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Mathematical reasoning recently has been shown as a hard challenge for neural systems. Abilities including expression translation, logical reasoning, and mathematics knowledge acquiring appear to be essential to overcome the challenge. This paper demonstrates that some abilities can be achieved through abductive combination with discrete systems that have been programmed with human knowledge. On a mathematical reasoning dataset, we adopt the recently proposed abductive learning framework, and propose the ABL-Sym algorithm that combines the Transformer neural models with a symbolic mathematics library. ABL-Sym shows 9.73% accuracy improvement on the interpolation tasks and 47.22% accuracy improvement on the extrapolation tasks, over the state-of-the-art approaches. Online demonstration: http://math.polixir.ai, Comment: Appeared in ICML 2020 Workshop on Bridge Between Perception and Reasoning: Graph Neural Networks & Beyond, Vienna, Austria, 2020. Code at https://agit.ai/Polixir/ABL-Sym | Video presentation available at https://slideslive.com/s/yangyang-hu-38188 | Online demonstration available at http://math.polixir.ai