Mathematical Reasoning Over Visual Data

via “visual mathematical dataset curation and annotation”

Visual mathematical reasoning benchmark.

Unique: Newly created datasets (IQTest, FunctionQA, PaperQA) are purpose-built for compositional visual-mathematical reasoning rather than repurposed from general vision-language tasks. Includes auxiliary annotations (OCR, captions) enabling evaluation of text-only models as baselines, revealing how much visual understanding contributes to performance vs. text-based reasoning alone.

vs others: More comprehensive than single-source mathematical reasoning datasets because it aggregates 28 existing datasets plus 3 new ones, providing broader coverage of visual mathematical domains and reducing bias from any single source's annotation style or problem distribution.

via “arithmetic and mathematical reasoning evaluation”

23 hardest BIG-Bench tasks where models initially failed.

Unique: Focuses specifically on multi-step arithmetic and mathematical reasoning through few-shot examples, isolating numerical reasoning capability from general language understanding. Tasks test both calculation accuracy and mathematical inference patterns.

vs others: More focused on mathematical reasoning than general reasoning benchmarks; more accessible than formal mathematics verification because it uses natural language problem statements rather than symbolic notation.

Mistral's 124B multimodal model with vision capabilities.

Unique: Achieves 69.4% on MathVista benchmark (outperforming all tested models) through integrated visual parsing and mathematical reasoning in a single 124B model, without requiring separate symbolic math engines or specialized mathematical libraries

vs others: Outperforms GPT-4o, Gemini-1.5 Pro, and Claude-3.5 Sonnet on MathVista while being available for self-hosted deployment, eliminating API dependency for educational or research mathematical analysis

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 “visual-reasoning-over-complex-scenes”

Open multimodal model for visual reasoning.

Unique: Trained on 77K complex reasoning samples (49% of instruction-tuning dataset) generated by GPT-4, explicitly optimizing for multi-step inference over visual content; this heavy weighting toward reasoning tasks differentiates it from captioning-focused vision models

vs others: Outperforms general-purpose vision models on reasoning-heavy benchmarks like Science QA (92.53% accuracy) because nearly half its training data is reasoning-focused, whereas models like CLIP or standard captioning systems optimize for classification or description

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-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”

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 “extended reasoning with chain-of-thought for complex visual tasks”

Qwen3-VL-30B-A3B-Thinking is a multimodal model that unifies strong text generation with visual understanding for images and videos. Its Thinking variant enhances reasoning in STEM, math, and complex tasks. It excels...

Unique: Integrates extended reasoning directly into the model's forward pass for visual tasks, rather than using post-hoc prompting techniques like 'think step-by-step', enabling the model to allocate compute dynamically to reasoning-heavy visual problems

vs others: More reliable than prompt-based chain-of-thought for visual reasoning because reasoning is baked into model weights, not dependent on prompt engineering; produces more consistent intermediate steps for STEM tasks

via “mathematical reasoning evaluation”

UGI-Leaderboard — AI demo on HuggingFace

Unique: Isolates mathematical reasoning as a distinct evaluation dimension on the leaderboard, enabling models to be ranked separately on math vs general generation, revealing capability specialization.

vs others: Simpler than running MATH or GSM8K locally with custom evaluation scripts, but less transparent than open-source math benchmarks regarding problem selection and difficulty.

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 “nonverbal reasoning and abstract visual pattern recognition”

* ⭐ 03/2023: [PaLM-E: An Embodied Multimodal Language Model (PaLM-E)](https://arxiv.org/abs/2303.03378)

Unique: Demonstrates reasoning on abstract visual tasks (Raven IQ tests) through multimodal pretraining rather than task-specific training, suggesting transfer of reasoning capabilities from language to visual domain

vs others: Tests general reasoning transfer from language to vision, whereas specialized visual reasoning models are trained specifically on these tasks; demonstrates broader generalization

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 “multimodal reasoning with extended thinking for stem and mathematical problem-solving”

Qwen3-VL-235B-A22B Thinking is a multimodal model that unifies strong text generation with visual understanding across images and video. The Thinking model is optimized for multimodal reasoning in STEM and math....

Unique: Unifies visual and textual reasoning through a single 235B parameter model with explicit thinking tokens, rather than treating vision and language as separate processing streams. The architecture uses a shared transformer backbone with vision-language fusion at intermediate layers, allowing mathematical reasoning to operate directly over visual features (e.g., reasoning about graph structure while reading axis labels).

vs others: Outperforms GPT-4V and Claude 3.5 Sonnet on STEM benchmarks (MATH-Vision, SciQA) because thinking tokens enable explicit symbolic reasoning over visual content, whereas competitors rely on implicit visual understanding without intermediate reasoning artifacts.

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 “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

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 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