中文摘要：

大数据问题的关键技术挑战在于：找到隐含在低价值密度数据中的价值;在希望的时间内完成。指出前者需要将领域知识和数据技术结合,这种结合的理论和新型算法构成大数据的分析基础和应用基础;后者需要设计新的计算机、集群体系、计算框架、存储体系和数据管理方法,这些构成大数据的计算基础和数据基础。另外,这两个挑战都涉及数学理论,这是大数据的数学基础。系统地分析了大数据的数学基础、计算基础、数据基础、分析基础和应用基础等基础研究方向。

英文摘要：

The key technical challenges for big data lie in how to discover the value of the low-value-density data and how to complete the task in the desired time. The ways to take up these challenges from three aspects were discussed. First is that the former challenge requires the combination of domain knowledge and data technology. This combination of theory and new algorithms forms the basis of application and analysis of big data. Second is that the latter challenge needs to design new types of computer, cluster system, computing framework, storage system and data management method, which forms the basis of computing and data of big data. Thirdly, both challenges relate to mathematical theory, which is the basis of mathematics of big data. In conclusion, several foundation issues for big data research including the basis of mathematics, computing, data, analysis and application of big data were analyzed.