Best AI for Math and Reasoning
Best AI for Math and Reasoning
Math and logical reasoning are where AI models differ the most. Some models solve graduate-level math problems reliably. Others struggle with basic arithmetic. We benchmarked the major models on math and reasoning tasks to find which delivers the most accurate results.
AI model comparisons are based on publicly available benchmarks and editorial testing. Results may vary by use case.
Overall Rankings
| Rank | Model | MATH | GSM8K | GPQA | Logical Reasoning | Cost |
|---|---|---|---|---|---|---|
| 1 | o3 | 88.9% | 97.2% | 73.4% | 9.5/10 | $$$ |
| 2 | Claude Opus 4 | 78.3% | 95.1% | 65.1% | 9.0/10 | $$$ |
| 3 | Gemini Ultra | 76.8% | 94.5% | 64.3% | 8.5/10 | $$ |
| 4 | GPT-4o | 74.6% | 93.8% | 61.8% | 8.0/10 | $$ |
| 5 | Claude Sonnet 4 | 71.2% | 92.4% | 58.5% | 8.0/10 | $ |
| 6 | Llama 3 405B | 68.4% | 91.0% | 55.7% | 7.5/10 | Free* |
| 7 | Mistral Large | 58.1% | 87.2% | 48.9% | 7.0/10 | $ |
What the Benchmarks Mean
MATH: Competition-level math problems covering algebra, geometry, number theory, and calculus. This is a demanding benchmark.
GSM8K: Grade-school math word problems. Tests basic mathematical reasoning. Most modern models score well here.
GPQA: Graduate-level science questions (physics, chemistry, biology). Tests deep subject-matter reasoning.
Logical Reasoning: Our editorial assessment covering syllogisms, puzzles, constraint satisfaction, and multi-step inference.
Why o3 Dominates
OpenAI’s o3 is a reasoning model that generates internal “thinking tokens” before producing an answer. It essentially works through math problems step by step, checking its logic and trying different approaches. This deliberate reasoning approach gives it a massive advantage on problems that require careful, multi-step work.
The tradeoff is speed and cost. o3 is 5-10x slower than standard models and significantly more expensive per query. But when accuracy matters, the premium is worthwhile.
Category Breakdown
Arithmetic and Computation
Winner: o3 (but all models are decent)
For straightforward calculations, most modern models are reliable. Where they diverge is on multi-step calculations, especially with fractions, percentages, and unit conversions. o3 handles these nearly perfectly.
Tip: For pure computation, consider using a model’s code execution capability. Having the AI write and run Python code for calculations eliminates arithmetic errors entirely.
Algebra and Equation Solving
Winner: o3
o3 solves algebraic equations, systems of equations, and polynomial problems with high reliability. Claude Opus 4 is the strongest runner-up, handling most algebra correctly. Standard GPT-4o and Gemini occasionally make sign or factoring errors on complex problems.
Geometry
Winner: o3
Geometry problems that require spatial reasoning and multi-step proofs are where the gap between reasoning and standard models is widest. o3’s step-by-step approach handles geometric proofs and area/volume calculations significantly better than competitors.
Statistics and Probability
Winner: Claude Opus 4 / o3 (tied)
Both handle probability distributions, hypothesis testing, and statistical inference well. Claude’s advantage is in explaining the reasoning clearly, which matters for educational use. o3 is more likely to get the numerical answer correct.
Word Problems and Applied Math
Winner: o3
Multi-step word problems that require translating English into mathematical operations are o3’s strongest domain. The thinking process helps it correctly identify what math to apply and in what order.
Proofs and Formal Mathematics
Winner: o3
Mathematical proofs require maintaining logical coherence across many steps. o3’s reasoning approach handles this better than any other commercially available model.
Practical Tips for Math Tasks
- Always ask for step-by-step work. Adding “show your work step by step” improves accuracy for all models, not just reasoning models.
- Verify critical calculations with code. Ask the model to write and execute Python code for numerical computations.
- Use LaTeX formatting. Asking for LaTeX output helps models organize mathematical expressions correctly.
- Break complex problems into parts. Feed one part at a time and verify each step before proceeding.
- Cross-check with multiple models. For important calculations, run the problem through two models and compare.
Prompt Engineering 101: Get Better Results from Any AI
Cost Comparison for Math Tasks
| Model | Cost per Complex Math Problem | Accuracy | Value Rating |
|---|---|---|---|
| o3 | ~$0.50-2.00 | Highest | Best for critical accuracy |
| Claude Opus 4 | ~$0.10-0.30 | Very High | Best balance |
| GPT-4o | ~$0.02-0.05 | High | Best for routine math |
| Claude Sonnet 4 | ~$0.02-0.05 | High | Great value |
o3’s cost varies widely because thinking token usage depends on problem complexity.
Key Takeaways
- o3 is the clear leader for math and reasoning tasks, with a 10+ percentage point lead on the hardest benchmarks.
- The o3 advantage comes from deliberate step-by-step reasoning, but at the cost of speed and higher prices.
- Claude Opus 4 is the strongest non-reasoning model for math and offers better value for most applications.
- For critical calculations, use code execution (Python) rather than relying on the model’s mental math.
- All models benefit from chain-of-thought prompting: asking for step-by-step work improves accuracy significantly.
Next Steps
- Test math problems across models: AI Model Playground: Side-by-Side Comparison.
- See all benchmark scores: AI Benchmark Leaderboard: MMLU, HumanEval, MATH.
- Learn reasoning prompting techniques: Prompt Engineering 101: Get Better Results from Any AI.
- Compare model costs for your workload: AI Cost Calculator: Estimate Your Monthly API Spend.
This content is for informational purposes only and reflects independently researched comparisons. AI model capabilities change frequently — verify current specs with providers. Not professional advice.