

• The self-augmenting add_finding loop — the AI web-finds a missing statement, embeds it, and fuses it into the live index at runtime: 59.1% vs TheoremSearch's 45.0% theorem Hit@20 on their own 110-query benchmark (see above).

• Zero-false-positive discipline — every tier returns an independently-checkable fact or an honest "nothing"; measured false-positive rate is 0 across all tiers (RESULTS.md).

• Free, no API key, provenance-labeled — every result carries where it came from (known_constant, conjectured_relation, web_added, external:loogle, …), and the index is built 100% from openly-licensed data.

(sympy-mcp is a fine CAS-manipulation server — its scope barely overlaps: it rewrites expressions you give it; mathlas finds, scopes, and verifies existing math.)

Official MCP registry

mathlas is published as io.github.Archerkattri/mathlas (see docs/REGISTRY_PUBLISH.md and server.json).

mcp-name: io.github.Archerkattri/mathlas