Reasoning Models: Why o3, Claude, and Gemini Think Differently

Table of Contents

• What Are AI Reasoning Models?
• How Reasoning Models Work (Chain-of-Thought at Scale)
• The Top 5 Reasoning Models Compared
• Benchmark Breakdown: Math, Code, and Science
• When to Use Reasoning Models (and When Not To)
• Cost and Speed Comparison
• Practical Guide: Getting the Best Results
• Frequently Asked Questions
• Sources and References

What Are AI Reasoning Models?

Reasoning models are AI systems that perform explicit step-by-step thinking before producing an answer. Unlike standard language models that generate responses token-by-token in a single pass, reasoning models first work through a chain of thought — breaking problems into sub-steps, evaluating different approaches, checking their work, and backtracking when they find errors.

The result: dramatically better performance on tasks that require logic, mathematics, and multi-step problem solving. OpenAI's o3 model scored 87.5% on the ARC-AGI benchmark, nearly tripling the score of its predecessor o1. That's the kind of capability gap that matters for real applications.

If you've used chain-of-thought prompting — asking a standard model to "think step by step" — reasoning models do the same thing, but at a much deeper level. The thinking isn't a prompt trick; it's built into the model's architecture. The model allocates more compute to harder problems, spending more time reasoning through complex questions than simple ones.

How Reasoning Models Work (Chain-of-Thought at Scale)

The Standard Model Approach

Standard models (GPT-4o, Claude Sonnet, Gemini Flash) generate each word based on the previous words. They're fast because they commit to each token immediately. This works well for most tasks — writing, summarization, translation, Q&A — because these tasks don't require deep logical reasoning.

The Reasoning Model Approach

Reasoning models add an explicit "thinking" phase before answering. The model generates internal reasoning tokens that you may or may not see, depending on the provider. OpenAI's o3 uses a "private chain of thought" — the model reasons internally but only shows you a summary. Claude's extended thinking and DeepSeek R1 make their reasoning visible, letting you see the full thought process.

This thinking phase costs extra tokens and time. A reasoning model might take 10-30 seconds on a problem that a standard model answers in 2 seconds. But for hard problems — AIME-level math, complex debugging, legal analysis — the extra time produces answers that standard models simply can't match.

When Extra Thinking Helps

Reasoning models allocate compute proportional to problem difficulty. A simple factual question gets minimal thinking. A graduate-level physics problem gets thousands of internal reasoning tokens. This adaptive computation is why reasoning models are worth their cost: they don't waste resources on easy tasks but bring enormous capability to hard ones.

The Top 5 Reasoning Models Compared

1. Gemini 2.5 Pro (Google)

The current leader on math and competitive programming benchmarks. Gemini 2.5 Pro scores 92.0% on AIME and 77.1% on LiveCodeBench. Its 1-million-token context window is unmatched, making it the best choice for tasks that require analyzing very long documents while reasoning about their content.

Best for: Mathematical proofs, long-document analysis, multimodal reasoning (combining text, images, and code), competitive programming.

2. OpenAI o3

OpenAI's flagship reasoning model. o3 achieved the breakthrough 87.5% on ARC-AGI and scores 91.6% on AIME. Its structured reasoning approach excels at technical domains where step-by-step problem decomposition matters most.

Best for: Structured problem solving, technical reasoning, science tasks. The trade-off: private chain-of-thought means you can't see or control the reasoning process as precisely as with DeepSeek R1 or Claude.

3. Claude Opus (Anthropic)

Claude Opus takes a different approach — it excels not on pure math benchmarks but on tasks requiring nuanced understanding, creative analysis, and comprehensive debugging. In legal reasoning tests, Claude Opus demonstrated "deep comprehension of both theoretical foundations and practical applications" that other models missed.

Best for: Legal analysis, creative writing, code debugging, tasks requiring both analytical depth and clear communication. Claude's extended thinking mode lets you see the full reasoning chain. For a broader comparison of Claude's capabilities, see our ChatGPT vs Claude vs Gemini comparison.

4. Grok 3 (xAI)

The surprise leader on AIME math benchmarks at approximately 93%. Grok 3's unique advantage: free access through X (Twitter) integration and real-time information access. For pure math reasoning on a budget, nothing beats it.

Best for: Mathematics, quick reasoning tasks, users who want reasoning capabilities without API costs.

5. DeepSeek R1 (Open Source)

DeepSeek R1 proved that open-source models can match proprietary reasoning quality. It scores 87.5% on AIME (91.4% on the 2024 version) and its reasoning is fully transparent. The biggest advantage: it's 4x cheaper than o3 on both input and output tokens.

Best for: Cost-conscious production workloads, self-hosted deployments with full data privacy, research requiring transparent reasoning chains, and scenarios where you need to inspect and audit the model's thought process.

Benchmark Breakdown: Math, Code, and Science

Mathematics (AIME)

The American Invitational Mathematics Examination (AIME) is a high school math competition used as a standardized AI reasoning benchmark. Two years ago, no AI model could score above 30%. Now the top models hit 90%+. This progress reflects genuine reasoning improvement, not just memorized answers — AIME problems require multi-step creative mathematical thinking.

Competitive Programming (LiveCodeBench)

LiveCodeBench tests models on competitive programming problems that require algorithmic thinking, optimization, and edge case handling. Gemini 2.5 Pro leads at 77.1%, but all major reasoning models significantly outperform standard models on this benchmark. The practical implication: reasoning models produce better algorithm designs and catch more edge cases when coding with AI assistants.

Science (GPQA Diamond)

GPQA Diamond tests graduate-level science questions written by domain experts. o3 scored 87.7% on this benchmark — a level that some researchers consider approaching expert human performance in specific science domains. This benchmark matters for drug discovery, materials science, and engineering applications where AI needs to reason about complex scientific concepts.

When to Use Reasoning Models (and When Not To)

Use Reasoning Models For:

• Complex math and logic problems — where standard models consistently fail
• Multi-step code debugging — tracing through execution paths, identifying race conditions, understanding system interactions
• Legal and regulatory analysis — where nuanced interpretation of complex rules is required
• Scientific reasoning — analyzing experimental results, designing studies, evaluating hypotheses
• Architectural decisions — designing software systems, evaluating trade-offs, planning complex projects

Don't Use Reasoning Models For:

• Simple Q&A — "What's the capital of France?" doesn't need extended thinking
• Summarization — standard models summarize text perfectly well without reasoning overhead
• Translation — no benefit from extended thinking, just extra latency and cost
• Content generation — blog posts, marketing copy, and creative writing rarely improve with reasoning models
• High-volume classification — where speed and cost matter more than deep analysis

The rule of thumb: if a human would solve the problem instantly without writing anything down, use a standard model. If a human would need paper, diagrams, or extended thinking, use a reasoning model.

Cost and Speed Comparison

Reasoning models are significantly slower and more expensive than standard models because they generate internal thinking tokens. A problem that GPT-4o answers in 2 seconds might take o3 15-30 seconds — but o3's answer will be correct where GPT-4o's might not.

The cost differential is substantial. DeepSeek R1 is 4x cheaper than o3 on both input and output tokens with comparable quality on many reasoning tasks. For production workloads processing thousands of queries, this cost difference compounds quickly.

Cost optimization strategy: Use a router that sends simple queries to standard models and complex queries to reasoning models. The classification itself can use a fast, cheap model. This hybrid approach gives you reasoning quality where you need it without paying reasoning prices for every query.

Practical Guide: Getting the Best Results

Let the Model Think

Don't rush reasoning models with short context or demanding formatting constraints. Give them the full problem context and let them work through it. Reasoning models perform worse when you force them into structured output immediately — give them room to think, then extract the structured answer.

Verify with Standard Models

An efficient pattern: use a reasoning model to solve the problem, then use a standard model to verify the answer is coherent and well-formatted. The reasoning model does the heavy lifting; the standard model does quality control at lower cost.

Use Model-Specific Prompting

Each reasoning model responds differently to prompts. Claude's extended thinking works best with XML-structured context. o3 prefers concise problem statements with clear success criteria. DeepSeek R1 performs best when you explicitly ask it to show its reasoning chain. Model-specific prompt engineering matters more for reasoning models than for standard models.

Build for Multi-Agent Reasoning

The most powerful pattern: combine multiple reasoning models in a multi-agent setup. One model generates solutions, another critiques them, and a third synthesizes the best approach. This debate pattern consistently outperforms any single model working alone on complex problems.

The Future of Reasoning Models

Reasoning models are improving faster than standard models. The jump from o1 (2024) to o3 (2025) tripled performance on ARC-AGI in just one year. If this trajectory continues, reasoning models will solve problems in 2027 that are currently considered impossible for AI — complex mathematical conjectures, novel scientific hypotheses, and multi-domain engineering designs.

The practical implication for developers and businesses: build your systems to route between standard and reasoning models today. The routing cost is minimal, and as reasoning models get faster and cheaper, you can gradually shift more workloads to them without redesigning your architecture. Companies that treat reasoning models as a separate, specialized resource — rather than a replacement for standard models — will get the most value from both.

Frequently Asked Questions

Are reasoning models better than regular AI models?

On complex tasks (math, coding, logic, analysis), yes — significantly. On simple tasks (summarization, translation, basic Q&A), no — they're slower and more expensive with no quality improvement. The right approach is using both: reasoning models for hard problems, standard models for everything else.

Which reasoning model should I use?

For math and code: Gemini 2.5 Pro or o3. For legal and creative analysis: Claude Opus. For cost efficiency: DeepSeek R1 (4x cheaper than o3). For free access: Grok 3. For production workloads needing full data privacy: self-hosted DeepSeek R1.

Will reasoning models replace standard models?

No. Reasoning models are 5-15x slower and more expensive. For 80%+ of AI tasks, standard models are better because they're faster and cheaper. Reasoning models serve the 10-20% of tasks where getting the answer right requires genuine multi-step thinking. The industry is moving toward routing architectures that automatically select the right model type for each query.

Can I run reasoning models locally?

DeepSeek R1 is open-source and can be self-hosted. The full model requires significant GPU resources (4x A100 or equivalent), but distilled versions run on consumer hardware. All other top reasoning models (o3, Gemini 2.5 Pro, Claude Opus, Grok 3) are available only through APIs.

How do reasoning models affect AI coding assistants?

Reasoning models produce better code for complex algorithmic problems, catch more edge cases, and provide deeper debugging analysis. Most AI coding assistants now offer reasoning model options (Claude Code uses extended thinking, Cursor integrates o3). For routine coding, standard models remain faster and cheaper.

Sources and References

• Labellerr — 5 Best AI Reasoning Models of 2026: Ranked
• PromptLayer — OpenAI o3 vs DeepSeek R1: Reasoning Model Analysis
• WorkOS — How Well Are Reasoning LLMs Performing?
• Vellum — Claude 3.7 Sonnet vs OpenAI o1 vs DeepSeek R1
• HumAI — DeepSeek R1 vs OpenAI o3 Comparison
• Composio — Claude 3.7 Sonnet Thinking vs DeepSeek R1