Claude Sonnet 4.6 vs R1 0528 for Math

What Math demands: accurate multi-step symbolic reasoning, stable step-by-step derivations, ability to follow and produce structured solutions, long-context handling for multi-part proofs, and reliable faithfulness (no hallucinated steps). When an external benchmark exists, it is the primary measure: on MATH Level 5 (Epoch AI), R1 0528 scores 96.6% — this is the main signal we use to call the winner for Math. Supporting internal signals: both models score 5 on long_context and 5 on faithfulness, and both have 5/5 on tool_calling (useful for tool-assisted computation). Differences that explain nuance: Claude Sonnet 4.6 scores 85.8 on AIME 2025 (our internal proxy) and 75.2 on SWE-bench Verified (coding-related math), plus top marks in strategic_analysis (5) and creative_problem_solving (5), indicating strong multi-step tradeoff reasoning and inventive solutions. R1 0528 has a lower AIME 2025 internal score (66.4) but the decisive MATH Level 5 result (96.6%) and good internal marks in structured_output (4) and tool_calling (5). Also note R1's quirks: it is a reasoning_model that uses reasoning tokens and can return empty responses on structured_output unless configured with high max_completion_tokens — this can affect short, strictly formatted prompts. Claude Sonnet 4.6 offers a far larger context window (1,000,000 tokens) and explicit structured_outputs support, which matters for very long derivations or multimodal math workflows.

1. High-stakes MATH Level 5 style problem sets (external benchmark alignment): R1 0528 — scores 96.6% on MATH Level 5 (Epoch AI), so expect the most consistent success on that specific benchmark. 2) AIME-like contest practice and step-by-step olympiad reasoning: Claude Sonnet 4.6 — AIME 2025 internal score 85.8 vs R1 66.4, so Sonnet is stronger on our AIME proxy and may produce better contest-style derivations or creative solution strategies. 3) Very long derivations, notebooks, or multimodal math (images→text): Claude Sonnet 4.6 — context_window 1,000,000 and modality text+image->text help for long proofs or image-based problems. 4) Cost-sensitive bulk grading or automated problem solvers: R1 0528 — input_cost_per_mtok $0.50 and output_cost_per_mtok $2.15 vs Claude Sonnet 4.6 at $3.00 input / $15.00 output per mtoken (Sonnet is ~7× more expensive by our priceRatio). 5) Strict JSON solutions or short structured outputs: both tie on structured_output (4/5), but R1 has a quirk where it may return empty responses on structured_output unless given a high max completion token budget — plan prompt/config accordingly.

For Math, choose R1 0528 if you need top performance on MATH Level 5 problems (96.6% on MATH Level 5, Epoch AI) or are cost-sensitive. Choose Claude Sonnet 4.6 if you need higher AIME-style performance (AIME 2025: 85.8 in our tests), massive context windows or multimodal math workflows, or stronger strategic/creative reasoning despite higher cost.