Reasoning models for competition math, quantitative analysis, and step-by-step problem solving
| Features | |||||
|---|---|---|---|---|---|
| $5.00 | $25.00 | $0.25 | |||
| $12.50 | $62.50 | $0.31 | |||
| $4.40 | $22.00 | $0.44 | |||
| $0.67 | $2.35 | $0.17 | |||
| $11.00 | $55.00 | $1.10 | |||
| $0.39 | $1.57 | $0.08 | |||
| $6.25 | $31.25 | $0.63 | |||
| $1.57 | $3.14 | $0.13 | |||
| $5.50 | $33.00 | $0.55 | |||
| $33.00 | $198.00 | — | |||
| $33.00 | $198.00 | — | |||
| $23.10 | $184.80 | — | |||
| $1.21 | $4.84 | $0.30 |
Math is where reasoning models earn their keep: spending thinking tokens before answering dramatically improves accuracy on competition problems, proofs, and multi-step quantitative work. The strongest options are OpenAI's Pro-tier models, Claude Opus, and Gemini Pro — and, at a much lower price, open-weight reasoners like DeepSeek V4, Qwen's thinking models, and Xiaomi's MiMo.
All of them are available through the same API here, so you can tune thinking budgets, compare answers across models, and route easy problems to cheap models while sending the hard ones to a Pro tier.
GPT-5.5 Pro and GPT-5.4 Pro top most math evaluations, with Claude Opus 4.8 and Gemini 3.1 Pro close behind. DeepSeek V4 Pro and Qwen's 235B thinking model get remarkably close at a fraction of the cost, which makes them the default choice for high-volume math workloads.
For anything beyond arithmetic and simple algebra, yes. Reasoning models work through problems step by step before answering and are far more reliable on competition-style and multi-step problems. Most models here let you cap the thinking budget so you control cost per problem.
Not blindly. Models still make arithmetic slips inside otherwise-correct reasoning, so for production use pair the model with tool calling — let it call a calculator or run code — and use the LLM for setting up and interpreting the math rather than raw number crunching.
Reasoning tokens bill as output tokens, and hard problems can burn thousands of them. That's why per-token price matters double for math: DeepSeek V4 Pro at $0.87 per million output tokens can be orders of magnitude cheaper per problem than a Pro-tier frontier model — compare output prices in the list above.