Top picks for Math Proofs (2026)
Formal proof construction and verification. Ranked from 405 live models on the OpenRouter catalog, weighted for reasoning quality, context window.
| # | Model | Score | In / 1M | Out / 1M | Context | |
|---|---|---|---|---|---|---|
| 1 | Anthropic: Claude Opus 4.7 (batch)anthropic/claude-opus-4.7:batch | 178 | $2.50 | $12.50 | 1,000,000 | Details → |
| 2 | Anthropic: Claude Sonnet 4.6anthropic/claude-sonnet-4.6 | 173 | $3.00 | $15.00 | 1,000,000 | Details → |
| 3 | Anthropic: Claude Sonnet 4.6 (batch)anthropic/claude-sonnet-4.6:batch | 173 | $1.50 | $7.50 | 1,000,000 | Details → |
| 4 | Anthropic: Claude Opus 4.7anthropic/claude-opus-4.7 | 173 | $5.00 | $25.00 | 1,000,000 | Details → |
| 5 | Anthropic: Claude Opus 4.8 (batch)anthropic/claude-opus-4.8:batch | 169 | $2.50 | $12.50 | 1,000,000 | Details → |
| 6 | OpenAI: GPT-5.5 (batch)openai/gpt-5.5:batch | 168 | $2.50 | $15.00 | 1,050,000 | Details → |
| 7 | OpenAI: GPT-5.4openai/gpt-5.4 | 167 | $2.50 | $15.00 | 1,050,000 | Details → |
| 8 | OpenAI: GPT-5.4 (batch)openai/gpt-5.4:batch | 167 | $1.25 | $7.50 | 1,050,000 | Details → |
| 9 | Anthropic: Claude Fable 5 (batch)anthropic/claude-fable-5:batch | 166 | $5.00 | $25.00 | 1,000,000 | Details → |
| 10 | DeepSeek: DeepSeek V4 Prodeepseek/deepseek-v4-pro | 165 | $1.17 | $2.34 | 1,048,576 | Details → |
| 11 | Z.ai: GLM 5.2 (batch)z-ai/glm-5.2:batch | 165 | $0.70 | $2.20 | 512,000 | Details → |
| 12 | Z.ai: GLM 5.2z-ai/glm-5.2 | 164 | $0.50 | $3.15 | 1,048,576 | Details → |
| 13 | Anthropic: Claude Opus 4.8anthropic/claude-opus-4.8 | 164 | $5.00 | $25.00 | 1,000,000 | Details → |
| 14 | Claude Opus 5 (batch)anthropic/claude-opus-5:batch | 161 | $2.50 | $12.50 | 1,000,000 | Details → |
| 15 | SpaceXAI: Grok 4.6x-ai/grok-4.6 | 161 | $2.00 | $6.00 | 500,000 | Details → |
How we ranked these
For Math Proofs, we weight models on reasoning quality, context window. Scores combine each model's public specs with independent benchmark results (Aider Polyglot coding scores, Artificial Analysis intelligence/coding/agentic indices) and live pricing. See full methodology →
About Math Proofs
Math proof verification is the process of constructing formal logical arguments and checking their validity against axioms and inference rules. You need this when submitting research papers, validating theorem statements, or automating correctness checks in computational mathematics. Good models handle symbolic manipulation, maintain logical consistency across multi-step arguments, and catch subtle gaps in reasoning. Poor performers confuse notation, drop quantifiers, or produce circular logic. The main constraint: proof verification at publication scale requires either human review afterward or integration with automated theorem verifiers like Lean or Coq, which adds latency compared to informal reasoning tasks.
When to use: Use this when you need to check whether a mathematical argument is logically sound, formalize an informal proof sketch, or generate a step-by-step derivation that could survive peer review.
Common questions
What is the difference between a model that "understands" proofs and one that just copies proof patterns?
A true proof-capable model traces dependencies between statements, verifies each step follows from prior ones, and flags unstated assumptions. Pattern-copiers produce syntactically correct-looking proofs that fail under scrutiny. Claude and GPT-4 both handle multi-step proofs, but neither should be trusted without symbolic verification tools.
How much faster is AI proof generation compared to writing proofs by hand?
AI can sketch a proof outline in seconds versus hours of manual work, but formal verification still requires human validation or automated checking. Speed gains are real at the draft stage, but zero at the publication stage if correctness is non-negotiable.