Qwen2.5-Math-72B

Qwen2.5-Math, released September 2024, is Alibaba's math-specialist line in 1.5B, 7B, and 72B sizes. The 72B base model set a new open-source state of the art on the MATH benchmark at 66.8 — up 5.3 points over Qwen2-Math-72B — and the instruct variant was, per the technical report, the best open mathematical model available at release. A distinctive feature is Tool-Integrated Reasoning (TIR) mode, where the model calls a Python interpreter mid-reasoning; in TIR mode the 72B approaches 90 on MATH.

Training mixed English and Chinese chain-of-thought data with self-improvement loops, the family also dramatically improved Chinese math problem-solving. All sizes are Apache 2.0 — fully open, commercial use included — which made Qwen2.5-Math-7B a favorite fine-tuning base for math research.

Honest caveats: it is a math specialist, not a generalist — don't expect strong coding or chat. The reasoning-model wave of 2025 (R1 and its distills) has since raised the bar. But for pure open math capability with a permissive license, the 72B remains a reference point.