README.md

---
language:
- en
license: mit
multilinguality:
- monolingual
pretty_name: AIME++ Sample
size_categories:
- n<1K
source_datasets:
- original
task_categories:
- question-answering
- text-generation
tags:
- mathematics
- mathematical-reasoning
- reasoning
- benchmark
- evaluation
- rlvr
- exact-match
- latex
- text
configs:
- config_name: all
  default: true
  data_files:
  - split: test
    path:
    - data/aime.jsonl
    - data/aime-hard.jsonl
    - data/aime-graduate.jsonl
    - data/aime-researcher.jsonl
- config_name: aime
  data_files:
  - split: test
    path: data/aime.jsonl
- config_name: aime-hard
  data_files:
  - split: test
    path: data/aime-hard.jsonl
- config_name: aime-graduate
  data_files:
  - split: test
    path: data/aime-graduate.jsonl
- config_name: aime-researcher
  data_files:
  - split: test
    path: data/aime-researcher.jsonl
---

# AIME++ Sample

**AIME++** is Ulam AI's exact-answer mathematical reasoning environment. It keeps one of the most useful properties of AIME-style evaluation—a compact, deterministic answer in the integer range `0–999`—and extends it across four levels of mathematical depth, from competition-style problems to research-level challenges.

This repository contains a **157-problem, MIT-licensed sample** of Ulam AI's much larger problem catalog. Every problem has a canonical integer answer and a zero-padded three-digit representation, making evaluation inexpensive, reproducible, and free of judge-model variance.

Ulam AI's broader database contains **100,000+ problems**. The commercially available AIME++ collections include **24,700+ AIME-family problems** spanning AIME and AIME Hard, **1,000+ AIME-Graduate problems**, and **100+ AIME-Researcher problems**. This repository is designed to let teams inspect the format and difficulty range before licensing a production-scale collection.

> **Name clarification:** In this dataset, AIME means **AI Mathematical Environment**. “AIME-style” describes the `0–999` answer format. This project is not affiliated with or endorsed by the Mathematical Association of America or its competitions, and the sample does not claim to contain official competition problems.

## Why AIME++

- **Verifier-friendly:** exact-match rewards are deterministic and require no subjective rubric or model judge.
- **One interface, four depths:** the answer contract stays fixed while the mathematical demands increase.
- **Evaluation-ready:** stable IDs, explicit tiers, a versioned JSON Schema, and a reference scorer are included.
- **Useful for capability profiling:** results can be compared overall and per tier without conflating output-format changes with problem difficulty.
- **Frictionless sample:** the MIT license allows teams to test the data in their own training and evaluation stacks before discussing a larger license.

The dataset is intentionally **answer-only**: each record contains a problem and its authoritative golden answer in `0–999`, not a worked derivation or chain-of-thought trace. For the AIME++ task, that final answer is the golden solution. A different normalized integer is incorrect.

## Difficulty tiers

| Config | Tier | Description | Records |
|---|---|---|---:|
| `aime` | **AIME** | Standard AIME-style mathematical problems | 34 |
| `aime-hard` | **AIME Hard** | Harder AIME-style mathematical problems | 98 |
| `aime-graduate` | **AIME-Graduate** | Graduate-level problems with AIME-style answers | 20 |
| `aime-researcher` | **AIME-Researcher** | Research-level problems with AIME-style answers | 5 |
| `all` | All four tiers | Default combined evaluation config | **157** |

All configurations expose a single `test` split. This is an evaluation sample, not a train/test partition.

## From sample to full catalog

| Collection | This sample | Larger Ulam collection | Scope |
|---|---:|---:|---|
| AIME family | 132 | 24,700+ | Standard and harder AIME-style problems |
| AIME-Graduate | 20 | 1,000+ | Graduate-level mathematics with AIME-style answers |
| AIME-Researcher | 5 | 100+ | Research-level mathematics with AIME-style answers |
| Broader Ulam problem database | — | 100,000+ | Mathematical reasoning problems across Ulam collections |

The sample exposes only a small fraction of the commercial inventory while providing enough material to test parsing, training, RLVR rewards, evaluation code, and tier-level behavior.

## Quick start

When the repository is published on Hugging Face, load the complete sample with:

```python
from datasets import load_dataset

dataset = load_dataset("ulamai/AIME-Plus-Plus", "all", split="test")
print(dataset[0])
```

Load a single tier by replacing `all` with `aime`, `aime-hard`, `aime-graduate`, or `aime-researcher`.

The release files can also be loaded before publication:

```python
from datasets import load_dataset

dataset = load_dataset(
    "json",
    data_files={"test": "data/*.jsonl"},
    split="test",
)
```

## Data schema

Each JSONL row has five fields:

| Field | Type | Description |
|---|---|---|
| `id` | string | Stable identifier, such as `aimepp-aime-0001` |
| `problem` | string | English problem statement with LaTeX markup |
| `answer` | integer | Canonical answer in `0–999` |
| `answer_str` | string | The same answer zero-padded to exactly three digits |
| `tier` | string | One of the four human-readable difficulty tiers |

Example:

```json
{
  "id": "aimepp-aime-0001",
  "problem": "Let $X,Y,Z>1$ and $W>1$ satisfy $\\log_X W=54$, $\\log_Y W=24$, and $\\log_{X^{3}Y^{2}Z^{2}}W=6$. Determine $\\log_Z W$.",
  "answer": 72,
  "answer_str": "072",
  "tier": "AIME"
}
```

The normative record definition is [schema/dataset.schema.json](schema/dataset.schema.json).

## Evaluation

Create a JSONL file with one prediction per problem:

```json
{"id":"aimepp-aime-0001","prediction":"072"}
{"id":"aimepp-aime-0002","prediction":314}
```

Then run:

```bash
python3 scripts/score.py predictions.jsonl
```

Use `--config aime-hard` (or another config name) to score only one tier. The default protocol accepts an integer or a string containing only a one-to-three-digit integer. `72` and `"072"` are equivalent. Missing, malformed, or out-of-range predictions are incorrect. The scorer reports overall and per-tier accuracy, always using the full selected gold set as the denominator.

For systems that emit worked reasoning, `--allow-boxed` also accepts the last `\boxed{N}` in a string. Report which parsing mode was used whenever publishing results.

## Intended uses

- Exact-answer evaluation of mathematical reasoning systems
- Reinforcement learning with deterministic verifiable rewards
- Test-time-compute and inference-strategy comparisons
- Per-tier capability profiling and regression testing
- Technical inspection by prospective data or evaluation partners

## Out-of-scope uses

- Treating this public-answer sample as a hidden or contamination-resistant benchmark
- Claiming broad mathematical, scientific, or safety capability from this sample alone
- Comparing scores produced with different prompts, tool policies, budgets, or answer parsers as if they were directly equivalent

## Creation and rights

All problems in this sample were created internally by Ulam AI, and Ulam AI holds the rights to the dataset. The records are original Ulam AI material rather than official competition questions. The dataset does not contain personal data or user-contributed content.

Worked derivations and reasoning traces are not part of this dataset's product format. The final integer supplied with each problem is its golden solution and the normative target used by the scorer.

## Quality and validation

The packaged files pass deterministic checks for schema conformance, stable and unique IDs, non-empty problems, answer range, answer-string consistency, duplicate problems, control characters, and balanced dollar-sign LaTeX delimiters.

Run the checks locally with no third-party dependencies:

```bash
make validate
```

See [QUALITY_REPORT.md](QUALITY_REPORT.md) for measured results. The supplied answers are the authoritative ground truth for AIME++ exact-match evaluation.

## Reproducible reporting

Every reported result should include:

- dataset version or immutable commit hash;
- config and record count;
- system and model version;
- prompt template;
- tool-access policy;
- sampling parameters and number of attempts;
- token or compute budget;
- strict or boxed answer parsing mode; and
- overall plus per-tier accuracy.

Once answers are distributed, those records should be treated as inspection, development, or training data rather than a private holdout. Ulam AI can create separately governed evaluation material for commercial partners.

## License and commercial access

The sample is distributed under the permissive [MIT License](LICENSE), allowing teams to inspect, evaluate, train on, modify, and redistribute the sample subject to the license terms.

The larger 24,700+ AIME-family, 1,000+ AIME-Graduate, and 100+ AIME-Researcher collections are available separately, as are custom difficulty mixes and private evaluation services. See [docs/COMMERCIAL_ACCESS.md](docs/COMMERCIAL_ACCESS.md) or visit [ulam.ai](https://ulam.ai/).

## Citation

Citation metadata is provided in [CITATION.cff](CITATION.cff). Until a paper or technical report is published, cite the dataset by organization, title, version, and repository URL.

## Version

This package is version `0.1.0`. See [CHANGELOG.md](CHANGELOG.md) for release notes.

Copyright © 2026 Ulam AI.