Mathematical Problem Solving With Step By Step Verification

via “mathematical problem-solving with outcome-based verification”

Alibaba's 32B reasoning model with chain-of-thought.

Unique: Trained with outcome-based rewards using accuracy verifiers that check final answer correctness, enabling the model to learn which reasoning paths lead to correct solutions rather than relying on human-annotated reasoning traces — this verification-driven approach achieves 79.5% on AIME 2024 with only 32B parameters

vs others: Achieves AIME performance comparable to much larger reasoning models (DeepSeek-R1 at 671B) through efficient RL training with outcome verification, making it deployable on single-GPU hardware while maintaining competitive mathematical reasoning capability

via “math problem solving with step-by-step explanations”

All-in-one AI assistant extension with GPT-4 and Claude.

Unique: Provides step-by-step math solutions with equation rendering directly in browser sidebar, supporting both text and image input without requiring separate math solver tools

vs others: More educational than Wolfram Alpha because it emphasizes step-by-step working and explanations rather than just final answers, though less comprehensive for symbolic computation

via “mathematical proof generation and verification reasoning”

OpenAI's most powerful reasoning model for complex problems.

Unique: Applies extended reasoning specifically to mathematical proof generation, exploring multiple proof strategies and backtracking on invalid paths before committing to a solution — this enables reasoning through proof correctness rather than pattern matching

vs others: Achieves competitive-level mathematics performance (87.5% on ARC-AGI) by reasoning through proof strategies and constraint satisfaction, outperforming GPT-4 and Claude which rely more on pattern matching and memorized proof structures

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 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 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 “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 “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”

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 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 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 “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-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 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 “multi-step-mathematical-reasoning”

Qwen3-Next-80B-A3B-Thinking is a reasoning-first chat model in the Qwen3-Next line that outputs structured “thinking” traces by default. It’s designed for hard multi-step problems; math proofs, code synthesis/debugging, logic, and agentic...

Unique: Combines 80B parameter scale with A3B architecture to maintain reasoning coherence across 50+ step mathematical derivations, outputting structured intermediate steps that expose algebraic transformations and logical justifications rather than black-box final answers

vs others: Outperforms GPT-4 and Claude 3.5 on formal proof generation by explicitly exposing reasoning traces, enabling verification of each step; stronger than specialized math models (Wolfram Alpha) because it generates human-readable justifications alongside symbolic results

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

DeepSeek R1 Distill Qwen 32B is a distilled large language model based on [Qwen 2.5 32B](https://huggingface.co/Qwen/Qwen2.5-32B), using outputs from [DeepSeek R1](/deepseek/deepseek-r1). It outperforms OpenAI's o1-mini across various benchmarks, achieving new...

Unique: Distills R1's mathematical reasoning capability to generate complete step-by-step derivations with intermediate justifications, making mathematical problem-solving transparent and verifiable

vs others: Provides more detailed reasoning than standard LLMs and more cost-effective reasoning than o1-mini while maintaining educational value through explicit derivation steps

via “mathematical proof verification and derivation”

May 28th update to the [original DeepSeek R1](/deepseek/deepseek-r1) 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...

Unique: Applies reinforcement-learning-trained reasoning to mathematical proof tasks, producing explicit step-by-step reasoning that can be audited for logical correctness. Unlike standard LLMs that generate plausible-sounding proofs, R1's reasoning approach enables identification of subtle logical gaps through visible intermediate steps.

vs others: More reliable than GPT-4 for proof verification due to explicit reasoning; slower than specialized proof assistants (Lean, Coq) but more accessible and requires less formal notation expertise.