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Uncle Paul
By Mari Bengston
3/27/07
Uncle Paul
People throughout the world seem to hold a strange affection for the quirky geniuses of the human race. Whether it is the solitary creature of Henry David Thoreau or the wild haired, E=mc² touting Albert Einstein, people love to hear the intimate stories of men or women who have revolutionized modern man’s beliefs in the structure of their world. One of the quirkiest and most interesting would have to be the mathematician Paul Erdös. As one of the most remarkable mathematicians of the 20th century, Paul Erdös led a unique life, which enabled him to travel the world and to heavily contribute to several different fields of mathematics.
Even Paul’s birth in Budapest, Hungary on March 26th 1913 greatly shaped the tenor of his life. Just one day after Paul’s birth, his two older sisters died from scarlet fever leaving a huge scar upon his mother’s psyche. Paul’s mother, Anna Erdös, and father, Lajos Erdös, were Secondary Math Teachers in Hungary. At the time of WWI, Paul’s father was deployed to the front and was subsequently captured by the Russians. He spent 6 years in Siberia at which point he taught himself English. Upon his return to Hungary, Lajos taught Paul how to speak English. Paul would joke that the reason for his thick accent was because he learned to speak English from a non-native English speaker.
While his father was away Paul’s mother taught school in a nearby town leaving Erdös to be raised by a German governess. Erdös would spend the time counting the days until his mother would return. His genius for numbers shown through at this time as he would multiply two four-digit numbers in his head or he would amuse adults by asking them how old they were and then he would calculate their age in seconds. Erdös calculated the distance from the Earth to the Sun when he was three years old by asking his mother how long it would take to get their by train.
In 1919, Hungary began a long stretch of political problems that would come to affect Erdös throughout his life. The communists were trying to gain power as well as an increase in the social uprising against the Jewish community. At this time, Erdös’ mother was the principal of her school. She was told to strike against the communists but refused because she felt that the students’ education was too important to be interrupted (3 pg 69). As a result, Erdös’ mother lost her job and failed to gain another one until 26 years later (3 pg. 69). It was at this time that his mother’s scar from loosing her daughters had time to amplify. All of her time and commitment was then placed upon Paul, through home schooling and devotion to Paul’s basic needs.
His mother catered to Paul to the point that he was unable to perform even the simplest tasks or at least he felt that other people should do it for him. Even up through his high school years Erdös’ mother would bathe, dress and feed him. He was well into his twenties before he had to butter his own bread. Due to his mother’s fear of germs, Paul never attended primary school and only attended every other year of high school. This did not hinder Erdös’ math ability.
Erdös met one of his good friends, Andrew Vázsonyi, because of his genius. Andrew’s father was a cobbler and lived in the same town as Erdös. He wanted his son to be a genius as well so he had Erdös come over to talk about math with his son (1 pg. 120). Andrew remembers the story quite well of his first meeting with Erdös:
“I was sitting at the back of the shop one day, when Erdös knocked at the door and
entered. ‘Give me a four digit number,’ he said. ‘2,532,’ I replied. ‘The square of
it is 6,411,024. Sorry, I am getting old and cannot tell you the cube,’ said he. In
retrospect it is funny to see that Erdös during his entire life, even in his youth,
referred to his old age, his old bones, etc. …[Paul said] ‘I must run,’ and with that
he left. At that moment Kathy, the sales woman in the store, asked me who the
weirdo was. Puzzled I asked ‘why?’ ‘I have never met anyone who knocked at the
door of a store before entering,’ she replied” (1 pg. 120).
This conversation was quite typical of Erdös who would immediately jump into mathematical proofs or problems at the beginning of any of his conversations. Even his letters followed the same format of “Dear John, suppose n is a natural number…” For Erdös the only thing of importance was mathematics, everything else was just “trivial.”
At the time when Erdös was “attending” high school, the Hungarian government wanted to increase the number of “mathematical geniuses” in the country, so as a way to discover mathematical talent in the country several local papers dedicated only to math were created which would pose mathematical questions and would offer a prize (published credit in the paper) if the students would answer the questions correctly. Erdös and several others who would later become his friends, worked hard to be one of the chosen few who could publish in their local paper, Matematikai es Fizikai Lapok (MFL).
One of Erdös’ early contributions of a simplified version of the proof for Chebyshev’s Theorem was so elegant but yet visionary that several of the leading mathematicians at the paper did not want to include it in the paper because they didn’t think it was correct. It was only after László Kalmár took the time to study the proof that it was deemed correct (1 pg. 121). The proof led to Erdös’ acceptance into the University Pázmány Péter in 1930 (4). This was a great feat since the universities in Hungary had quotas for the maximum amount of Jewish students that were allowed to attend the university. Paul studied for 4 years and graduated with his BA and his PhD, becoming the youngest person in Hungarian history to get his PhD in Mathematics (1 pg.126). While attending University, Paul and several of his friends would spend hours contemplating math theorems and problems. One of their favorite places to think was at a statue in a park near campus. The statue was called “Anonymous” after a great Hungarian, Medieval historian. Several great mathematicians worked in this study group, among them were Andrew Vázsonyi, Esther “Epszi” (short for Epsilon) Klien, and György “George” Szekeres (3 pg. 74). Paul started the habit of calling each other by the names they used on their proofs such as “E. P.” for Epszi or “Szekeres Gy.” for George (3 pg. 74, 76).
This was not the first time Erdös created nicknames. In fact Erdös created a new language mainly using mathematical terms in place of words or by distorting the nicknames that other people used. Part of the reason behind this was due to the large number of spies in the country at the time. Since his countrymen and even his fellow mathematicians were arrested due to political disagreements with the government, Erdös started using “code” when he spoke. Some of the political code words translated into “sam” or “samland” as the US or “joe” or “joedom” for the USSR. When a person was a communist they thought “along a long wavelength” since the predominant color for communism was red and red wavelengths are long in the color spectrum for light. When a person was put in jail they were “studying the theorem of Jordan” where they “verified that the interior of a prison cell is not in the same component as the exterior” which was also known as the “Jordan curve theorem” (6 pg. xx).
Not all of Erdös’ words were political. Erdös absolutely loved to entertain “Epsilons” and “Epsilons squared” (children and grandchildren) by showing off his quick reflexes with his trick of catching a quarter before it hit the ground after he dropped it from his shoulder. Erdös always worked with “noise” (classical music) and from time to time he would enjoy an “epsilon of poison” (a small amount of alcohol). Out of the love for his mother, Erdös inverted the popular belief in Hungary of men as “bosses” and women as “slaves” preferring to call men “slaves” and women “bosses.” One of the most hideous things a mathematician could do would be to “die” (stop working on math) and those mathematicians who “left” actually died.
Anything and everything that was bad would be “Fascist” with God as the “Supreme Fascist” or “SF.” If anything went wrong Erdös would blame it on the SF such that if he lost his passport it actually was the SF that hid the passport from him. Erdös felt that we (humans) were involved in a game with the SF where the SF would gain points based upon our behavior. “If you did something bad” then the SF would gain 2 points (2). “If you don’t do something good which you could have done” then the SF would gain at least 1 point (2). “If you are ok” then zero points are awarded (2). The entire purpose of life was then to “Prove and conjecture and keep SF score low” (2).
Another aspect of the SF is the “Book” which holds all of the possible mathematical proofs in their most exquisite form. Erdös strove to find the most elegant proof, which would be known as the “Book proof.” The highest compliment Erdös would give another mathematician would be “that proof is straight from the book” (1 pg. something). Vázsonyi joked that Erdös said “God has the Big Book; the beautiful proofs of mathematical theorems are listed here” and Vázsonyi’s response was “Lucifer has a Little Black Book; all beautiful theorems for which God has no proofs are listed here” (1 pg. 131). Any proofs that had been proven in Vázsonyi’s eyes moved from the Little Black Book to the Big Book.
Erdös finished his education with an invitation to Manchester in the late 1930’s at the urging of Professor Mordell “for a four- year postdoctoral fellowship” (3 pg. 78). It was at this time that Erdös met G. H. Hardy and worked with him. Erdös’ feet begun to itch, with his trip to the UK, leading him to a lifetime of travel. It was not uncommon to have Erdös travel to England for 3 days, to Budapest for a month, then to Australia (“Land of Ned”) for a week, then China for 10 days and on and on. Erdös did not own his own place; in fact he didn’t even have a job (apart from being a guest lecturer “preacher”).
His constant traveling and lack of a committed home often would get him into trouble. Erdös and other Jews were being “encouraged” to leave Hungary in the late 1930’s, which was another reason why he ended up going to Manchester (4). During the time of the creation of the atom bomb, Erdös traveled to the US along with several other prominent mathematicians. Unfortunately he was never allowed to work at Los Alamos because he professed that he missed Hungary (3 pg. 98). Not only that but in 1941, Erdös, Arthur Stone, and Shizuo Kakutani had gone for a walk in order to discuss mathematics. They were so engrossed in math that unfortunately none of them noticed a keep out sign and they ended up walking next to a “military radio transmitter,” which “actually may have been a secret radar facility” (3 pg. 99). Their arrest made front-page news marking them as alien spies even though the FBI looked into their story and discovered they were not spies.
In the 1950’s, Erdös ran into trouble again. With the McCarthy red scare in the US, he became a suspected communist due to his frequent visits to his mother in communist Hungary and the US denied his return visa. In typical Erdös fashion, when the US “asked him whether he was a communist,…he said it depended on what they meant by being a communist” (1 pg. 129).
Erdös preferred to travel from one mathematician to another and make himself the unintended houseguest. One place he did stay the most was in CA with Fan Chung and Ron Graham. In fact Ron became Erdös’ unofficial assistant often receiving Erdös’ mail, writing his checks, and housing his published and unpublished papers after Erdös’ mother passed away. Erdös would always travel with two half-empty suitcases (all of his possessions that he had in this world) and would show up on someone’s doorstep asking if their “brain was open.” Erdös became the intellectual bee that traveled from place to place spreading knowledge (2).
When he stayed with other mathematicians he would expect them to care for him by feeding him or laundering his clothing. Reported to be an “early riser” Erdös would either refuse to eat until the owners of the house had come down to fix his food for him or he would wake them in order to get them to feed him. One time when Erdös was staying with Andrew Vázsonyi, he refused to eat until Andrew’s wife, Laura, fixed Erdös a breakfast of “toast, choice of cereal with brown sugar, raisins, nuts, and jam, and an egg, however he wished, and sat down with him” while he ate (1 pg. 127). Another time Erdös was staying with one of his favorite couples Fan Chung and Ron Graham and wanted Graham to fix breakfast for him at 5:00AM. So Erdös banged around in the kitchen until Graham got up and Erdös asked him if he had grapefruit fully knowing that Graham did and where it was located (3 pg. 20). Trying to get Erdös to fix the grapefruit on his own Graham told him that it was in the refrigerator (3 pg. 20). Erdös took the fruit and a butter knife and tried to saw his way though until Graham picked up the fruit and fixed it himself (3 pg. 20). Even Graham knew that it was just an act as he explained
“It can’t be by chance…that he so often used the dull side of the knife, trying to force
his way through. It’ll be squirting like mad, all over himself and the kitchen. I’d say,
‘Paul, don’t you think you should use a sharper knife?’ He’d say, ‘It doesn’t matter,’
as the juice shoots across the room” (3 pg. 20).
Erdös had other needs that he required his fellow mathematicians to provide. He didn’t know how to drive leaving his boarder to shuttle him around the town. If the boarder couldn’t do it at the time that he needed then Erdös would just call another mathematician in the area and they would shuttle him around. For a while he reluctantly had a girlfriend, which he used to chauffeur him around. The relationship was purely platonic and he called her OW (other woman – other than his mother). As a matter of fact one time Paul, OW, Vázsonyi, and Laura had to stay at a hotel. There were only two rooms left at the hotel and Paul pitched such a fit at having to share a room with OW that he went to another hotel to get a room (1 pg. 138). Ironically, as he grew older, Paul would take his mother with him as he traveled. She would pitch a fit about the hotel room until Paul would order a cot and sleep in the room with her (1 pg. 138). In the end there was only room in Paul’s life for one woman (his mother) so OW decided to quit being used and left Paul who didn’t seem to even notice that she had left.
Erdös worked constantly through most of the night and would need little amounts of sleep. Unfortunately for the mathematician whom he was staying, Erdös would hold the mathematician to the same working hours as Erdös. Paul was also known to just invite other mathematicians (known as “Paul Sitters”) to come and stay at the house because he was lonely fully expecting the owner of the house to welcome these new additions until Erdös grew tired of them. Paul would soon wear out his welcome, especially with the wives of the mathematicians since they spent most of the time taking care of him and would stay at the place until they told him to move on. Then he would quite happily move into a nearby hotel to stay until he was finished.
Erdös was known as the “Bob Hope of Mathematics” (2). He had a few standard jokes which he would tell during his lectures and which he had perfected to a “T”. One of his jokes came from his self-anointed title: Paul Erdös pgom ld ad ld cd. Even as a young man Paul joked about his old body and aching bones. The “pgom” refers to “poor great old man” which was his main title. The first “ld” refers to “living dead” which he gave himself after the age of 60. When he turned 65 he added “ad” or “archeological discovery.” With the 2nd “ld” he called himself “legally dead” at the age of 75. The final “cd” at the age of 75 means “counts dead” because the Hungarian Academy of Sciences no longer counts their members as a member after the age of 75 revoking all of their privileges (3 pg. 12).
As fascinating as his lectures were, Erdös’ real contribution to the world was through his mathematics. Erdös wrote or coauthored a known 1525 papers with some of the greatest mathematicians in the world (12). He potentially has over 100 more papers that have yet to be published or that have been lost bringing his total to well over 1600. Although he is not the most prolific in history, Erdös contribution is unusual since it spans several different mathematical disciplines. Erdös has made contributions to
“almost every domain of the theory of numbers, in set theory and combinatorics, in the theory of designs, graph theory, probability and its applications (to number theory, group theory, and generally to the study of random structures), in real