R. H. Bing

R. H. Bing (October 20, 1914 – April 28, 1986) was an American mathematician who worked mainly in the areas of geometric topology and continuum theory. His work in studying the geometric topology of three-dimensional space was so fundamental and distinctive that the area is often referred to as "Bing-type topology".

Early life and education Bing was born on October 20, 1914, in Oakwood, Texas. His father, Rupert Henry Bing, was a teacher who became superintendent of the Oakwood School District, where he met Bing's mother, Lula May Thompson, a primary school teacher. He then worked as a high-school teacher in Palestine, Texas, from 1935 to 1942, where his duties included coaching the football and track teams and teaching various subjects including mathematics and typing.

Mathematical contributions Bing's mathematical research focused almost exclusively on 3-manifold theory and the geometric topology of . One notable example was Michael Freedman's use of Bing's shrinking criterion to prove the four-dimensional Poincaré conjecture in 1982.

Metrization Around 1950, one of the great unsolved problems in general topology was the problem of giving a topological characterization of the metrizability of topological spaces. Jun-iti Nagata and Yuri Smirnov proved similar, independent results at about the same time, so the result is now known as the Bing–Nagata–Smirnov metrization theorem. He showed that the double of a solid Alexander horned sphere was the 3-sphere, demonstrating the existence of wild involutions on the 3-sphere with fixed point set equal to a wildly embedded 2-sphere.

Poincaré conjecture Bing was fascinated by the Poincaré conjecture and made several major attempts to prove it, contributing to its reputation as an extremely difficult problem.

Bing initiated research into what became known as the Property P conjecture, including giving it its name, as a potentially more tractable approach to the Poincaré conjecture. Property P was proven in 2004 as a culmination of work from several areas of mathematics, with some irony, this proof was announced shortly after Grigori Perelman announced his proof of the Poincaré conjecture itself.

Notable examples Along the way, Bing produced many counterexamples with nicknames: "The Bing Sling"—a simple closed curve that pierces no disk (1956); "Bing's Sticky Foot Topology"—a connected countable Hausdorff space (1953); and "Bing's Hooked Rug"—a wild 2-sphere in 3-space that contains no wild arc (1961). At Wisconsin he was appointed Rudolph E. Langer Research Professor in 1968 and served as department chairman from 1958 to 1960. Chairman of Division of Mathematics of the National Research Council (1967–1969) President of the Mathematical Association of America (1963–1964)

Published works