Mathematical Problem Solving With Step By Step Reasoning

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 “multi-step mathematical reasoning benchmark evaluation”

8.5K grade school math problems — multi-step reasoning, verifiable solutions, reasoning benchmark.

Unique: Uses linguistically diverse, human-authored grade school problems (not synthetic) that require genuine multi-step reasoning with basic arithmetic, combined with a standardized answer extraction format (#### delimiter) that enables reproducible evaluation across heterogeneous model outputs

vs others: More challenging than simple arithmetic benchmarks (requires 2-8 reasoning steps) yet more accessible than advanced math benchmarks, making it ideal for measuring practical reasoning improvements in production models

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

text-generation model by undefined. 1,37,84,608 downloads.

Unique: Qwen2.5-7B-Instruct includes explicit training on mathematical reasoning datasets (including GSM8K, MATH, and proprietary datasets) with emphasis on showing intermediate steps and justifying answers. The instruction-tuning includes prompts that encourage the model to 'think step by step' and 'show your work', which are known to improve mathematical reasoning through in-context learning effects.

vs others: Outperforms base Qwen2.5-7B on mathematical reasoning benchmarks by 15-20% due to instruction-tuning; more accessible than specialized math models (like Minerva) for general-purpose 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 “mathematical problem solving with step-by-step verification”

text-generation model by undefined. 38,71,385 downloads.

Unique: Trained via RL to optimize for mathematical correctness with explicit intermediate step generation; learns to recognize and correct errors during reasoning rather than committing to incorrect paths

vs others: Outperforms GPT-4 on MATH and AIME benchmarks (94.3% vs 80%+ on AIME) through learned reasoning allocation; provides more transparent reasoning than Gemini while maintaining higher accuracy

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

Talk to Claude, an AI assistant from Anthropic.

via “mathematical reasoning and word problem solving”

text-generation model by undefined. 47,03,591 downloads.

Unique: Integrates Microsoft's Orca-Math-Word-Problems-200K dataset (200K curated math problems with reasoning traces) with Dolphin's chain-of-thought training, enabling the model to produce explicit intermediate reasoning steps rather than just final answers, making solutions auditable and educational

vs others: Provides transparent step-by-step reasoning for math problems unlike black-box proprietary models; smaller and faster to deploy than specialized math models like Minerva while maintaining competitive accuracy on word problems within training distribution

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

DeepSeek R1 is here: Performance on par with [OpenAI o1](/openai/o1), but open-sourced and with fully open reasoning tokens. It's 671B parameters in size, with 37B active in an inference pass....

Unique: Achieves o1-level mathematical reasoning performance with fully transparent step-by-step verification, enabling educators and students to validate each calculation. The 671B parameter model with sparse activation maintains reasoning coherence across multi-step proofs while keeping inference costs lower than dense alternatives.

vs others: Superior to GPT-4 on complex math problems due to explicit reasoning, and more transparent than o1 which hides intermediate steps, making it ideal for educational and verification use cases.

via “mathematical-reasoning-and-step-by-step-derivation”

Llama-3.3-Nemotron-Super-49B-v1.5 is a 49B-parameter, English-centric reasoning/chat model derived from Meta’s Llama-3.3-70B-Instruct with a 128K context. It’s post-trained for agentic workflows (RAG, tool calling) via SFT across math, code, science, and...

Unique: Post-trained on mathematical reasoning tasks as part of agentic workflow optimization, enabling more reliable step-by-step derivations than base Llama-3.3-70B, though without symbolic computation integration

vs others: Better mathematical reasoning than GPT-3.5-Turbo at comparable latency, though less capable than specialized math models like Wolfram Alpha or Mathematica for symbolic computation

via “logical reasoning and problem-solving with step-by-step decomposition”

The Meta Llama 3.3 multilingual large language model (LLM) is a pretrained and instruction tuned generative model in 70B (text in/text out). The Llama 3.3 instruction tuned text only model...

Unique: Instruction-tuning explicitly includes chain-of-thought examples for reasoning tasks, enabling the model to learn step-by-step decomposition patterns; 70B parameter scale provides sufficient capacity for multi-step reasoning without external symbolic engines

vs others: More reliable step-by-step reasoning than Llama 2 70B; comparable to GPT-3.5 on reasoning benchmarks; lower cost than GPT-4 for reasoning tasks while maintaining competitive accuracy on standard benchmarks

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

OpenAI o3-mini is a cost-efficient language model optimized for STEM reasoning tasks, particularly excelling in science, mathematics, and coding. This model supports the `reasoning_effort` parameter, which can be set to...

Unique: Applies reasoning_effort to control derivation depth and detail, enabling educators to generate solutions at varying levels of explanation without prompt changes. This differs from static math solvers (Wolfram Alpha) by providing reasoning traces and educational explanations.

vs others: More educational than symbolic solvers (shows reasoning); more flexible than static problem banks; enables personalized explanation depth through reasoning_effort parameter.

via “mathematical reasoning and symbolic computation”

DeepSeek-V3.1 Terminus is an update to [DeepSeek V3.1](/deepseek/deepseek-chat-v3.1) that maintains the model's original capabilities while addressing issues reported by users, including language consistency and agent capabilities, further optimizing the model's...

Unique: V3.1 Terminus improves mathematical reasoning accuracy through enhanced chain-of-thought formatting and better handling of multi-step algebraic manipulations, addressing base V3.1's occasional sign errors and simplification mistakes

vs others: Matches GPT-4's mathematical reasoning quality while providing more transparent derivation steps; outperforms Claude 3.5 on competition-level math problems requiring deep symbolic reasoning