Arquimedes: Math Problem Database

A structured, deduplicated database of competition and benchmark mathematics: 1,038,963 problems across 9 datasets, each with a normalized LaTeX statement, calibrated Mohs difficulty (1.0 to 10.0), answer metadata, and solutions in a uniform JSON schema (v2).

• 1,038,963 problems with full statements and 99.98% domain categorization
• 797,671 written solutions: proof-sketch (797,631), strategy (22), answer-only (18)
• 277,002 model-reasoning traces (deepmath dataset, JSONL shards)
• 1,219 diagram images (SVG and JPG), content-addressed by hash
• Unified Mohs difficulty (1.0–10.0) populated across all 1,038,963 records
• Fast CLI & MCP Server: installable via uv (arquimedes CLI and arquimedes-mcp server)
• Decontaminated Train/Eval Splits: one-command export (972,458 decontaminated train / 10,533 canonical eval)
• Interactive Web Explorer: minimalistic browser catalog in site/ ready for GitHub Pages

Datasets

Category Distribution

Per-dataset category breakdowns and field notes: docs/datasets.md.

Competition Coverage

The source.collection field labels records that come from a named competition or benchmark:

• AMC program (core): AHSME 1,810 · AMC 8 1,025 · AMC 10A 625 · AMC 10B 625 · AMC 10 50 · AMC 12A 625 · AMC 12B 625 · AMC 12 50 · AIME I 405 · AIME II 405 · AIME 255 · USAMO 153 · USA TST 45 · USA TSTST 48
• IMO (core): 156
• HMMT (core): February 2,606 · November 1,072 · Invitational 65
• CEMC (cemc): Gauss (Grade 7) 174 · Gauss (Grade 8) 166 · Pascal (Grade 9) 134 · Cayley (Grade 10) 150 · Fermat (Grade 11) 168
• AoPS (aops): IMO Shortlist 102 · USAJMO 91 · Canadian MO 83 · APMO 28 · Putnam 7
• OlympiadBench (olympiadbench): 1,389
• MATH (math): 12,401

Records in omnimath, deepmath, numina, and bigmath carry origin and domain labels in source.tags.

CLI & MCP Server (uv)

arquimedes ships a zero-dependency Python package with both a fast CLI (arquimedes) and a Model Context Protocol server (arquimedes-mcp) backed by SQLite + FTS5 (with automatic JSONL shard fallback when SQLite is absent).

Install from PyPI

The package name is arquimedes-mcp. It does not contain the problems. Download them once from the Hugging Face dataset (about 1.3 GB of shards, then a lean index of about 0.8 GB):

uvx arquimedes-mcp fetch

That copy lives in the user data directory (~/Library/Application Support/arquimedes on macOS), so the next uvx run finds it.

{
  "mcpServers": {
    "arquimedes": {
      "command": "uvx",
      "args": ["arquimedes-mcp"]
    }
  }
}

uvx --from arquimedes-mcp arquimedes stats
uvx --from arquimedes-mcp arquimedes search "Cauchy-Schwarz" --min-mohs 7.0 -n 5

From a checkout

# Build the local 1.7 GB SQLite + FTS5 database (~50 seconds)
uv run arquimedes build
# or a 0.8 GB index that reads solutions from the shards
uv run arquimedes build --lean

# Show corpus summary
uv run arquimedes stats

# Sub-20ms full-text search across 1,038,963 problems
uv run arquimedes search "Cauchy-Schwarz" --min-mohs 7.0 -n 5

# Sample calibrated problems by competition, category, or Mohs difficulty
uv run arquimedes sample --competition IMO --category geometry -n 3

# Inspect a full problem record with choices, answer, hints, and proof
uv run arquimedes show prob.ahsme-1950-p10

MCP server from a checkout

Add to your mcp.json or claude_desktop_config.json when the shards are already in a checkout:

{
  "mcpServers": {
    "arquimedes": {
      "command": "uv",
      "args": ["--directory", "/path/to/arquimedes", "run", "arquimedes-mcp"]
    }
  }
}

Exposed MCP tools (all read-only; arguments in docs/usage.md):

• arquimedes_get_stats: dataset, category, competition, and solution counts
• arquimedes_search_problems: full-text search with category, dataset, competition, and min_mohs/max_mohs filters
• arquimedes_sample_problems: uniform random draw among problems matching the filters, repeatable with a seed
• arquimedes_get_problem: full LaTeX statement, choices, answer, hints, solutions, and optional deepmath reasoning traces by id

Stability (1.x)

From 1.0.0 on, these interfaces only change in backward-compatible ways until a 2.0.0 release:

• the v2 problem record schema in docs/schema.md: fields are not removed or renamed, and their types do not change
• the MCP tool names, their arguments, and the shape of their results
• the arquimedes CLI commands and flags, and their --json output
• the SQLite tables and columns built by arquimedes build
• the ArquimedesEngine methods get_stats, search, sample, and get_problem

New fields, tools, flags, and data fixes can arrive in minor and patch releases. Corrections to individual records (a wrong answer, a mislabeled category) are data fixes, not breaking changes. Counts and difficulty.mohs values can change as records are corrected; mohs is a calibration, not a measured difficulty. Changes are listed in CHANGELOG.md.

Decontaminated Train / Eval Splits

For LLM post-training and RLVR (Reinforcement Learning with Verifiable Rewards), tools/export_splits.py (or uv run arquimedes splits) produces a decontaminated training set and a canonical evaluation benchmark:

uv run arquimedes splits --out-dir splits/

• Evaluation split (splits/eval.jsonl.gz — 10,533 problems): math test split (4,974), omnimath (2,640), olympiadbench (1,389), core 2023+ contests (931), aops (311), and cemc 2023+ contests (288).
• Decontaminated training split (splits/train.jsonl.gz — 972,458 problems): filters out 46,057 unverifiable records and strips 9,915 near-duplicate benchmark leaks detected via 5-gram token shingle overlap across numina, bigmath, core, math, deepmath, and cemc.

Quickstart (Python & SQLite)

Read a problem directly from a shard with the Python standard library:

import gzip, json

with gzip.open("problems/core/shard-00000.jsonl.gz", "rt", encoding="utf-8") as fh:
    prob = json.loads(fh.readline())

print(prob["title"], "Mohs:", prob["difficulty"]["mohs"])
print(prob["statement"])               # raw LaTeX with \( \) delimiters
print(prob["answer"])                  # {'letter': 'd', 'value': '3+\\sqrt6'}
print(prob["solutions"][0]["text"][:200])

Query SQLite + FTS5 directly:

SELECT p.id, p.title, p.difficulty_mohs, p.answer_value
FROM problems_fts f
JOIN problems p ON p.rowid = f.rowid
WHERE problems_fts MATCH '"pigeonhole"'
  AND p.difficulty_mohs BETWEEN 5.0 AND 8.5
LIMIT 10;

Layout

problems/<dataset>/shard-*.jsonl.gz   gzipped JSON Lines, one v2 problem record per line
images/<hash>.svg, images/<hash>.jpg  1,219 content-addressed diagram files
data/index.json                       summary index (counts by dataset, category, competition)
data/problems.sqlite                  queryable SQLite + FTS5 database (build locally)
arquimedes/                           uv-installable CLI and MCP server package
site/                                 minimalistic interactive web explorer (GitHub Pages)
tools/                                converters, shard normalizer, split exporter, DB builder
docs/                                 schema, usage, and dataset documentation

Documentation

• docs/schema.md: full v2 record reference, shard format, SQLite + FTS5 schema, LaTeX convention, image store
• docs/usage.md: CLI, MCP server, SQL & FTS5 queries, reasoning traces, decontaminated splits
• docs/datasets.md: per-dataset contents, field notes, category distributions, deduplication rules, and upstream licenses

License

Code in arquimedes/, tools/, and site/ is MIT. The Mohs calibration, the category labels assigned by this project, and data/index.json are CC BY 4.0. Problem statements, solutions, answers, and diagrams are not relicensed; the upstream terms are in docs/datasets.md. A Hugging Face copy keeps every record and stamps the holder's notice on it: richard01172000/arquimedes. See LICENSE.