The programming language widely used for data science and machine learning applications is R. R is a dynamic language specifically designed for statistical computing and graphics, allowing users to perform complex data analyses and visualize results effectively. Its vast collection of packages, such as ggplot2 and dplyr, supports data manipulation and visualization tasks, making it a preferred tool among statisticians and data scientists. Moreover, R's capabilities in handling large datasets and its compatibility with machine learning frameworks enable users to leverage predictive modeling and data analysis easily.