Abstract : This paper is intended to communicate to a general audience current directions in the discipline of statistics, and in my own research. It consists of three parts. Part I (Sections 1-3) explores perspectives on the future development of the science of statistics, and the importance to statisticians and society that each understand the interplay between mathematics, science, and statistics. Definitions are given of mathematical beauty and utility, soft and hard mathematics, mathematical modeling, the distinction between pure science and professional science, and finally statistical science. Part II (Sections 4-7) discusses the steps of statistical reasoning (including exploratory data analysis and statistical model identifications), the quantile and density-quantile approach to statistical data analysis, and time series analysis. Part III (Section 8) presents a model of statistics for organization of graduate instruction. (Author)