Contributions to Mathematics
R.H. Bing's area of research was topology, which he described as “geometry with a modern slant.” Topology is the study of objects such as curves, surfaces, and solids, and their features that are preserved under continuous deformations, including stretching and bending.
Bing authored more than one hundred papers as well as his book The Geometric Topology of 3-Manifolds. In his paper "The Mathematical Works of R.H. Bing," Morton Brown reflected, “no fewer than twenty of his papers would have to be called major contributions. At least ten others are referred to as basic or seminal in their respective areas.”
His major accomplishments include solving the Kline sphere characterization problem, the Bing-Nagata-Smirnov theorem, the side-approximation theorem, and the development of Bing shrinking.
Bing was a great spokesman for mathematics. From 1963–1964, he served as president of the Mathematical Association of America; he was also president of the American Mathematical Society from 1977–1978. Beyond leading those organizations, he was an active member of the National Academy of Sciences, the National Science Board, the National Research Council, and the Conference Board for the Mathematical Sciences. Bing was awarded the MAA Gung and Hu Distinguished Service to Mathematics Award in 1974. He received the Distinguished Alumnus Award from Southwest Texas State University in 1979.