An Arbitrary Number of Years Since Mathematician Paul Erdős’s Birth

Today would’ve been the 100th birthday of the Hungary-born mathematician who published so many papers--and many with such great impact--that a playful measure of one’s academic affiliation with him has been created

Erdős—who had a lifelong affair with caffeine, and later amphetamines—regularly worked 20 hours a day. Into his 70s, Erdős was publishing more papers per year than many good mathematicians publish during their lifetimes. During a short break he had taken from amphetamines to prove he wasn’t addicted, Erdős noted a drop in his productivity, and proclaimed that mathematics had been set back a month.

This tremendous volume of work, spread out over various disciplines and all over the world, has left the mathematician with a very fitting legacy: the Erdős number.

By the simplest definition, a person’s Erdős Number is their degree of separation from Erdős via a published paper. If you collaborated with him on a paper, your Erdős number is 1. If you’re a co-author with someone who was a co-author with Erdős, you get a 2, and so on. Only Erdős’ has 0 as an Erdős number. If you have no collaborative connection, your Erdős number is infinite. As time has gone on the highest reported Erdős number has increased: from 8 in 2000 to 15 in 2013.

Other versions demand that publications may only have two authors in order to be counted toward an Erdős number. There is an Erdős-Bacon number that sums a person’s Erdős number with their Bacon number: a degree-of-separation value based on the same postulate but applied to a person’s film connection to actor Kevin Bacon (some players allow non-film connections) . The first recorded source noting the idea of counting degrees of separation from Erdős was in a mathematics paper published in 1969 by a colleague. The Erdős Number Project, founded by Jerrold Grossman and Patrick Ion, and hosted by Oakland University in Michigan, started in 1995 and is the most extensive resource on Erdős’s publications and Erdős numbers.

Erdős numbers have no actual consequence—it’s a game. And like most games, it pops up, I’ve found, between classes, over drinks at meetings and during work breaks. Paul Erdős believed that mathematics was a collaborative activity, and the Erdős number, perhaps unintentionally, reflects that. It brings people together; gives them something to share. Sometimes when a great scientist dies, he or she is remembered with a statue, an institute, a street name or a school, but Erdős has been immortalized with something highly unique: a game derived from his work, and reflecting his collaborative spirit.

(Please note that a large portion of the research for this article comes from Paul Hoffman’s book on Erdős, The Man Who Loved Only Numbers.)

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1. 1. stargene 03:18 AM 3/27/13

If memory serves, Erdos once stated, perhaps
only half in jest, "A mathematician is a device
which turns caffeine into theorems!" :-)

2. 2. Germanicus 09:02 AM 3/27/13

Name the device that turns theorems into mal de tete.

3. 3. SJK1943 09:55 AM 3/27/13

I admire his contribution and talent. However, there is a sadness in this bio.

4. 4. Germanicus 11:14 AM 3/27/13

Erdos [urdish] claimed he'd never suffered carnal desire & knew he was peculiar in many aspects of temperament.

5. 5. Pazuzu 04:10 PM 3/27/13

My father, Stewart Scott Cairns, was a mathematician (topology) and after WWII, when I was a child, Erdös was a guest in our home several times, both in Syracuse and Urbana. I can attest to his oddness as a house guest; I never experienced the tomato soup or pot banging episodes, but we always needed to bring in a plumber to snake out the drain when he visited. He called me "epsilon," and our very friendly little dog, Patches, was "hell hound." God, of course, was the "supreme fascist in the sky."

Perhaps the most remarkable memory I have of him was of a dinner party at our home in Syracuse, it must have been 1947 or 1948 (I was 12 or 13), with him and several other mathematicians; he carried on several mathematical conversations at once. My father said he frequently did this. The topics were completely unconnected and on quite different topics, much like a chess master playing multiple games simultaneously.

Although Erdös had no income, he would regularly offer prizes (if I recall, up to \$1,000) to students if they could prove a challenging theorem. Then, when a student succeeded, it was up to his supporters (e.g., my father) to come up with the money.

My father admired him immensely. He was truly a mathematics machine, as well as a very generous man.

I don't agree with SJK1943 that there is a sadness in this bio. Erdös did with his life exactly what he wanted to do, namely mathematics. His use of caffeine and speed were in the service of doing math. I see a beauty in this bio, not sadness.

Also, Germanicus, it's [ɛrdø∫] in the International Pnonetic Alphabet, with stress on the first syllable. The [ø] is what we phonologists call (roughly) a mid, front rounded vowel, like the 'e' in 'bet' pronounced with the lips rounded as in the word 'boat,' and, as you indicated, the Hungarian 's' is pronounced as the 'sh' in English. The first vowel, 'e,' is closer to the English vowel in 'bet' than to the 'u' you indicated. The Wikipedia entry on him gives the correct IPA transcription.

6. 6. Pazuzu in reply to Pazuzu 09:06 PM 3/27/13

To make a minor correction in my description of how pronounce his name: the last syllable has a long vowel, pronounced about twice as long as a "normal" vowel. The stress (emphasis) remains on the first syllable.

7. 7. Pazuzu in reply to SJK1943 09:06 PM 3/27/13

Sadness? I think he was beautiful.

8. 8. larkalt 07:35 AM 3/28/13

There's a part of me that wants to live the way Erdos lived, with minimal possessions and minimal attachments in the world. Attachments create obligations and chores.

9. 9. mikpar 12:11 PM 3/31/13

I believe the book "the Man Who Loved Numbers" pointed out that Hank Aaron (or was it another baseball great?) had an Erdos number of one, Erdos & Aaron have both autographed the same baseball!

10. 10. tamasger 04:39 PM 4/3/13

I study physics at the university where Erdős Pál studied. It's kind of a great feeling :)

11. 11. Sinibaldi 11:51 AM 4/8/13

Fantaisie.

Un groupe de
feuilles, un
souffle de
lumière où
vient la pensée,
le son de la
neige qui
chante le matin....

Francesco Sinibaldi

12. 12. e b here 12:31 PM 4/16/13

b ( 2 ) B =

13. 13. yak4love 07:27 AM 5/30/13

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14. 14. yak4love 07:27 AM 5/30/13

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