With the rapid evolution of web technology and Internet, the mathematical web has emerged as a new research trend, which changes the traditional manner of mathematical scientific researching, mathematical production sharing, mathematical knowledge engineering and mathematical education. In addition, the acquisition of mathematical knowledge and the integration of diversiform of mathematical software are also taken into considers on the web environment. In this paper, we will present a web-based, user adaptive learning and grid computing environment that employs content encoded in a semantic representation of mathematical knowledge and integrates mathematics software as services. We have brought forward a concept which makes the mathematical computing environment working more efficiently. This mathematics computing environment mainly offers a powerful and convenient mathematics computing environment for end users and service providers. From the view of computing, this environment is a web-based service-oriented environment, built on three-layered resource model. From the view of end users, the formal representation allows semantics-based retrieval of distributed mathematical facts, giving mathematicians a tool and an easy-to-learn mathematical language to access and query the present mathematical knowledge and services. On the other hand, we use grid toolkits, which have the capabilities to aggregate and coordinate the computational power of geographically distributed, heterogeneous and dynamic resources efficiently, to organize and manage the mathematical resources.