Modern interdisciplinary research in statistical science encompasses a wide field: agriculture, biology, biomedical sciences along with bioinformatics, clinical sciences, education, environmental and public health disciplines, genomic science, industry, molecular genetics, socio-behavior, socio-economics, toxicology, and a variety of other disciplines. Statistical science has historically had mathematical perspectives dominating theoretical and methodological developments. Yet, the advent of modern information technology has opened the doors for highly computation intensive statistical tools (i.e., software), wherein mathematical aspects are often de-emphasized. Knowledge discovery and data mining (KDDM) is now becoming a dominating force, with bioinformatics as a notable example. In view of this apparent discordance between mathematical (frequentist as well as Bayesian) and computational approaches to statistical resolutions, and a genuine need to formulate training as well as research curricula to meet growing demands, a critical appraisal of statistical innovations is made with due respect to its mathematical heritage, as well as scope of application. Some of the challenging statistical tasks are illustrated.