  Recent advancements in large language models, such as GPT-4, have
demonstrated remarkable capabilities in processing standard queries. Despite
these advancements, their performance substantially declines in
\textbf{advanced mathematical problems requiring complex, multi-step logical
reasoning}. To enhance their inferential capabilities, current research has
delved into \textit{prompting engineering}, exemplified by methodologies such
as the Tree of Thought and Graph of Thought. Nonetheless, these existing
approaches encounter two significant limitations. Firstly, their effectiveness
in tackling complex mathematical problems is somewhat constrained. Secondly,
the necessity to design distinct prompts for individual problems hampers their
generalizability. In response to these limitations, this paper introduces the
\textit{Multi-Agent System for conditional Mining} (\textbf{MACM}) prompting
method. It not only resolves intricate mathematical problems but also
demonstrates strong generalization capabilities across various mathematical
contexts. With the assistance of MACM, the accuracy of GPT-4 Turbo on the most
challenging level five mathematical problems in the MATH dataset increase from
$\mathbf{54.68\%} \text{ to } \mathbf{76.73\%}$. The code is available in
\url{https://github.com/bin123apple/MACM}.
