The Kline Sphere Characterization Problem, 1945

Shortly after he received his Ph.D. in May 1945, Bing authored the paper that marked him as a promising young mathematician. Bing solved the Kline Sphere Characterization Problem, a problem whose solution had eluded many accomplished mathematicians.

"In one case, shortly after I received my degree from [Moore], I proved one of the big theorems that had been baffling quite a few people; namely, the Kline sphere characterization. After writing this up, I submitted it as an abstract to the American Mathematical Society and also to a journal without ever having shown or discussed it with Moore. When it became known that I had announced the result, we were flooded with phone calls, telegrams, and letters—mostly addressed to Moore—asking if I had gotten the result and if it had been checked.

Moore's reply was to turn these letters over to me to be answered because he had not seen proof. Yet, he did not ask me for the proof. I think he thought that by asking me, he would show lack of confidence in my ability to check the proof myself. I also did not show him the proof because I felt that this might show that I did not have self-confidence and needed someone else to help me check the result.

At Chicago I announced the result... I do recall [a fellow mathematician] asking me at that meeting whether I had had a first-class mathematician check the proof. I rather resented this because I thought that it was a first-class mathematician who had provided the proof."