mammoth
**MAmmoTH** is a **mathematics-specialized language model created by fine-tuning Code Llama on diverse mathematical problem-solving data including step-by-step solutions, alternate solution methods, and domain specialization**, achieving state-of-the-art mathematical reasoning by applying multi-stage fine-tuning and instruction optimization specifically designed to capture the diversity of mathematical solution approaches.
**Multi-Method Training Strategy**
MAmmoTH uniquely trains on **multiple solution approaches** per problem:
| Training Approach | Benefit | Example |
|------------------|---------|---------|
| **Step-by-Step** | Explicit reasoning decomposition | "First derive, then substitute" |
| **Alternate Methods** | Teaching problem-solving diversity | Calculus vs algebraic approaches |
| **Code Generation** | Symbolic verification | Generate SageMath code to verify answer |
Mathematics problems rarely have one solution method—MAmmoTH teaches models the **flexibility** to switch approaches based on problem structure.
**Fine-Tuning Strategy**: Multi-stage training first on mathematical texts, then on solved problems with explicit step-by-step reasoning, finally on code generation for symbolic verification—accumulating mathematical skills progressively.
**Performance**: Achieves **53.9% on MATH (university-level problems)**—beating Llama-2-70B and approaching GPT-4 capability despite being open-source and much smaller.
**Approach Diversity**: A key finding—models that learn multiple solution methods generalize better to novel problems than those trained on single fixed approaches.
**Legacy**: Established that **training diversity matters as much as scale**—teaching multiple problem-solving methods enables better mathematical reasoning across diverse domains.