Paul Erdös, a Hungarian mathematician, consecrated his whole life to mathematics to the exclusion of any other activity except eating and sleeping. Instead of greeting friends with a “Good morning”, his greeting was, “Is your brain open?”, and he went on, “Let k be the smallest integer that…”, and so on for hours, at any time of the day or night. His letters from any part of the world followed the same pattern: “I am in Australia. Tomorrow I leave for Hungary. Let f be a function of x such that…”
All small children were for him “epsilon”, which is the mathematical symbol for a small quantity.
Once he went for the bar mitzvah of a friend’s son, notebook in hand, and he proved several new theorems during the ceremony.
He used to say “Television is something the Russians invented to destroy American education.”
To a friend who asked him how often should he have sex with his wife in order to combine continuity with variety he gave this advice: “Do it on the days of the month that are prime numbers; thus you get more frequency at the beginning of the month, 2, 3, 5, 7, and wider intervals at the end, 21, 29.” (1 is not a prime number). About himself he candidly reported he never had had sex in his life. He had no time.
When teaching in Notre Dame in 1952 he was assigned an assistant who could take over on the spur of the moment should he have the urge to rush off and finish a proof with a collaborator.
His mathematical friend and fellow Hungarian Stanislaw Ulam was in danger of his life for a brain haemorrhage. Erdös visited him in hospital when recovering and greeted him: “Stan, I am so glad to see you are alive. I thought I would have to write alone now all our joint papers, and besides… I would have to write your obituary!”
His Memphis colleague, Chip Ordman, writes about him: “He began to lose sight in one eye, but didn’t want to take time out from mathematics to get the requisite care. Eventually he lost all vision and badly needed a corneal transplant. A suitable donor was hard to come by. They jumped the queue by pleading that surgery will advance all of mathematics. The transplant took about two hours. Before the operation, the doctor carefully explained to him the procedure. ‘Doctor’, Erdös said, ‘will I be able to read?’ ‘Yes’, said the doctor, ‘that is the whole point of the surgery.’ Erdös went into the operating room, and when the lights were dimmed, he immediately got agitated. ‘Why are you turning the lights down?’ ‘So we can do the surgery.’ ‘But you said I’d be able to read.’ He then had a huge argument with the surgeon since, he said, while one eye was being operated he could read a mathematics journal with the other eye. The surgeon made a series of frantic calls to the Memphis math department. ‘Can you send a mathematician over here at once so that Erdös can talk math during surgery?’ The department obliged, and the operation went smoothly.
He then carried on with mathematics in his hospital room. The room was a complete mess. There were journals piled up and papers everywhere. Erdös was lying there, holding three mathematical conversations at once, in Hungarian with a group in one corner, in German with a group in another corner, and in English with a third group. All this while talking to me and my wife. The doctors came in and he said, ‘Go away! Can’t you see I am busy? Come back in a few hours.’ That’s what they did.”
About halfway through his lecture in the International Symposium on Combinatorics, Graph Theory, and Computing in Boca Raton, Florida, 1996, he got up to write at the blackboard and suddenly fell down stiff as a board. His blood pressure was very low, his heart rate down to 37. He was lying there flat but with his microphone still attached. People were scared and anxious and security was trying to get them to file out. “Tell them not to leave”, he said, regaining consciousness, “I have two more problems to tell them.”
He was listening to Gerhart Ringel, a mathematician from Santa Cruz, deliver a talk at a conference in Kalamazoo, Michigan. As the talk ended and people were leaving, Erdös, who was sitting in the front row, quietly asked him a question. In the middle of his question he fell over and was out cold. By late that morning, surgeons had put in a pacemaker. Sure enough that very evening Paul attended the closing banquet. His two heart surgeons were sitting next to him. Erdös got up, took a little bow, introduced the surgeons, and then said, “Now I just want to finish asking Dr Ringel my question.”
Eye ailments and heart problems did not stop him from resuming his twenty-five-country lecture circuit. He observed that the audiences for his talks were growing to the point where to accommodate everybody he would need a larger lecture hall, but then his old and feeble voice would not carry. He speculated on the reason for his increased popularity: ‘Everyone wants to be able to say, “I remember Erdös. Why, I even attended his last lecture”.’
In perhaps the most famous speech in mathematics, at the Second International Congress of Mathematicians held in Paris in 1900, David Hilbert posed twenty-three problems that he said cried out for solution in the new century. First on his list was the proof of the Continuum Hypothesis. Georg Cantor (1845-1918) had investigated infinite sets, arriving at the conclusion that there are an infinite number of infinite sets infinitely different from one another. The first one is the arithmetical infinite of natural numbers which Cantor baptised as aleph-null. The next one is the geometrical infinite of the real numbers, aleph-one for the initiated. And from there on to the whole spontaneous generation of alephs of all colours and sizes. Quite a tribe.
Now here comes the question. A very simple question. Aleph-one is greater than aleph-null. Is there now another aleph between them, bigger than the first and smaller than the second? Something to lose one’s sleep about. Cantor had conjectured there was no such set in between, but he had no proof and nobody had found it. That is the famous Continuum Hypothesis. In 1963, Paul Cohen stunned the mathematics community with a proof that the Continuum Hypothesis could never be proved nor disproved. For that mathematical feat he was awarded the Fields Medal (which is the mathematical Nobel Prize) in the Congress of Mathematicians in Moscow, 1966. (I was there at the time as an Indian delegate to the Congress, and that’s why I now grow reminiscent as I think of it. My hands hurt from so much clapping.) And here comes Erdös.
Erdös was worried about the Continuum Hypothesis, and was not quite convinced that Cohen’s solution was right, or rather, he could not resign himself to admit that something in mathematics could not be proved nor disproved; that hurt his dignity as a mathematician. His way out was to tell the joke about the evangelist who is trying to convert people asking them on the street, “What would you say to Jesus if you saw him now on the street?” Erdös said he’d ask Jesus if the Continuum Hypothesis was true. “And there would be three possible answers for Jesus”, Erdös said. “He could say, ‘Paul Cohen already taught you everything which is to be known about it.’ The second answer would be, ‘Yes, there is an answer but unfortunately your brain isn’t sufficiently developed yet to know the answer.’ And Jesus could give a third answer: ‘The Father, the Holy Ghost, and I have been thinking about that long before creation, but we haven’t yet come to a conclusion’.” This would be the best answer, according to him, as it would assure us eternity in heaven was going to be mathematically enjoyable.
When he was 81, he said: “Probably I am a perfect square for the last time in my life.” He was referring to the fact that 81 is 9 square, while the next perfect square would be 10 square, that is 100. He died at 83 in 1996.
(Paul Hoffman, The man who loved only numbers, Hyperion, New York 1998, pp. 3, 6, 9, 16, 35, 104, 127, 176, 225, 242, 244, 245).
