A Machine for Turning Coffee into Theorems

The Man Who Loved Only Numbers by Paul Hoffman (1998, Fourth Estate)

“A mathematician,” the Hungarian mathematician Alfréd Rényi (1921-1970) used to say, “is a machine for turning coffee into theorems.” Rényi’s colleague Paul Erdős well embodied the statement. Erdős (pronounced “air-dish”) had neither wife nor children, neither job nor hobbies. Having first played with numbers at the age of three, Erdős had, since the death of his mother in 1971, started devoting nineteen hours per day(!) to the discipline he was so obsessed with. He kept himself fortified with 10 to 20 milligrams of Benzedrine or Ritalin, strong espresso and caffeine tablets. When friends urged him to slow down, he would always respond: “There’ll be plenty of time to rest in the grave.” He passed away in 1996 while attending a conference in Warsaw, after having become one of the most prolific mathematicians in history with 1500+ published papers.

His extraordinary life is the subject of The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth, an informative and highly readable biography by the American science writer Paul Hoffman (@hoffmanpaul), president and CEO of the Liberty Science Center in New Jersey. Hoffman was introduced to Erdős in 1986 by Ronald Graham (born 1935), a close friend and collaborator of the mathematician, who has served as director of information services at AT&T, past president of the International Jugglers Association and currently teaches at the University of California at San Diego. He and his wife Fan Chung, a Taiwanese émigré and also a mathematician, would provide Erdős with a shelter and base during his stays in America.

 

Paul Erdős (Left) with Ronald Graham and his wife Fan Chung in Japan in 1986 by User “Che Graham”, CC BY 3.0, Wikimedia Commons

 

Paul Erdős in 1992 in Budapest by User “Kmhkmh”, CC BY 3.0, Wikimedia Commons

Paul Erdős was born in Budapest, Austria-Hungary to Anna and Lajos Erdős, non-observant Jews and both high school mathematics teachers, on March 26, 1913 – the very day his two sisters Klára and Magda, aged 3 and 5, died of scarlet fever. His mother, fearing childhood contagion, mostly tutored him at home. The prodigious Erdős was awarded a Ph.D. in mathematics at the age of 21 from the University of Budapest. Later, as a scholar, he remained simple and basic. “Some French socialist said that private property was theft,” he once said. “I say that private property is a nuisance.” Also, he boldly defied the stereotype of the asocial genius. He never holed himself up in a musty study, surrounded by stacks of books and papers with no living soul around. The pursuit of knowledge, for Erdős, was a group activity. Hoffman explains:

He lived out of a shabby suitcase and a drab orange plastic bag from Centrum Aruhaz (“Central Warehouse”), a large department store in Budapest. In a never-ending search for good mathematical problems and fresh mathematical talent, Erdős  crisscrossed four continents at a frenzied pace, moving from one university or research center to the next. His modus operandi was to show up on the doorstep of a fellow mathematician, declare, “My brain is open,” work with his host for a day or two, until he was bored or his host was run down, and then move on to another home.

 

Erdős’s motto was not “Other cities, other maidens” but “Another roof, another proof.” He did mathematics in more than twenty-five different countries, completing important proofs in remote places and sometimes publishing them in equally obscure journals. Hence the limerick, composed by one of his colleagues:
“A conjecture both deep and profound / Is whether the circle is round. / In a paper of Erdős / Written in Kurdish / A counterexample is found.” When Erdős heard the limerick, he wanted to publish a paper in Kurdish but couldn’t find a Kurdish math journal.

Mathematics for Paul Erdős, was the search for lasting beauty and ultimate truth. It was order at its purest; it transcended the physical world. As his life was torn asunder by the major political dramas of the twentieth century – the Communist revolutions in Hungary, the rise of Fascism and anti-Semitism in Europe, World War II, the Cold War and McCarthyism, Erdős never lost sight of that elusive yet definite branch of study. It was his anchor, tells Hoffman, “in a world that he regarded as cruel and heartless, although he believed in the goodness and innocence of ordinary individuals.” In addition to being reliable and unambiguous, mathematics was a tremendous unificatory power. Violence and disruption could continue, but here was something that could and would always bring and hold together the most diverse of peoples and cultures. The aim of life, Erdős emphasized, was to prove and conjecture. “Mathematics is the surest way to immortality,” he’d say. “If you make a big discovery in mathematics, you will be remembered after everyone else will be forgotten.”

 

Soviet tanks in Budapest during the Hungarian Revolution of 1956 by Nagy Gyula uploaded by User “Fae”, CC BY-SA 3.0, Wikipedia. Hoffman writes: “In 1955, two years after Stalin’s death, Erdős visited Hungary when well-connected friends, arguing that Erdős was a singular asset to the world culture of mathematics, convinced the government to grant him a special passport that said he was a Hungarian citizen but acknowledged his Israeli residency…The special passport-which was granted only to Erdos – allowed him to go in and out of Hungary whenever he pleased. In 1956, a pro-democracy revolution in Budapest was crushed by Soviet tanks. The new Soviet-installed dictator, János Kádár, who would rule Hungary for thirty-two years, reaffirmed Erdős’s unusual passport.”

 

Erdős spoke his own language. In Erdősese, the United States was “Samland” (for Uncle Sam), the USSR was “Joedom” (for Joseph Stalin), women were “bosses”, men were “slaves”, alcohol was “poison”, music was “noise”, children were “epsilons” (the Greek alphabet used to denote small quantities in calculus).

 

In this photo from 1985 taken at the University of Adelaide, Paul Erdős – who loved “epsilons” – explains a problem to the then 10-year-old Terence Tao (born 1975), an Australian-American mathematician. Photo by Billy or Grace Tao grabbed by User “PaulTheOctopus” from Tao’s Google+ Profile, CC BY-SA 2.0, Wikimedia Commons

 

Technically an agnostic-atheist, Erdős had a perversely comic name for God – SF – the Supreme Fascist. “With so many bad things in the world,” he would say, “I’m not sure that God, should He exist, is good…The SF created us to enjoy our suffering. The sooner we die, the sooner we defy His plans.” This SF, though somewhat malevolent, was frustratingly, the origin and repository of all arithmetical and geometrical information. He was always tormenting Erdős by hiding his glasses, stealing his Hungarian passport and by keeping to Himself the elegant solutions to all sorts of intriguing mathematical problems.

“I’m not qualified to say whether or not God exists,” Erdős said. “I kind of doubt He does. Nevertheless, I’m always saying that the SF has this transfinite Book – transfinite being a concept in mathematics that is larger than infinite – that contains the best proofs of all mathematical theorems, proofs that are elegant and perfect.” The strongest compliment Erdős could give to a colleague’s work was to say, “It’s straight from the Book.”

“There’s an old debate,” Erdős explained, “about whether you create mathematics or just discover it. In other words, are the truths already there, even if we don’t yet know them? If you believe in God, the answer is obvious. Mathematical truths are there in the SF’s mind, and you just rediscover them.”

“The game of life,” he would repeat, “is to keep the SF’s score low. If you do something bad in life, the SF gets two points. If you don’t do something good that you should have done, the SF gets one point. You never score, so the SF always wins.”

 

Erdős considered mathematics a glorious combination of science and art. It was the science of certainty because its conclusions were logically unassailable. Unlike biologists, chemists, or even physicists, mathematicians proved things. Their conclusions follow syllogistically from premises, in the same way that the conclusion “Bill Clinton is mortal” follows from the premises “All presidents are mortal” and “Bill Clinton is a president.” Furthermore, mathematics has an aesthetic side. A conjecture can be “obvious” or “unexpected.” A result can be “trivial” or “beautiful.” A proof can be “messy,” “surprising,” or, as Erdős would say, “straight from the Book.”

 

Although Erdős avoided physical intimacy and remained celibate till the very end, he was always generous and compassionate and friendly. Whenever he learned of a good cause – a struggling classical music radio station, a fledgling Native American movement, a camp for wayward boys, an Israeli girls’ home – he immediately made a donation. Hoffman tells us:

What little money Erdős received in stipends or lecture fees he gave away to relatives, colleagues, students, and strangers. He could not pass a homeless person without giving him money. “In the early 1960s, when I was a student at University College London,” recalled D. G. Larman, “Erdős came to visit us for a year. After collecting his first month’s salary he was accosted by a beggar on Euston station, asking for the price of a cup of tea. Erdős removed a small amount from the pay packet to cover his own frugal needs and gave the remainder to the beggar.”

In the late 1980s, when Erdős heard of a promising high school student Glen Whitney struggling to put together his Harvard tuition, he made a contribution of $1000 and asked him to pay back only when it would not cause financial strain. A decade later, when Whitney had enough money and made an approach, Erdős simply told him “to do with the thousand dollars what I did.”

Learn more about this eccentric and endearing personality in the documentary and presentation below. A wonderful children’s book The Boy Who Loved Math: The Improbable Life of Paul Erdos authored by Deborah Heiligman and illustrated by LeUyen Pham was published by Roaring Brook Press in 2013. You can see samples on this post on Brain Pickings.

 

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A 1993 documentary on Paul Erdős by US writer and filmmaker of Hungarian parentage George Paul Csicsery. Used for educational purposes only. No copyright infringement intended.

 

A 2011 presentation given by Paul Hoffman on Paul Erdős at the National Museum of Mathematics in Manhattan.

 

Image Credit:

Featured: Pixabay

 

 


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5 thoughts on “A Machine for Turning Coffee into Theorems

      1. We had a family in my school with the family name of Erdos – some of the many Hungarian refugees who fled their home after the 1956 uprising. It reminded of the huge upheavals his country suffered. It would have aded to his feelings of being rootless.

        Liked by 1 person

      2. There’s a whole chapter in the book dedicated to the Hungarian experience. It mentions the devastation of WW2 but goes back to the early middle ages. “Temetni tudunk” (How to bury people-that IS one thing we know) – this is an old Magyar saying.

        I immediately thought of the national temperament of pessimism that the Hungarian painter Gyula Szabó – whom I recently featured – was speaking of: https://onartandaesthetics.com/2016/09/08/earthy-visions/

        Liked by 1 person

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