Mathematical Problem Solving With Symbolic 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 “mathematical reasoning with math benchmark 80+ and structured problem-solving”

Alibaba's 72B open model trained on 18T tokens.

Unique: Integrates three distinct reasoning paradigms (CoT for symbolic reasoning, PoT for code-based computation, TIR for external tool orchestration) within single 72B dense model, enabling flexible problem-solving strategies without model switching. 128K context window allows full problem histories and solution verification within single inference call.

vs others: Outperforms Llama 2 70B (significantly lower math performance) and matches Llama 3 70B on general benchmarks while offering specialized math reasoning patterns; Qwen2.5-Math 72B variant provides deeper specialization but general-purpose 72B enables seamless math-to-code-to-text transitions without model switching.

Latest compact reasoning model with native tool use.

Unique: Uses symbolic reasoning to manipulate mathematical expressions as abstract structures, not just pattern matching on numerical values. This enables solving novel problems through principled symbolic transformations rather than memorized solutions.

vs others: More capable than GPT-4o on symbolic math due to integrated reasoning; comparable to specialized symbolic math engines (Mathematica, SymPy) but with natural language reasoning about intent; faster than o1/o3 due to model size optimization.

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 reasoning and symbolic problem-solving”

text-generation model by undefined. 1,13,49,614 downloads.

Unique: DeepSeek-V3.2 was trained on mathematical reasoning datasets with explicit step-by-step annotations, enabling it to generate coherent multi-step proofs and derivations without external symbolic engines, though with pattern-matching rather than formal verification

vs others: Achieves 55-60% accuracy on MATH benchmark (vs. 50% for Llama-2-70B) by using specialized mathematical reasoning training, though still below GPT-4's 92% due to lack of formal verification and external tool integration

via “mathematical reasoning and symbolic computation”

Mistral Large — powerful reasoning and instruction-following

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 symbolic reasoning and proof verification”

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: Applies extended thinking specifically to mathematical reasoning, allowing the model to explore multiple solution paths, verify intermediate steps algebraically, and backtrack if a path leads to contradiction. This produces mathematically sound solutions rather than pattern-matched approximations.

vs others: Provides reasoning-enhanced mathematical problem solving comparable to specialized tools like Wolfram Alpha, but with natural language explanation and multimodal input support; less precise than symbolic math engines but more accessible and context-aware.

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-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”

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 symbolic reasoning”

Qwen3-8B is a dense 8.2B parameter causal language model from the Qwen3 series, designed for both reasoning-heavy tasks and efficient dialogue. It supports seamless switching between "thinking" mode for math,...

Unique: Integrates explicit thinking mode with mathematical training to enable symbolic reasoning within the model, allowing step-by-step problem decomposition without external symbolic engines

vs others: Outperforms general-purpose 8B models on mathematical reasoning due to thinking mode, though may underperform specialized math models or larger general models like GPT-4 on very complex problems

via “mathematical reasoning and symbolic problem-solving”

Qwen3, the latest generation in the Qwen large language model series, features both dense and mixture-of-experts (MoE) architectures to excel in reasoning, multilingual support, and advanced agent tasks. Its unique...

Unique: Qwen3's reasoning capabilities enable it to handle multi-step mathematical problems with implicit constraint tracking better than smaller models, while its multilingual training allows it to solve problems stated in non-English languages

vs others: Better at step-by-step mathematical reasoning than GPT-3.5 Turbo while maintaining lower cost than specialized mathematical reasoning models

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 reasoning and symbolic computation”

Qwen3-Max-Thinking is the flagship reasoning model in the Qwen3 series, designed for high-stakes cognitive tasks that require deep, multi-step reasoning. By significantly scaling model capacity and reinforcement learning compute, it...

Unique: Combines extended reasoning with mathematical domain knowledge to enable transparent, step-by-step mathematical problem-solving. Uses thinking tokens to represent intermediate mathematical steps and verification, making mathematical reasoning auditable and debuggable.

vs others: Provides better mathematical reasoning transparency than general-purpose LLMs while maintaining broader applicability than specialized mathematical AI systems, though with lower precision than dedicated computer algebra systems.

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

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

DeepSeek V3, a 685B-parameter, mixture-of-experts model, is the latest iteration of the flagship chat model family from the DeepSeek team. It succeeds the [DeepSeek V3](/deepseek/deepseek-chat-v3) model and performs really well...

Unique: Large parameter count enables deep mathematical reasoning and theorem application without explicit symbolic computation; MoE routing allows selective activation of mathematical reasoning experts

vs others: Better mathematical reasoning than smaller models; more accessible than specialized symbolic math tools but less precise than dedicated CAS systems

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 reasoning and symbolic problem-solving”

Qwen2.5 72B 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 series explicitly improves mathematical reasoning capabilities over Qwen2 through enhanced training on mathematical datasets and reasoning patterns; achieves improved performance on MATH and similar benchmarks while maintaining general conversational ability

vs others: More reliable mathematical reasoning than Llama 2 70B; comparable to GPT-3.5 for standard problems but at lower cost; weaker than specialized math models like Minerva but more general-purpose

Alibaba's QWQ — advanced reasoning model with improved math/logic capabilities

Unique: Combines RL-optimized reasoning with domain-specific training on mathematical problems, enabling the model to learn problem-solving heuristics (e.g., factoring, substitution) rather than just pattern-matching solutions. This allows generalization to novel problem structures.

vs others: Outperforms GPT-3.5 and Llama 2 on mathematical reasoning while remaining open-source and locally deployable, avoiding the latency and cost of cloud-based math solvers.