Chain Of Thought Mathematical Problem Solving

via “mathematical reasoning and step-by-step problem solving”

DeepSeek's 236B MoE model specialized for code.

Unique: Trained on 6 trillion tokens including mathematical reasoning datasets and code-based solutions, enabling both symbolic reasoning and code generation for mathematical problems in a single model without separate math-specific components

vs others: Provides integrated mathematical reasoning and code generation (unlike Copilot which focuses on code) while maintaining open-source weights and supporting local deployment

via “mathematical problem solving with symbolic reasoning”

Cost-efficient reasoning model with configurable effort levels.

Unique: Implements specialized mathematical reasoning patterns with step-by-step derivation generation, achieving competition-level math performance through domain-specific training rather than general reasoning

vs others: Matches o3 on mathematical benchmarks at lower cost; outperforms standard LLMs (GPT-4, Claude) on competition-level problems due to reasoning-grade capabilities

via “native chain-of-thought reasoning with extended thinking”

Google's most capable model with 1M context and native thinking.

Unique: Native thinking is baked into model architecture rather than achieved through prompt engineering; enables 94.3% accuracy on GPQA Diamond (scientific knowledge) without requiring explicit CoT prompting, and 77.1% on ARC-AGI-2 abstract reasoning puzzles

vs others: Outperforms GPT-4 and Claude 3.5 on reasoning benchmarks (GPQA 94.3% vs Sonnet 89.9%) because thinking is a first-class architectural feature, not a post-hoc prompt technique

via “multi-step mathematical proof generation and verification”

OpenAI's reasoning model with chain-of-thought problem solving.

Unique: Generates multi-step mathematical proofs through extended reasoning that explores proof strategies and backtracks when necessary, rather than pattern-matching to training examples. The reasoning phase is visible in the thinking tokens, enabling transparency into proof construction.

vs others: Outperforms standard LLMs on mathematical proof generation because the extended thinking phase allows exploration of proof strategies and verification of intermediate steps, resulting in more rigorous and correct proofs.

via “mathematical problem solving with step-by-step derivation”

Talk to Claude, an AI assistant from Anthropic.

via “reasoning and step-by-step problem decomposition with chain-of-thought”

ChatGPT by OpenAI is a large language model that interacts in a conversational way.

via “mathematical-problem-solving-with-symbolic-reasoning”

Gemini 2.5 Pro is Google’s state-of-the-art AI model designed for advanced reasoning, coding, mathematics, and scientific tasks. It employs “thinking” capabilities, enabling it to reason through responses with enhanced accuracy...

Unique: Leverages extended internal reasoning to explore multiple mathematical approaches and verify symbolic manipulations before responding, providing higher confidence in mathematical correctness than models without reasoning capabilities.

vs others: Exceeds GPT-4 and Claude on complex mathematics by using internal reasoning to validate symbolic steps, reducing hallucinated solutions and improving explanation quality for educational use cases.

via “mathematical reasoning and symbolic computation”

This is Mistral AI's flagship model, Mistral Large 2 (version mistral-large-2407). It's a proprietary weights-available model and excels at reasoning, code, JSON, chat, and more. Read the launch announcement [here](https://mistral.ai/news/mistral-large-2407/)....

Unique: Trained on mathematical datasets with chain-of-thought reasoning to prioritize step-by-step problem solving, using attention mechanisms that track variable relationships and equation transformations

vs others: Comparable to GPT-4 on mathematical reasoning, while maintaining lower cost; outperforms Llama 2 on complex multi-step problems due to larger parameter count and specialized training

via “chain-of-thought reasoning with explicit step-by-step generation”

Claude Sonnet 4.5 is Anthropic’s most advanced Sonnet model to date, optimized for real-world agents and coding workflows. It delivers state-of-the-art performance on coding benchmarks such as SWE-bench Verified, with...

Unique: Extended thinking mode allows explicit reasoning generation with token-level control, vs alternatives that only support prompt-based chain-of-thought, enabling more reliable and measurable reasoning improvements

vs others: More transparent reasoning than GPT-4 on complex tasks due to explicit thinking token generation, and faster than o1 while maintaining reasonable accuracy on most reasoning tasks

via “reasoning-enhanced-mathematical-and-logical-problem-solving”

Claude 3.7 Sonnet is an advanced large language model with improved reasoning, coding, and problem-solving capabilities. It introduces a hybrid reasoning approach, allowing users to choose between rapid responses and...

Unique: Allocates computational budget to internal reasoning before generating answers, enabling the model to explore solution spaces and verify correctness without exposing intermediate steps. This is more efficient than asking the model to show all work in the response.

vs others: More transparent reasoning than o1 (which doesn't show thinking) but faster than full reasoning models; better suited for educational contexts where understanding the approach matters.

via “reasoning and chain-of-thought decomposition”

Mistral Large 2 2411 is an update of [Mistral Large 2](/mistralai/mistral-large) released together with [Pixtral Large 2411](/mistralai/pixtral-large-2411) It provides a significant upgrade on the previous [Mistral Large 24.07](/mistralai/mistral-large-2407), with notable...

Unique: Mistral Large 2411 implements implicit chain-of-thought through training on reasoning-heavy datasets, enabling natural step-by-step decomposition without explicit prompting while maintaining efficiency through optimized token generation

vs others: Provides reasoning quality comparable to GPT-4 while maintaining lower latency and cost through more efficient token usage

via “mathematical-problem-solving-with-step-by-step-reasoning”

DeepSeek-V3.1 is a large hybrid reasoning model (671B parameters, 37B active) that supports both thinking and non-thinking modes via prompt templates. It extends the DeepSeek-V3 base with a two-phase long-context...

Unique: Implements explicit reasoning phase specifically optimized for mathematical decomposition, allowing the model to verify intermediate steps before producing final answers, rather than generating answers directly.

vs others: More reliable for complex math than GPT-4 due to explicit verification phase, and more transparent than o1 (which hides reasoning) by allowing users to request step-by-step explanations.

via “mathematical problem-solving with step-by-step validation”

Olmo 3 32B Think is a large-scale, 32-billion-parameter model purpose-built for deep reasoning, complex logic chains and advanced instruction-following scenarios. Its capacity enables strong performance on demanding evaluation tasks and...

Unique: Olmo 3 32B Think uses its reasoning phase to validate mathematical solutions internally, enabling it to catch calculation errors and backtrack on failed solution paths. This is distinct from models that generate solutions in a single pass without validation, which are more prone to arithmetic errors.

vs others: More accurate on complex math problems than GPT-3.5 Turbo; comparable to GPT-4 on standardized math benchmarks while offering lower latency and cost

via “reasoning chain decomposition and step-by-step problem solving”

Qwen Plus 0728, based on the Qwen3 foundation model, is a 1 million context hybrid reasoning model with a balanced performance, speed, and cost combination.

Unique: Implements chain-of-thought reasoning through prompt-based guidance rather than architectural modifications, enabling flexible reasoning depth control without model retraining

vs others: More cost-effective than specialized reasoning models (o1) for moderate complexity problems; produces transparent reasoning vs black-box outputs; trades off reasoning depth vs cost and latency

via “complex reasoning and chain-of-thought decomposition”

Command R7B (12-2024) is a small, fast update of the Command R+ model, delivered in December 2024. It excels at RAG, tool use, agents, and similar tasks requiring complex reasoning...

Unique: Command R7B's reasoning is optimized for RAG and tool-use contexts, where intermediate steps can reference retrieved documents or tool outputs, enabling grounded reasoning that combines external knowledge with logical inference

vs others: Outperforms GPT-4 on MATH and AIME benchmarks when combined with tool use for calculation, because it can delegate computation to tools rather than attempting symbolic math in-context

via “mathematical-reasoning-and-problem-solving”

Hermes 4 70B is a hybrid reasoning model from Nous Research, built on Meta-Llama-3.1-70B. It introduces the same hybrid mode as the larger 405B release, allowing the model to either...

Unique: Trained on mathematical problem datasets with explicit step-by-step annotations, enabling the model to generate intermediate steps that match human problem-solving patterns rather than jumping directly to answers

vs others: More transparent than Wolfram Alpha for showing reasoning steps, though less reliable for advanced mathematics; stronger than GPT-3.5 on symbolic manipulation due to larger parameter count

via “reasoning and step-by-step problem solving”

GPT-3.5 Turbo is OpenAI's fastest model. It can understand and generate natural language or code, and is optimized for chat and traditional completion tasks. Training data up to Sep 2021.

Unique: Instruction-tuned for chain-of-thought reasoning, generating intermediate steps explicitly rather than jumping to conclusions; trained on diverse reasoning tasks to apply reasoning patterns across math, logic, and code domains

vs others: More accurate on multi-step problems than direct answer generation because explicit reasoning reduces errors; more flexible than specialized solvers because it handles diverse problem types, though less accurate than domain-specific tools (calculators, debuggers)

via “mathematical reasoning and symbolic computation”

GLM 4 32B is a cost-effective foundation language model. It can efficiently perform complex tasks and has significantly enhanced capabilities in tool use, online search, and code-related intelligent tasks. It...

Unique: GLM 4 32B includes specialized training on mathematical reasoning datasets, enabling it to show work and explain reasoning — not just generate answers — which is critical for educational and verification use cases

vs others: More cost-effective than Wolfram Alpha for symbolic reasoning while providing better explanations than calculators, though less precise than dedicated symbolic engines for complex expressions

via “mathematical problem solving with step-by-step verification”

The o-series of models are trained with reinforcement learning to think before they answer and perform complex reasoning. The o3-pro model uses more compute to think harder and provide consistently...

Unique: Applies extended reasoning to mathematical problem-solving, enabling explicit step-by-step verification and error-checking within the reasoning phase. Unlike standard LLMs that may skip steps or make calculation errors, o3-pro's reasoning allows it to catch and correct mistakes before output.

vs others: Achieves 90%+ accuracy on AIME and MATH benchmarks compared to 50-70% for GPT-4, due to reasoning-enabled verification and multi-path exploration.

via “reasoning and problem-solving with chain-of-thought decomposition”

GPT-5.3 Chat is an update to ChatGPT's most-used model that makes everyday conversations smoother, more useful, and more directly helpful. It delivers more accurate answers with better contextualization and significantly...

Unique: GPT-5.3 uses improved training on reasoning-heavy tasks and synthetic chain-of-thought data to produce more reliable intermediate steps and better error detection compared to GPT-4, with architectural support for longer reasoning traces without proportional quality degradation

vs others: Produces more coherent and verifiable reasoning chains than Llama 2 or Mistral due to superior training on mathematical and logical reasoning tasks, though specialized reasoning models (e.g., AlphaProof) may outperform on formal mathematics