Saturday, December 28, 2013

190: Loving Only Numbers

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Before we start, I'd like to thank listeners sblack4, WalkerTxClocker, and LaxRef for some more nice reviews on iTunes.  Thanks guys!

Now, on to today's topic.   During this holiday season in the U.S., many of you are spending time with your families, and taking pity on those who don't have many relatives to visit.     (Or  taking pity on those with too many relatives visiting.)    Sometimes this might bring to mind the strange story of one  mathematician who chose never to marry or have children, instead devoting his entire life to his mathematics:   Paul Erdos, as profiled in Paul Hoffman's famous biography "The Man Who Loved Only Numbers".   Erdos was a Hungarian Jew born in Budapest in 1913.  He originally left his country out of fear of  anti-Semitism soon after receiving his doctorate, and then spent the rest of his life, until his death in 1996, traveling from university to university taking various temporary and guest positions.

There are many surprising and contradictory aspects to Erdos's life.   You would think that someone who chose not to start a family or even to settle in one place would be some kind of social recluse, but Erdos was the opposite.   He considered mathematics to be a social activity, not the domain of isolated geniuses behind closed doors.   His travels were constantly motivated by the desire to collaborate with other mathematicians, where he would help them solve particularly tough problems.   Though he wasn't the leader in any single field of mathematics, never winning the Fields Medal for example, he co-authored about 1525 papers in his lifetime, with 511 different co-authors.   Despite being very odd, and sometimes coming across like a homeless drug addict due to his lack of social graces, he was very popular and well-liked in the mathematical community. 

Due to his large number of co-authors, the concept of an 'Erdos Number' became a common in-joke in the math world.   If you wrote a paper with Paul Erdos, your number was 1.  If you wrote a paper with a co-author of his, your number was 2, and so on.  It is said that nearly every practicing mathematician in the world has an Erdos number of 8 or less.  Incidentally, I found a cool Microsoft site online (linked in the show notes)  to search for collaboration distances between two authors, and found that despite being an engineer rather than a mathematician, I have the fairly respectable Erdos number of 4.   Perhaps the most famous person with a low Erdos number is baseball legend Hank Aaron.   Since he and Erdos once signed the same baseball, when they were both granted honorary degrees on the same day and thus were sitting next to each other when someone requested an autograph, Aaron's Erdos number is said to be 1. 

But as you would expect with someone who constantly travelled and never settled down, Erdos had a rather quirky personality that people who worked with him would need to get used to.   He had his own unique vocabulary, for example.   Children would be referred to as "epsilons", referencing the Greek letter typically used to refer to infinitesmally small quantities.   Women and men were "bosses" and "slaves", while people who got married or divorced were "captured" and "liberated".    Perhaps this reflected an internal attitude that negatively impacted his potential for dating, even if he had ever given a thought to such things.    If someone retired or otherwise left the field of mathematics, Erdos would refer to them as having "died".   At one point he was very sad about the "death" of a teenage protegee, having to clarify to symathetic friends that the cause of death was his discovery of girls.    The United States and Soviet Union were "Sam" and "Joe".   He referred to God as the "Supreme Fascist" or "SF" for short, apparently in protest at being expected to obey the will of divine beings. 

Related to proving mathematical results, Erdos had one piece of private vocabulary that was very important to him.   He always imagined that somewhere up in the heavens, God had a Book in which were listed the most elegant and direct proofs for every conceivable mathematical result.    He wasn't sure if he believed in God, but he definitely believed in the Book.    So if he heard a solution to a problem that he liked, he would always say, "That's one from the Book".   And if he heard a proof that was valid but seemed very awkward or roundabout, he would acknowledge its validity, but still want to search for the one in the Book.   A classic example of a non-Book proof might be Andrew Wiles's famous proof of Fermat's Last Theorem:  while it was fully valid and a work of genius, it took hundreds of pages and is understood by very few people in the world.   Many still hope that a more elegant solution is out there somewhere, waiting to be found.

Despite Erdos's genius and his sociability, there were many aspects of modern life that either baffled him, or were simply considered beneath his notice, and as a result he constantly depended on his many friends to help him get by.   He didn't learn to butter his bread until the age of 21, for example, and always needed help tying his shoes.     If left alone in a public place, he would panic and have a lot of difficulty finding his way back to his university or hotel room.    If he suddenly thought of a solution to a problem he had been working on, he would call his colleagues at any hour of the day or night, with no consideration for whether it might be a convenient time.    He didn't like owning anything, travelling with a single suitcase and requiring his hosts to wash his clothes several times per week.  (It always had to be his hosts doing the washing, since he never bothered to learn how to use a washing machine.)    The last novel Erdos read was in the 1940s, and he did not watch movies since the 1950s.

On the positive side, his lack of concern for money made him quite generous to fellow mathematicians and others in need.   When he won the $50000 Wolf Prize, he used most of the money to establish a scholarship fund in Israel.   He would sometimes give small loans of $1000 to struggling students with strong potential in math, telling them to pay him back whenever they had the money.   At one point he was seen to take pity on a homeless man just after cashing his paycheck:  he took a few dollars out of the envelope to meet his own needs, then handed the rest of the envelope to the stunned beggar.    In addition, Erdos would put out "contracts" on math problems he wanted help solving, ranging from $10 to $3000 depending on his estmates of the difficulty.   Some of his friends pledged to continue honoring the contracts after his death; at the time, it was estimated that he had about $15000 in contracts still outstanding.

Anyway, this short summary just touches on a few of the bizarre personality quirks in the unusual life of Paul Erdos.    If you are as intrigued as I was, be sure to check out Hoffman's biography, "The Man Who Loved Only Numbers".    And may the Supreme Fascist grant you a happy new year.

And this has been your math mutation for today.


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