#### Richard E. Goodrick

“Many years ago, I was fortunate enough to study under R H Bing at the University of Wisconsin. His approach to teaching was most unusual and I remember one incident in particular.

“Early one morning I was awakened by Professor Bing and asked if I would like to join him traveling to a meeting about 200 miles away. I and a group of other students sat in Professor Bing’s car, while he drove at high speed down a two-lane road. Unfortunately, the windows were fogged up, but Professor Bing took the opportunity to use these windows as blackboards while driving.

“At these time, the math *Notices* had short research abstracts. So, during the trip we were quizzed as to the possible details of the results. At one point I remember blurting out something and Professor Bing was delighted that I might have filled in some detail of a proof. Actually, I was trying to say that we just sped through a stop sign.”

#### Barry C. Mazur

“Rob Kirby asked me to write a few sentences remembering the great mathematician R H Bing. I’m delighted to do so. Bing did his work blessed with a certain purity of vision and breathtaking originality. What comes to my mind, when I think of him is no specific anecdote, but rather a mood of thought: the vivacity of how he presented his ideas, and the way he savored ideas.

“His geometric insight was so powerful, so capable of being directly conveyed — almost with no technical dressing. It is the rare newly-found mathematical explanation that can be told in a single phrase; but Bing was the source of many that could. I don’t know who came up with the marvelous hint *think of a light-bulb hung from the ceiling* for the proof that it is impossible to ‘knot’ an arc that goes from one boundary component to another in __\( \mathbb{S}^2\times [0, 1] \)__. Even if this was not Bing’s idea it radiates a Bing-like style—bursting, as it does, with such simplicity and urgency.

“Perhaps irrelevantly, I also can’t help thinking of the *musicality* of his explanations. Now, surely, the way in which he pronounced the phrase ‘Antoine’s Necklace’ — with a lingering Texas twang to the ‘toine’ part — has nothing to do with his mathematics, but it works well with the way he he presented his ideas — songs that vibrate with sheer geometric insight. What muse of geometry offered those gifts to him? Each of his famous results expands our notion of what topology can do. And, thinking about them half a century after they were conceived, they remain no less astounding: Bing’s theorems are news that stays news. Who else would imagine that the topological three-dimensional sphere could be represented as the double of the bad-component complement of the Alexander Horned Sphere?”

#### Steve Armentrout

“R. L. Moore was proud of his students and he was especially proud of R H Bing.

“Shortly after he received his Ph.D., Bing solved a long-outstanding
and difficult conjecture known as the Kline 2-sphere
characterization
[e2].
In the period 1915–1920, Moore
[e1]
had developed a topological characterization of the
2-sphere. A space __\( X \)__ is a 2-sphere if and only if __\( X \)__ is a
compact, connected, locally connected metric space of more than one
point such that

- no point separates
__\( X \)__, __\( X \)__satisfies the Jordan Curve Theorem, and- each point has arbitrarily small neighborhoods bounded by simple closed curves.

“J. R. Kline, Moore’s first Ph.D. student, conjectured that the three conditions above could be replaced by

- no point separates
__\( X \)__, and - each simple closed curve in
__\( X \)__separates__\( X \)__.

“Bing planned to submit his paper to the *Bulletin of the A.M.S.*
He was
going to an A.M.S. meeting shortly and found out that the editor to whom
he would submit the paper would be at the meeting. He took his paper
with him and handed it to the editor, saying he wanted to submit it to
the *Bulletin*. When the editor saw Bing’s result he looked at Bing and
said, ‘Have you had this paper read by a reputable mathematician?’
Without missing a beat, Bing replied, ‘Yes, I have read it.’

“I can still remember the smile on Dr. Moore’s face and the twinkle in his eyes as he finished telling this story.”

#### Edgar H. Brown, Jr.

“I first met R H Bing in 1949 when I was an undergraduate at the University of Wisconsin and I took his course, Topology of the Plane, which he gave in the method of his thesis advisor, R. L. Moore. Bing gave the students four or five pages beginning with definitions of open and closed sets, etc., and a list of statements about them, some of which were true and some false; the students were to prove them or prove them false. In each class he would give a few examples and talk about the subject but didn't prove any of the theorems. Then, going down the list, day to day, the students were to prove or disprove the statements, at the blackboard. I recall that the first problem for the class was to show that the union of two open sets was open, which, after two days of proofs consisting of assertions that it was true, I proved it. The hardest one I did was that a continuous function on a closed interval is uniformly continuous. Fourteen years later, I met up with Bing at the Institute for Advanced Study and he commented that on my performance in that class he was not surprised to find me a mathematician.”