Mathlas

mathlas

Available on mcp.so · Glama · listed in awesome-mcp-servers and best-of-lean4.

**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).

Every verdict from the real Lean 4.31.0 kernel / PSLQ + an independent re-eval — no LLM inside. Real in-process tool outputs, captured by assets/gen/capture_outputs.py .

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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.

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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 docs/methods.md for the one-line setup of each.

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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", " ")

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

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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 table above, at a glance — 0 false positives across every tier (0/8 structureless inputs produced a false hit), 100% recovery on knowns. Numbers: RESULTS.md §1–2b.

Agent-in-the-loop, honestly reported (2026-06-10, Claude Fable 5): the same headless agent given 18 math tasks WITH the live mathlas MCP server as its only tool vs WITHOUT any tools scores 18/18 vs 15/18. The original 10-task set is saturated (10/10 both ways: a frontier model passes it from parametric knowledge alone, and we say so plainly), so an 8-task hard set was added where verification, not recall, is the bottleneck: that set goes 8/8 WITH vs 5/8 WITHOUT. The bare model times out on 50-digit integer-relation detection (PSLQ) and cannot name obscure OEIS sequences that shadow Catalan/Fibonacci prefixes and only diverge at depth. The bare passes it does earn are remarkable and we report them: it evaluated a 6-term constant relation to 45 digits by hand (residual 1.475e-27, correct), simulated IEEE-754 rounding bit-for-bit in its head (with one wrong exponent in prose), and proved a Machin-like formula exactly via Gaussian integers, all in-context at 3-9x the latency of a tool call. Every ground truth is a deterministic computation recorded in the bench; full table and provenance: RESULTS.md §2c. Run: benchmarks/agent_bench.py.

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.)

Open corpus on Hugging Face. The text + metadata side of that index is published at kattri15/mathlas-corpus: 3,683,428 theorem-level documents plus the small findings config, split into theoremsearch, dolma, and findings configs. It includes slogans, LaTeX statements, source URLs, titles, labels, categories, citation counts where known, and provenance keys. It does not include the 30 GB embedding matrices or local benchmark slices. Licenses are per config: TheoremSearch subset CC BY-SA 4.0, Dolma statements ODC-BY 1.0 with our slogans CC BY 4.0, and findings CC BY 4.0. Full audit: docs/HF_DATASET_LICENSING.md.

from datasets import load_dataset

ts = load_dataset("kattri15/mathlas-corpus", "theoremsearch", split="train") dolma = load_dataset("kattri15/mathlas-corpus", "dolma", split="train")

Quantized laptop tier (opt-in). The fp16 matrix is 30 GB on disk (~60 GB fp32 resident) — fine on the build box, not on a laptop. MATHLAS_QUANTIZED=binary (or quantized="binary" on HybridRetriever.from_index) serves the SAME index from memmapped quantized sidecars instead: sign-bit Hamming over 1.9 GB shortlists 1000 candidates, exact rescore picks the top-k — measured on the full 3.68M index with the same n=3000 protocol as the headline, it is recall-lossless (R@1 0.6143 vs 0.6140 fp16, R@10 equal at 0.8323; int8 mode: R@1 0.6147, 15 GB) at 2.4 s/query on 4 CPU threads. Honest caveat: this shrinks the *document* side only — queries must still be embedded by the same Qwen3-Embedding-8B (a small 0.6B encoder lives in a different vector space). The true end-to-end small-encoder tier is the 0.6B tier below. Numbers, build command, and the caveat in full: docs/QUANTIZED_TIER.md.

0.6B end-to-end laptop tier (opt-in). The SAME 3,683,428-doc corpus re-embedded once with Qwen3-Embedding-0.6B (1024-d, row-aligned with the served meta), so the query encoder itself runs on a laptop CPU: MATHLAS_ENCODER=0.6b (composes with MATHLAS_QUANTIZED=binary). Measured with the identical n=3000 cross-representation protocol, queries re-encoded by the 0.6B model: R@1 0.545 / R@10 0.745 (binary + int8 rescore; the 0.6B fp16 exact scan is 0.544 / 0.745, so quantization is again lossless within the tier). The honest price vs the 8B tier (0.614 / 0.832) is about 7-9pp recall; the dual-channel 8B configuration (0.965 / 0.999) stays the big-box quality ceiling. The laptop headline: end-to-end 0.67 s/query on 4 CPU threads (0.88 s on 2), query encoding included, over all 3.68M documents. Dense-channel footprint: binary sidecar 0.47 GB + 0.6B encoder ~1.2 GB (~1.7 GB; int8 rescore source 3.77 GB recommended; full fp16 sibling index 7.54 GB). On the TheoremSearch-110 corpus-only probe the tier scores Hit@20 8.2% / 10