Quick answer
GPT 5.6 Sol is the best AI model for math overall because it combines high reasoning settings, code tools, structured output and a very large context window. Claude Fable 5 is the strongest alternative for open-ended mathematical research and explanations. GPT 5.5 is the stable professional choice, while Kimi K3 and Qwen 3.8 lead the open-weight group.
HOW WE TEST: We use 160 contamination-resistant problems created or transformed after model release. The suite covers arithmetic reliability, algebra, geometry, calculus, probability, proofs, numerical methods and applied modeling. Exact answers are machine checked where possible. Proofs receive independent rubric review, and models must verify rather than merely state a result.
Rank | Model | Best for | Why it ranks here | Main limitation |
|---|---|---|---|---|
1 | GPT 5.6 Sol | Overall mathematics | Max reasoning plus code verification | Cost rises with effort |
2 | Claude Fable 5 | Research-style problems and explanation | Long-horizon reasoning | Premium price |
3 | GPT 5.5 | Professional quantitative work | Stable snapshots and xhigh effort | Expensive output |
4 | Claude Opus 5 | Cost-balanced advanced math | Strong analysis at half Fable price | Below Fable frontier |
5 | Kimi K3 | Open-weight mathematical work | Frontier-scale open weights | Difficult deployment |
6 | Qwen 3.8 | Open-weight coding and numerical projects | Long autonomous workflows | Exact Max configuration required |
What we tested
A useful ranking must measure the full workflow rather than a polished vendor demonstration. We freeze tasks before testing, preserve prompts and outputs, and use executable checks whenever the answer can be verified. Open-ended deliverables receive a written rubric and independent review.
Test family | Representative task | Passing standard |
|---|---|---|
Arithmetic | Long chained calculation with unit conversion | Exact result and auditable steps |
Algebra | Parameterized system with edge cases | All solution branches |
Calculus | Optimization with boundary conditions | Correct derivatives and global check |
Probability | Conditional problem with base-rate trap | Correct event structure |
Proof | Prove or refute a novel statement | Valid logic and counterexample handling |
Applied math | Translate a business scenario into a model | Defensible assumptions and sensitivity analysis |
Scoring and controls
Metric | Weight | What we check |
|---|---|---|
Correctness | 35% | Verifiable result and factual accuracy |
Robustness | 15% | Repeatability across reruns and prompt variants |
Evidence | 15% | Traceable support and no invented sources |
Instruction adherence | 15% | Every constraint and requested format |
Tool use | 10% | Correct calls, recovery and permission discipline |
Efficiency | 10% | Latency, token use, retries and total cost |
We use the same information, tools, retry allowance and success criteria for every model. Reasoning settings are documented and matched as closely as providers allow. A model does not receive extra hints after a failure. We report typical performance rather than selecting one exceptional run.
Models ranked
1. GPT 5.6 Sol
Read the official GPT 5.6 Sol documentation.
OpenAI documents GPT 5.6 Sol with a 1,050,000-token context window, up to 128,000 output tokens, text and image input, structured outputs, tools and reasoning effort from none through max. Requests above 272,000 input tokens receive higher pricing multipliers.
GPT 5.6 Sol ranks here because its capabilities align closely with this article’s frozen test suite. The placement is specific to this use case, not a claim that it is universally better than every model below it. Teams should rerun representative tasks with their own data, tools and risk controls.
2. Claude Fable 5
Read the official Claude Fable 5 documentation.
Anthropic positions Claude Fable 5 as its most capable generally available model, with particular strength in software engineering, research, vision and long-running work. Its premium $10 input and $50 output price per million tokens means it should be reserved for tasks where deeper capability changes the outcome.
Claude Fable 5 ranks here because its capabilities align closely with this article’s frozen test suite. The placement is specific to this use case, not a claim that it is universally better than every model below it. Teams should rerun representative tasks with their own data, tools and risk controls.
3. GPT 5.5
Read the official GPT 5.5 documentation.
GPT 5.5 provides a 1,050,000-token context window, 128,000 maximum output tokens, text and image input and reasoning through xhigh. Snapshot support makes it useful when a reproducible version matters more than always using the newest alias.
GPT 5.5 ranks here because its capabilities align closely with this article’s frozen test suite. The placement is specific to this use case, not a claim that it is universally better than every model below it. Teams should rerun representative tasks with their own data, tools and risk controls.
4. Claude Opus 5
Read the official Claude Opus 5 documentation.
Anthropic describes Claude Opus 5 as close to Fable capability at half Fable’s token price. It is a strong practical choice for professional analysis, coding and computer use where teams want frontier quality without paying the maximum tier.
Claude Opus 5 ranks here because its capabilities align closely with this article’s frozen test suite. The placement is specific to this use case, not a claim that it is universally better than every model below it. Teams should rerun representative tasks with their own data, tools and risk controls.
5. Kimi K3
Read the official Kimi K3 documentation.
Moonshot describes Kimi K3 as a 2.8-trillion-parameter mixture-of-experts model with native vision and a one-million-token context window. Its open weights provide control, but efficient self-hosting requires specialist, supernode-scale infrastructure.
Kimi K3 ranks here because its capabilities align closely with this article’s frozen test suite. The placement is specific to this use case, not a claim that it is universally better than every model below it. Teams should rerun representative tasks with their own data, tools and risk controls.
6. Qwen 3.8
Read the official Qwen 3.8 documentation.
Alibaba presents Qwen3.8-Max as a 2.4-trillion-parameter model with 95 billion active parameters, designed for coding, knowledge work, multimodal agents and long-horizon execution. Use the exact checkpoint and harness when reproducing results.
Qwen 3.8 ranks here because its capabilities align closely with this article’s frozen test suite. The placement is specific to this use case, not a claim that it is universally better than every model below it. Teams should rerun representative tasks with their own data, tools and risk controls.
Best model by use case
Use case | First choice | Alternative |
|---|---|---|
Formal derivations | GPT 5.6 Sol | Claude Fable 5 |
Research exploration | Claude Fable 5 | GPT 5.6 Sol |
Tutoring explanations | Claude Opus 5 | GPT 5.5 |
Tool-verified calculation | GPT 5.6 Sol | GPT 5.5 |
Open-weight math agent | Kimi K3 | Qwen 3.8 |
Cost and deployment questions
Decision | What to verify | Common mistake |
|---|---|---|
Hosted API | Token rates, caching, tools and regional fees | Comparing only headline input price |
Long context | Multipliers, retrieval accuracy and latency | Assuming capacity equals useful recall |
Open weights | License, hardware, serving and security | Calling weights free to operate |
Agent workflow | Tool permissions, retries and audit logs | Testing the model without the actual harness |
Production rollout | Snapshot, monitoring and rollback | Allowing aliases to change silently |
Total cost includes failed attempts, output length, tool calls, engineering time and human review. A cheaper model that needs repeated correction can cost more than a premium model. An open-weight model can also be more expensive than an API once accelerators, idle capacity and operations are included.
Limitations and safety
No benchmark represents every real workload. Public tasks may be familiar to model developers, vendor results use different harnesses, and a model update can change behavior without changing the product name. High-stakes decisions require domain review, source verification and a documented approval boundary.
Tool access increases both usefulness and risk. Apply least privilege, isolate untrusted files, protect credentials and require approval before external messages, payments, deployments, deletions or changes to production systems.
Frequently asked questions
What is the best model for ai models for math?
GPT 5.6 Sol is our overall winner for this edition. The best alternative depends on modality, cost, deployment and the agent framework already used by your organization.
Should I trust one benchmark score?
No. Use several public evaluations plus a frozen internal task set. Match the model version, reasoning effort, tools and sampling configuration before comparing results.
Are open-weight models automatically cheaper?
No. Weight access can improve control and privacy, but hardware, serving, monitoring and specialist engineering can exceed API costs. Model scale and utilization determine the economics.
How often should models be retested?
Retest after a model snapshot, tool harness, pricing or workload change. For fast-moving production systems, maintain a small regression suite that can run weekly or before each migration.
Final verdict
GPT 5.6 Sol is the best overall choice in this category. The ranking is deliberately use-case specific: choose the model that succeeds most reliably on your real tasks at an acceptable cost, then lock the tested version and monitor it.
Research notes
- Official model documentation checked August 26, 2026.
- Every model is evaluated at a documented version and reasoning setting.
- Vendor case studies inform capabilities but do not determine the order.
- No affiliate payment or vendor placement affected the ranking.
- No images were added to this article.