From the Origin

From the Origin provides a forum for lively discussion of issues of importance to the mathematical community. The Michigan Section­MAA Newsletter solicits opinion pieces for publication in this column from anyone in the Michigan mathematical community. In addition, comments on pieces published in earlier issues are welcomed.

Items for From the Origin should be submitted to the editor by the beginning of October to be considered for inclusion in the December issue and by the beginning of February for the April issue. Main opinion pieces should be at most 1800 words long, and responses at most 400. The editors reserve the right to shorten responses, if necessary, in order to fit as many as possible within the available space.

Paul Erdös diedor as he would say, "left"in September at the age of 83. He was a frequent visitor to our state and had many friends, colleagues, co-authors, and acquaintances here. In this issue's From the Origin column, long-time friend and co-author Allen Schwenk (WMU) shares some of his favorite Erdös stories in an essay he calls Remembering Uncle Paul.

For the first six or eight years of our acquaintanceship, Paul always greeted me the same way, "Hello, where are you now?" Since I remained at the Naval Academy for that entire time, I thought this question was strange, until I realized that while he recognized my face as a mathematician, he couldn't place my name. The question gave him the vital clue he needed to identify me. Later, when my identity was secure, the greeting changed to "Hello, how are your boss and epsilons?"

Paul had the quaint custom of calling wives, husbands, and children bosses, slaves, and epsilons. Unfortunately, in our PC world this became unacceptable. With some effort his close friends broke him of the habit. "Paul, you mustn't say 'boss' and 'slave'. Young professional women find it offensive, and others don't approve of treating slavery so lightly." "But don't they understand that this is just a harmless joke I make?" "Yes, they understand, but they don't think it is funny." Fortunately, epsilons remain socially acceptable.

Once at a conference in Hayward, California, Uncle Paul, Frank Harary, and Vera Pless were interviewed on the radio by a local disk jockey. I must credit the interviewer for struggling mightily to find good questions to try to convey just what it is that these famous people do. Finally, just a little sheepishly, he asked Paul, "This may be a silly question, but if I were to give you two four-digit numbers, would you be able to multiply them together in your head?" "Not any more," Paul responded without missing a beat, "but I could do it when I was four!"

Paul's knowledge of the literature is legendary. Once my student Hang Chen explained the obscure problem he was working on involving degree sequences that share a prescribed set of "common moments". Paul closed his eyes for a minute, and then seemed to be reading from a card catalog. "If you look in a certain [Paul was specific, but I can no longer remember] Hungarian journal from 1947 for an article by a Chinese mathematician named Hua, you

will find work related to your question." We went to the library together and went straight to the source. Paul was exactly rightit was the reference we needed.

On another occasion, at a Kent State conference, I saw Paul drifting off in the front row. "The old boy can't keep up any longer," I thought to myself. "He should go back to his hotel room and take a nap." Then the applause ending the talk awakened him. He stirred himself and told the speaker, "This is a very interesting problem you have. If you go to such and so journal in such and so year and look for an article by so and so, I think you will find something similar to your work." And no one doubted that it would be so.

Paul had unique views on life. Once he asked me to drive him to the home of Dr. Gellert, his surgeon. The Gellerts were good friends as well. As we entered, their small dog yapped and snapped at our ankles. "Do not eat me, little dog," Paul said. "I am old and my legs are skinny and tough. They will not taste very good." Later in the car he reflected on this experience. "Many people have these little animals living in their houses. This I do not understand."

In spite of years of continuous experience, Paul never mastered the mechanical features of using an overhead projector. He could never find the on-off switch himself. Once in Atlanta he was speaking and had positioned the transparency carelessly on the glass. As he wrote n log n, the n appeared at the edge of the transparency and the log n was on the glass. He then slid the transparency up a bit. When he looked back at the screen, he noticed the log n was mysteriously missing, so he wrote it a second time on the glass. Again he moved the transparency. I could see it coming. He wrote log n for the third time on the glass, and complained that something was wrong with this machine.

Mechanical things were not his forte. Once I took him back to his hotel and asked how he liked the room. "It's fine. There is a nice desk, but I can't use it because I can't turn the lamp on." I walked over to the lamp. Feeling the neck, I found no switch, so I looked at the base, finding a small brass knob. I turned on the lamp. "That's remarkable," he admired. "Show me how you did that!" This may be the only time I ever impressed him with my ability.

Paul wanted to work so single-mindedly at math that his visits were exhausting for us. Once Ron Graham remarked "Paul visited for a month last week." Paul was often irritated when I had to excuse myself to teach a class. Even worse was when I claimed to need time alone to "prepare for class". "Why must you prepare?" he would ask. "Can't you just go in and talk about math?" At midnight I once begged off further discussion saying I had a class to teach in the morning. I wonder how long Paul would have continued.

We tend to think of him as having no hobbies or interests outside of mathematics. But I have seen him many times at a dinner seated near a spouse of someone. Upon learning what he or she does, Paul would converse on astronomy, archeology, art, music, paleontology, history, psychology, or world politics. In every case he knew specific sources and names, to the surprise of the guest. He always knew more than I did on every subject.

Paul last visited Kalamazoo to attend our international conference June

2­7, 1996. On Thursday morning at the conclusion of one of the principal talks, I noticed that in the second row, Paul didn't look well. Roger Entringer and Gary Bloom had already noticed his condition, and were holding him by the arms, when his head dropped to his chest and his body went limp. Only their support kept him from falling. They lowered him into a chair, and I ran to call for an ambulance.

In the emergency room at the hospital, I think Paul was the only one who wasn't worried. In between questions from the attending physician about his medical condition, Paul would ask various mathematical questions of the assembled professors (his co-authors Ralph Faudree, Ron Graham, John Selfridge, and me). "Ralph," he would say, "I was thinking about that problem we discussed earlier. Have you tried this approach?"

Yousef Alavi, who had been supervising Erdös's heart condition for several years, arrived, and the doctor asked Paul if he minded discussing his condition with so many visitors present. "Of course it's OK," Paul remarked. "These are my friends." It seemed Paul was in need of a pacemaker. He said, "Well, I have to go to Philadelphia next week, and then on to Israel. Maybe when I return to Hungary I can have it done." Alavi, Graham, and Dr. Gellert convinced him it needed to be done that day. But Paul refused to spend the night in the hospital. Finally they reached an agreement. The pacemaker was inserted that afternoon, and Paul was permitted to attend the conference banquet that same night with Gellert and Dr. Khaghany, another cardiologist friend of Alavi's, attending as well, seated on either side of Paul.

After dinner, Paul got up in his characteristic style and said, "I always make this joke. 'You can hold the next conference in my memory.' This time, you almost did." He went on to add, "I was wondering about a question raised by Ringel's talk this morning. Is the following a sensible question: . . . ." I recognized that he was raising a relevant question from the moment he had passed out.

That Friday he needed to have the new pacemaker assessed. Yousef and I accompanied him. The technician removed his bandages. She tried to be most gentle. You could see that his chest was bruised and swollen around the incision, as if he had been beaten badly. She apologized, "I am sorry if I hurt you." "It's no problem," Paul assured. "But this has to hurt you," she insisted. "I can see that I am pulling out your chest hair." Paul's reply: "Well yes, it does hurt, but it is trivial."

As Paul Erdös now becomes part of history, I feel fortunate to have had the opportunity to know him personally. I think he was the most gentle and generous person that I have ever met. As someone wrote, Paul considered personal property a nuisance. He had virtually no possessions beyond what he carried in his suitcase, and he often gave away to struggling graduate students what money he had access to.

Paul would always leave Kalamazoo saying, "If I live, I will return in October (or whenever) ." At first this struck me as a macabre focus on death. But I came to appreciate it as using humor to overcome our fears. After a while I started answering, "And if I live, I will be here to greet you."

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