  We introduce MAmmoTH, a series of open-source large language models (LLMs)
specifically tailored for general math problem-solving. The MAmmoTH models are
trained on MathInstruct, our meticulously curated instruction tuning dataset.
MathInstruct is compiled from 13 math datasets with intermediate rationales,
six of which have rationales newly curated by us. It presents a unique hybrid
of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also
ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT
not only unleashes the potential of tool use but also allows different thought
processes for different math problems. As a result, the MAmmoTH series
substantially outperform existing open-source models on nine mathematical
reasoning datasets across all scales with an average accuracy gain between 16%
and 32%. Remarkably, our MAmmoTH-7B model reaches 33% on MATH (a
competition-level dataset), which exceeds the best open-source 7B model
(WizardMath) by 23%, and the MAmmoTH-34B model achieves 44% accuracy on MATH,
even surpassing GPT-4's CoT result. Our work underscores the importance of
diverse problem coverage and the use of hybrid rationales in developing
superior math generalist models.
