Mathematical reasoning---a core ability within human intelligence---presents
some unique challenges as a domain: we do not come to understand and solve
mathematical problems primarily on the back of experience and evidence, but on
the basis of inferring, learning, and exploiting laws, axioms, and symbol
manipulation rules. In this paper, we present a new challenge for the
evaluation (and eventually the design) of neural architectures and similar
system, developing a task suite of mathematics problems involving sequential
questions and answers in a free-form textual input/output format. The
structured nature of the mathematics domain, covering arithmetic, algebra,
probability and calculus, enables the construction of training and test splits
designed to clearly illuminate the capabilities and failure-modes of different
architectures, as well as evaluate their ability to compose and relate
knowledge and learned processes. Having described the data generation process
and its potential future expansions, we conduct a comprehensive analysis of
models from two broad classes of the most powerful sequence-to-sequence
architectures and find notable differences in their ability to resolve
mathematical problems and generalize their knowledge.

该研究针对数学领域中的推理、学习、应用规则等独特挑战，提出了一个数学问题套件的任务，用于测试和评估神经架构等系统的性能、能力和失效模式。通过生成数据并运用序列到序列的最强模型，可以从不同角度评估模型在数学问题解决和知识推广方面的能力。