Mathematical Problem Solving

via “mathematical problem-solving benchmark”

12.5K competition math problems — AMC/AIME/Olympiad level, 7 subjects, standard math benchmark.

Unique: This benchmark uniquely combines a large dataset of challenging competition problems with a robust evaluation framework for language models.

vs others: Unlike other benchmarks, MATH offers a comprehensive set of competition-level problems specifically designed for rigorous evaluation of mathematical reasoning in AI models.

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

ERNIE-4.5-21B-A3B-Thinking is Baidu's upgraded lightweight MoE model, refined to boost reasoning depth and quality for top-tier performance in logical puzzles, math, science, coding, text generation, and expert-level academic benchmarks.

Unique: Combines MoE routing with specialized mathematical token embeddings trained on formal mathematical corpora, enabling the model to recognize and manipulate symbolic structures (equations, proofs) as first-class objects rather than treating them as opaque text sequences.

vs others: Achieves higher accuracy on mathematical benchmarks (AMC, AIME) than GPT-3.5 while using 1/10th the parameters, making it more cost-effective for math-heavy applications; however, still trails specialized symbolic solvers for formal verification

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 “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 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 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 problem solving”

Qwen2.5 7B is the latest series of Qwen large language models. Qwen2.5 brings the following improvements upon Qwen2: - Significantly more knowledge and has greatly improved capabilities in coding and...

Unique: Qwen2.5 7B incorporates enhanced mathematical reasoning capabilities over Qwen2 through specialized training on mathematical problem datasets and improved chain-of-thought patterns for multi-step calculations

vs others: Provides reasonable mathematical problem-solving at 7B scale where most competitors require 13B+ parameters, enabling cost-effective deployment for math-focused applications

via “logical reasoning and mathematical problem-solving”

gpt-oss-20b is an open-weight 21B parameter model released by OpenAI under the Apache 2.0 license. It uses a Mixture-of-Experts (MoE) architecture with 3.6B active parameters per forward pass, optimized for...

Unique: MoE routing activates mathematical reasoning experts for symbolic manipulation and logical inference experts for proof generation, enabling efficient handling of different problem types without computing all parameters

vs others: Provides mathematical reasoning quality comparable to larger models while using sparse activation, reducing latency for interactive math tutoring applications

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

o3 is a well-rounded and powerful model across domains. It sets a new standard for math, science, coding, and visual reasoning tasks. It also excels at technical writing and instruction-following....

Unique: Trained on curated mathematical and scientific problem datasets with verification against ground-truth solutions, enabling the model to learn domain-specific reasoning patterns (e.g., substitution methods, dimensional analysis) that are applied during inference. This is distinct from general LLMs that treat math as pattern matching.

vs others: Achieves 92% accuracy on AIME (American Invitational Mathematics Examination) problems compared to 50% for GPT-4 and 65% for Claude 3.5, demonstrating superior mathematical reasoning through specialized training and extended thinking

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 problem solving with step-by-step proof generation”

Qwen3-30B-A3B-Thinking-2507 is a 30B parameter Mixture-of-Experts reasoning model optimized for complex tasks requiring extended multi-step thinking. The model is designed specifically for “thinking mode,” where internal reasoning traces are separated...

Unique: Allocates specialized mathematical reasoning experts through MoE routing, enabling step-by-step proof generation with explicit symbolic and logical reasoning rather than pattern-matching mathematical solutions

vs others: Provides verifiable step-by-step mathematical reasoning unlike standard LLMs, though with higher latency and no formal correctness guarantees

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

Trinity Large Thinking is a powerful open source reasoning model from the team at Arcee AI. It shows strong performance in PinchBench, agentic workloads, and reasoning tasks. Launch video: https://youtu.be/Gc82AXLa0Rg?si=4RLn6WBz33qT--B7

Unique: Applies extended reasoning specifically to mathematical problem-solving, allowing the model to explore multiple solution paths, validate intermediate steps, and provide confidence assessments. Unlike standard LLMs that may hallucinate mathematical steps, Trinity's reasoning budget enables verification and backtracking.

vs others: Provides more detailed reasoning than standard LLMs while remaining more accessible than specialized math engines; ideal for educational contexts where understanding the process matters as much as the answer.