Which LLM for math, reasoning, and complex problem-solving in May 2026?
A practical guide to choosing the best LLM for math and reasoning tasks, with specific model picks at every price point.
FindLLMMay 16, 2026
reasoningmathproblem-solvingmodel-selectionguide
The short answer
For math, reasoning, and complex problem-solving, use GPT-5.5 if accuracy matters more than cost. It leads the quality index at 60.2, a clear gap above every other model. If you need to stay under $2/M tokens, Kimi K2.6 at $1.42/M input tokens delivers 53.9 quality and is open-source, making it the best reasoning model you can actually afford to run at volume.
The middle ground belongs to Gemini 3.1 Pro Preview. At 57.2 quality and $4.50/M tokens, it sits just 3 points below GPT-5.5 while costing 60% less. For reasoning workloads where you're running thousands of inference calls per day, that price gap compounds fast.
Why quality index matters for reasoning
Higher quality scores correlate directly with fewer reasoning failures. In multi-step math problems, a model that scores 60.2 vs. 53.9 doesn't just get "slightly more" answers right. It handles the hard tail better: longer chains of logic, ambiguous problem setups, edge cases in formal proofs. When you're building a pipeline that checks its own work (e.g., generating solutions then verifying them), the stronger model needs fewer retries, which offsets its higher per-token cost.
That said, quality alone doesn't tell you everything. Inference latency and throughput shape how you architect the system around the model.
GPT-5.5 costs 2.5x more than Gemini 3.1 Pro Preview for 5% more quality. Whether that's worth it depends on your error tolerance. If a wrong answer triggers an expensive downstream failure (bad financial calculation, incorrect proof step in a formal verification chain), pay for GPT-5.5. If you can validate outputs cheaply or tolerate occasional retries, Gemini gives you nearly the same reasoning capability at a fraction of the cost.
Gemini's 135 tok/s throughput is the highest in this tier by a wide margin. That's roughly 2x faster than GPT-5.5's 65 tok/s. For interactive reasoning applications where a human waits for output, this difference is the gap between usable and frustrating.
What about the Anthropic models?
Claude Opus 4.7 (Anthropic) scores 57.3 quality at $10.00/M tokens. It's essentially tied with Gemini 3.1 Pro Preview on quality but costs more than double. I can't recommend it for reasoning workloads unless you're already locked into Anthropic's ecosystem. The adaptive reasoning variant of Opus 4.6 drops to 53.0 quality at $10.94/M, which is worse quality than Kimi K2.6 at nearly 8x the price.
When to use Kimi K2.6
Kimi K2.6 is the standout budget pick. At $1.42/M tokens with 53.9 quality, it's the cheapest model above the 53-point threshold. Its 41 tok/s inference speed is the slowest of the top picks, which makes it a poor fit for real-time applications. But for batch reasoning jobs (grading problem sets, generating solution candidates overnight, running chain-of-thought evaluations across large datasets), the low cost per token matters far more than latency.
Being open-source also means you can self-host it, eliminating API dependency for sensitive workloads. No other model in this quality range offers that option with comparable reasoning performance.
My recommendation
Start with Gemini 3.1 Pro Preview for most reasoning workloads. It hits the best balance of quality, speed, and cost. Upgrade to GPT-5.5 only when you've measured that the quality gap actually affects your outcomes. Drop to Kimi K2.6 when budget constraints dominate or you need self-hosting.
Run your own eval on your specific problem distribution before committing. These quality scores are aggregates; your mileage on, say, combinatorics vs. calculus vs. formal logic will vary. Use the LLM Selector to filter by reasoning performance and price, or browse the full rankings on Explore.