Think
Choosing an LLM for math and logic
Ranked by human ratings on math problems with definite answers.
- Highest rated
- △Gemini 4 Argon $4
- On a budget
- GLM-5.3 Flash Z.ai Open weights $0.24
- Rating gap 28
- Within the margin of error, so about the same
About the same rating as the cheaper GLM-5.3 Flash ($0.24); the gap is within the margin of error, so GLM-5.3 Flash is enough.
Rating and price
The closer to the top left, the cheaper and better rated the model.
OpenAIGoogleZ.aiXiaomiStepFunAlibabaAnthropicMistralCohereMetaMiniMaxxAIDeepSeekMoonshotNVIDIAMicrosoftOther
Best-rated model at each price
First line: model / Human rating, second line: price estimate
| Model | Developer | Human rating | Price |
|---|---|---|---|
| △Gemini 4 Argon | $4 (in $2, out $10) | ||
| △Gemini 3.8 Flash | $1.5 (in $0.75, out $3.75) | ||
| GLM-5.3 Flash | Z.ai | $0.24 (in $0.15, out $0.5) | |
| MiMo-V2.6 Flash | Xiaomi | $0.18 (in $0.14, out $0.28) | |
| Step 3.5 Flash | StepFun | $0.16 (in $0.1046, out $0.3138) | |
| GPT-5 nano | OpenAI | $0.14 (in $0.05, out $0.4) |
All models (highest human rating first)
Second line: price (input / output) / context / released / supports Tools Image JSON □ Compare
| Pick | Compare | Model | Developer | Human rating | Advanced math (%) | Mock AIME (%) | Proofs (%) | Input $ /1M | Output $ /1M | Context | Supports | Weights | Released | Price and specs |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Gemini 4 Argon | 90.5 | 100.0 | 99.0 | $2 | $10 | 1.05M | $2 / $10 1.05M 2026-09 | |||||||
| Claude Fable 5.1 | Anthropic | 94.9 | 100.0 | 100.0 | $10 | $50 | 1M | $10 / $50 1M 2026-09 | ||||||
| Gemini 3.8 Flash | 72.0 | 98.9 | 48.0 | $0.75 | $3.75 | 1.05M | $0.75 / $3.75 1.05M 2026-09 | |||||||
| Claude Fable 5 | Anthropic | 91.6 | 100.0 | 95.0 | $10 | $50 | 1M | $10 / $50 1M 2026-06 | ||||||
| Claude Opus 5 | Anthropic | 90.1 | 98.9 | 99.0 | $5 | $25 | 1M | $5 / $25 1M 2026-07 | ||||||
| Claude Opus 4.6 | Anthropic | 69.4 | 94.4 | 50.0 | $5 | $25 | 1M | $5 / $25 1M 2026-02 | ||||||
| GPT-6.1 Sol | OpenAI | 98.6 | 100.0 | 99.0 | $2 | $10 | 1.05M | $2 / $10 1.05M 2026-09 | ||||||
| Claude Opus 5.5 | Anthropic | 96.0 | 100.0 | 100.0 | $4 | $20 | 1M | $4 / $20 1M 2026-09 | ||||||
| Muse Spark 1.3 | Meta | 78.3 | 99.2 | 58.0 | $1.25 | $4.25 | 1.05M | $1.25 / $4.25 1.05M 2026-09 | ||||||
| Gemini 3.7 Flash | 75.3 | 97.2 | 58.0 | $0.75 | $3.75 | 1.05M | $0.75 / $3.75 1.05M 2026-08 | |||||||
| Gemini 3.6 Flash | 62.0 | 94.2 | 36.0 | $0.75 | $3.75 | 1.05M | $0.75 / $3.75 1.05M 2026-07 | |||||||
| Claude Opus 4.7 | Anthropic | 73.9 | 97.8 | 54.0 | $5 | $25 | 1M | $5 / $25 1M 2026-04 | ||||||
| GLM-5.3 Flash | Z.ai | 58.7 | 93.9 | 21.0 | $0.15 | $0.5 | 1M | $0.15 / $0.5 1M 2026-08 | ||||||
| Claude Sonnet 5.5 | Anthropic | 93.4 | 100.0 | 100.0 | $2 | $10 | 1M | $2 / $10 1M 2026-09 | ||||||
| GPT-5.5 | OpenAI | 89.8 | 100.0 | 50.0 | $5 | $30 | 1.05M | $5 / $30 1.05M 2026-04 | ||||||
| GLM-5.3 | Z.ai | 72.4 | 91.1 | 49.0 | $1.4 | $4.4 | 1M | $1.4 / $4.4 1M 2026-08 | ||||||
| Kimi K3 | Moonshot | 76.0 | 97.2 | 87.0 | $3 | $15 | 1.05M | $3 / $15 1.05M 2026-07 | ||||||
| Qwen3.8 Max | Alibaba | 78.7 | 99.4 | 58.0 | $2 | $6 | 1M | $2 / $6 1M 2026-08 | ||||||
| Gemini 3.5 Flash | 66.1 | 95.6 | 31.0 | $1.5 | $9 | 1.05M | $1.5 / $9 1.05M 2026-05 | |||||||
| GPT-5.6 Sol | OpenAI | 93.8 | 100.0 | 83.0 | $4 | $20 | 1.05M | $4 / $20 1.05M 2026-07 | ||||||
| Muse Wonder | Meta | 86.4 | 99.4 | 84.0 | $4 | $20 | 1.05M | $4 / $20 1.05M 2026-10 | ||||||
| DeepSeek-V4.1 Flash | DeepSeek | 70.9 | 98.3 | 54.0 | — | — | 1M | 1M 2026-09 | ||||||
| Claude Opus 4.8 | Anthropic | 84.2 | 98.3 | 69.0 | $5 | $25 | 1M | $5 / $25 1M 2026-05 | ||||||
| Muse Spark 1.1 | Meta | — | — | 39.0 | $1.25 | $4.25 | 1M | $1.25 / $4.25 1M 2026-07 | ||||||
| GPT-5.4 | OpenAI | 82.7 | 97.8 | 56.0 | $2.5 | $15 | 1.05M | $2.5 / $15 1.05M 2026-03 | ||||||
| Muse Spark 1.2 | Meta | — | — | 43.0 | $1.25 | $4.25 | 1.05M | $1.25 / $4.25 1.05M 2026-08 | ||||||
| Gemini 3.1 Pro (preview) | 62.8 | 95.6 | 26.0 | $2 | $12 | 1.05M | $2 / $12 1.05M 2026-02 | |||||||
| MiMo-V2.6 Pro | Xiaomi | — | — | 70.0 | $0.435 | $0.87 | 1.05M | $0.435 / $0.87 1.05M 2026-09 | ||||||
| GLM-5.2 | Z.ai | 62.3 | 86.4 | 35.0 | $1.4 | $4.4 | 1M | $1.4 / $4.4 1M 2026-06 | ||||||
| GPT-6 Astra | OpenAI | 98.6 | 100.0 | 99.0 | $10 | $50 | 1.05M | $10 / $50 1.05M 2026-09 | ||||||
| Qwen3.7 Max (preview) | Alibaba | — | — | — | — | — | — | — | ||||||
| Tencent HY3 | Tencent | — | — | — | — | — | 256K | 256K 2026-07 | ||||||
| GPT-5.6 Terra | OpenAI | 90.5 | 99.7 | 74.0 | $2 | $12 | 1.05M | $2 / $12 1.05M 2026-07 | ||||||
| Inkling | Thinking Machines | 35.1 | 88.9 | 0.0 | $1.87 | $4.68 | 262.1K | $1.87 / $4.68 262.1K 2026-07 | ||||||
| MiMo-V2.5 Pro | Xiaomi | — | — | 22.0 | $0.435 | $0.87 | 1.05M | $0.435 / $0.87 1.05M 2026-04 | ||||||
| Kimi K2.6 | Moonshot | 60.2 | 96.1 | 16.0 | $0.95 | $4 | 262.1K | $0.95 / $4 262.1K 2026-04 | ||||||
| GPT-5.6 Luna | OpenAI | 86.4 | 98.3 | 60.0 | $0.2 | $1.2 | 1.05M | $0.2 / $1.2 1.05M 2026-07 | ||||||
| ERNIE 5.1 | Baidu | — | — | — | — | — | 119K | — | 119K | |||||
| Gemini 3 Pro | — | — | — | — | — | 1.05M | 1.05M 2025-11 | |||||||
| GLM-5.1 | Z.ai | 38.8 | 93.3 | 22.2 | $1.4 | $4.4 | 200K | $1.4 / $4.4 200K 2026-04 |
How to read this page
- Also shown (not used for ranking): accuracy on advanced undergraduate to early research math problems, AIME-style math competition problems and math proof problems. 379 models have ratings.
- Bars are drawn from 800 to 1600.
- The human rating comes from people giving two models the same question and picking the better answer. With a gap of 50, the higher-rated model is picked about 57% of the time; 64% at 100 and 76% at 200 (a gap of 0 is even odds). Differences where the ± ranges overlap are within the margin of error, so about the same.
- Only some models have values for Advanced math, Mock AIME, Proofs.
- Only models rated higher than every cheaper model are listed, best first. For about the same rating, pick the cheapest row in this table. The top row without △ within the price you can pay is the pick. A △ row costs more than the row below it without △, yet its rating is about the same (the gap is within the margin of error).
- “On a budget” is the highest-rated model at $2 or less per million tokens (or at your price cap, when that is lower).
- △ marks rows whose rating gap is within the margin of error (about the same). A row without △ is rated higher than the nearest row below it without △, by more than the margin of error.
- Best at each price
- Prices are what developers pay to use a model through its API, separate from app subscriptions. The unit is one million tokens. A token is a small piece of text (about three quarters of an English word); one million tokens is roughly 8 to 10 novels. Reading (input) and writing (output) are priced differently; here they are blended 3 : 1. For example, at $4, one everyday question and answer (about 1,000 tokens) costs about 0.4 cents. Models without a known price are left out.
- In the Supports column the icons are, from left: can use tools / can read images / can answer in a fixed format (JSON); faded means not supported or unknown.
- Open-weights models have their contents (the weights) published, so you can also run them on your own computer or server. Models without the open-weights mark are normally used through the developer's own services (apps or API); for some models the weights status is unknown.
- Names such as ChatGPT next to a model are the consumer services its developer offers. Check on the service itself whether that model is available there.
- Vertical is Human rating, horizontal is price (the horizontal scale gets coarser to the right). Points joined by the step line are the best-rated models at each price. Hover or tap a dot to see the model's name.
Data: Arena, Epoch AI, Swallow LLM team (CC BY 4.0), Models.dev (MIT), updated 2026-10-24, data sources