Arquimedes

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

dataset	contents	problems	notable fields
numina	NuminaMath problems, the largest dataset	840,924	origin tags per problem, Mohs difficulty 1.0–9.5
deepmath	DeepMath problems with R1 reasoning traces	92,334	three model-reasoning traces per problem, difficulty rating 1–10
bigmath	Big-Math-RL-Verified problems with verified answers	77,527	Llama-8B solve-rate difficulty note, hierarchical domain tags
math	MATH benchmark problems	12,401	difficulty levels 1 to 5, train/test split tags
core	curated competition problems (AMC program, IMO, HMMT, and more)	10,645	concept tags, course/source difficulty ratings, progressive hints, solve time
omnimath	Omni-MATH olympiad problems	2,640	difficulty rating from 1 to 9.5, contest origin tags
olympiadbench	OlympiadBench olympiad problems	1,389	diagram images (JPG), answer-type tags
cemc	CEMC multiple-choice contests (Gauss, Pascal, Cayley, Fermat)	792	five answer choices per problem, reference URLs
aops	competition problems with community-written solutions	311	collection, year, and problem code per record

Category Distribution

category	problems	share
algebra	386,699	37.22%
geometry	243,231	23.41%
arithmetic	183,930	17.70%
number-theory	129,482	12.46%
probability	38,809	3.74%
combinatorics	35,493	3.42%
logic-foundations	19,935	1.92%
problem-solving-techniques	1,225	0.12%
uncategorized	159	0.02%

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.