# RiemannBench without tools (RiemannBench (no tools))

> Research-level mathematics problems with unique programmatically verified closed-form answers.

Canonical page: https://benchlm.ai/benchmarks/riemannbench

- Category: [Mathematics](/math)
- Last updated: September 27, 2026

## About RiemannBench (no tools)

- Year: 2026
- Tasks: 25 private research-level mathematics problems
- Format: Accuracy without tools
- Difficulty: Research mathematics
- Paper: [Claude Opus 5 System Card](https://www-cdn.anthropic.com/c5fbac3f0b1280a933ebd26d3cb8bb9f5bdeaf48/Claude%20Opus%205%20System%20Card.pdf)

Section 8.7 reports the mean over four max-effort attempts on a corrected private 25-problem setup without tools.

RiemannBench (no tools) is currently displayed on BenchLM for reference, but it is excluded from the weighted scoring formula.

## Leaderboard (1 models)

| Rank | Model | Creator | Score |
|------|-------|---------|-------|
| 1 | [Claude Opus 5](/models/claude-opus-5) | Anthropic | 60.0% |

## FAQ

### What does RiemannBench (no tools) measure?

Research-level mathematics problems with unique programmatically verified closed-form answers.

### Which model scores highest on RiemannBench (no tools)?

Claude Opus 5 by Anthropic currently leads with a score of 60.0% on RiemannBench (no tools).

### How many models are evaluated on RiemannBench (no tools)?

1 AI models have been evaluated on RiemannBench (no tools) on BenchLM.

### Does RiemannBench (no tools) affect BenchLM's overall score?

Not directly. RiemannBench (no tools) is still displayed on BenchLM for reference, but it is excluded from the weighted scoring formula.