**R. H. Bing** was an American mathematician who worked mainly in the areas of geometric topology and continuum theory.

- H." by his parents; he had no other names.
- He became the manager of several farms and owned a store.
- Bing missed a year out at school going into the third year at his primary school after finishing his first.
- He found this quite hard, particularly since the other boys, being older, were bigger than he was and better at athletics.
- We learned to approximate answers to harder problems.
- Bing took a job in the college cafeteria when he went to the Southwest Texas State Teacher's College to help pay the tuition fees.
- He was awarded his B.S. in 1935.
- Now a trained school teacher, Bing did just that and taught mathematics for four and a half years at three different high schools in Texas, the first being at the Palestine High School in Palestine, Texas.
- As well as teaching mathematics he coached the football and track teams, and taught other classes, one of which was typing.
- During this time he did more than just teach, however, taking mathematics courses at the University of Texas over the summer.
- The reason for this was that the Texas Legislature had devised a policy where a teacher with a Master's degree would receive a higher salary than a teacher with a Bachelor's degree.
- At the University of Texas Bing met R L Moore who, after initially believing that Bing could not be any good at mathematics since he had spent years as a school teacher, soon realised that he had great potential.
- Bing worked for his doctorate under R L Moore's supervision, undertaking research on simple plane webs.
- He wrote a paper on the work of his thesis which was published in the Transactions of the American Mathematical Society but although it was a fine piece of mathematics it was not of much interest to mathematicians at the time.
- When he had me write things, he wanted it in his own way rather than in mine.
- Moore felt that if it was said correctly, it didn't really matter whether or not it was easily understood because it was the reader's responsibility to dig it out.
- My feelings were that we should say things, often repeatedly, in an effort to make it more understandable.
- In 1943 Bing was appointed as an Instructor at the university of Texas.
- He completed work on his doctoral thesis and was awarded a Ph.D. in 1945.
- He continued to work as an Instructor at the University of Texas until he was offered the position of Assistant Professor at the University of Wisconsin.
- He had been invited by Lefschetz to join the Faculty at Princeton but only on the condition that he gave up topology which Lefschetz at this time seemed to consider as having little future.
- Bing declined preferring the offer from Wisconsin.
- He took leave of absence in 1949-50 and spent the year visiting the University of Virginia.
- At Wisconsin Bing was promoted to Associate Professor and then full Professor.
- He spent the year 1957-58 visiting the Institute for Advanced Study at Princeton, returning to Wisconsin to spend two years as Chairman of the Mathematics Department there.
- He made further visits to the Institute for Advanced Study at Princeton in 1962-63 and in 1967.
- At Wisconsin, he was appointed Rudolph E Langer professor in 1968 then, in 1973, he returned to the University of Texas, being Chairman of the Department of Mathematics there from 1975 to 1977.
- He held a chair at the University of Texas until he retired in 1985.
- Bing's work on topology ranged across many different areas of the subject.
- He wrote papers on general topology, particularly on metrization; planar sets where he examined in particular planar webs, cuttings and planar embeddings.
- He worked on topological classification of the 2-sphere, the 3-sphere, pseudo arcs, simple closed curves and Hilbert space.
- He studied partitions and decompositions of locally connected continua.
- He considered several different aspects of 3-manifolds including decompositions, maps, approximating surfaces, recognizing tameness, triangulation and the Poincaré conjecture.
- Bing published The geometric topology of 3-manifolds in 1983.
- Virtually everything that is known about 3-manifolds from the standpoint of geometric topology is included here.
- One has wild surfaces, the Schönflies theorem, triangulation, Dehn's lemma, the shrinking criterion, linking, the loop theorem, covering spaces, as well as the important side approximation theorem.
- Many of these results are applications of the side approximation theorem.
- The exposition is excellent and the student (not to say the teacher) would find the book understandable and stimulating.
- Bing served the American Mathematical Society in a number of ways.
- He served on the Council in 1952-54, he was Colloquium Lecturer in 1970, and served as President in 1977-78.
- He also served as President of the Mathematical Association of America in 1963-64 and as Chairman of the Division of Mathematics of the National Research Council in 1967-69.
- Among many honours he received was election to the National Academy of Sciences in 1965 and the Distinguished Service to Mathematics Award from the Mathematical Association of America in 1974.
- He left topologists a treasure-trove of theorems and techniques and left the University of Texas Mathematics Department with a goal and thirteen years of good progress toward it.
- He was a man of strong character and integrity who liked to understand things for himself.
- For example, he never claimed to understand a theorem unless he personally knew a proof of it.
- He made decisions based on his own experience - relying on his independent judgment of a person or a cause whenever possible, rather than averaging the opinions of others.
- He was a kind man and respected people for their own merits rather than measuring them on a single scale.
- He suffered from cancer and heart troubles during his last years; but he never complained about his health problems nor did he allow discomfort to dampen his enthusiasm and good spirits.
- He was an exemplary person.

Born 20 October 1914, Oakwood, Texas, USA. Died 28 April 1986, Austin, Texas, USA.

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Origin Usa, Topology

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive