Keeping It Short

One of the shortest Sunday reflections ever, courtesy of Paul Erdös:

"If numbers aren't beautiful, I don't know what is."

Vintage Erdös

In 1953, Paul Erdös was invited to spend a year teaching at the University of Notre Dame. In his volume, “My Brain Is Open” Bruce Schechter relays the following story:

“Erdös was an avowed atheist, and his friends at Notre Dame enjoyed teasing him about his working at a Roman Catholic university. ‘He said in all seriousness that he liked being there very much,’ Melvin Henriksen, a colleague from those days, recalled, ‘and especially enjoyed discussions with the [priests].’ Only one thing bothered him. ‘There were too many plus signs,’ he irreverently remarked."

The Saintly Erdös...

For Sunday reflection, commentary on Paul Erdös from Bruce Schechter in “My Brain Is Open”:

“To [Joel] Spencer and many other mathematicians, Erdös was a modern version of a medieval mendicant monk. Erdös is frequently called without a trace of irony, a saint. Indeed, there was something saintly in Erdös’s generosity, in his honesty and his support of the rights of the individual. But the essence of the saintliness his friends speak of was his total devotion to the mathematical pursuit of pure beauty. Erdös often said that ‘property is a nuisance.’ In fact, to Erdös all aspects of life — jobs, money, property, and intimate personal attachments — that interfered with his devotion to mathematics were a nuisance to be avoided. While few people would choose to emulate him, Erdös’s life was an example cherished by many.”

A Little Backstory… the Erdos/Tao photo

A substitute ‘Sunday reflection’ today, because of my experience with a tweet last evening….

I’ve always loved the above photo (brings me a smile everytime) of a 10-yr.-old Terry Tao with Paul Erdös, which I dropped into a tweet last night — the look on the faces, the synchronous postures, the concentration, the shared passion…  It originally showed up on the ’Net in 2013 courtesy of Terry himself, and went somewhat viral at the time within math circles:

https://plus.google.com/u/0/+TerenceTao27/posts/fiZbgKv4Yew

(...and a h/t to Patrick Honner who was the first to bring it to my own awareness, back then)

Is that not great! I thought it was iconic by now and viewed by everyone multiple times. But a few folks (responding to the tweet) apparently were not familiar with it, and while usually recognizing Erdös, were unsure of the youngster involved. So just to clear any confusion, am posting the little bit of history that I know (thanks again to Dr. Tao for sharing it originally -- apparently the pic comes from the University of Adelaide in Australia at an awards ceremony of the Australian Mathematics Competition,1985).

As some responders have noted, two people, bridging a large generation gap, one originally Hungarian, one originally Australian, who both came to America, and in different manners contributed so much to our joy of mathematics, and continue to delight us, in both death and life.

p.s... among Erdös' many noted linguistic idiosyncracies, he referred to young children as "epsilons," and as one of the commenters to Terry's original post says, he had finally found an interesting "epsilon." ;-)

Erdös Trivia...

Just a line I recently found surprising in the Wikipedia entry for Paul Erdös....

Though Erdös collaborated with over 500 different individuals in his lifetime, publishing more than 1500 mathematical articles, he not only never won the Fields Medal himself, "nor did he coauthor a paper with anyone who did, a pattern that extends to other prizes." That struck me as remarkable (and I assume it's accurate, unless someone knows a counter-example?). I'm not quite certain what the last phrase ("a pattern that extends to...") even means -- does it mean he never collaborated with the winner of any prize he had not himself won??? Anyway, apparently there have never been any Fields Medalists with "Erdös numbers" of "1" -- wouldn't have guessed that!

Your Tax Money At Work (back when Erdös was around)

Somewhere in the Great Beyond, Paul Erdös may be saying, 'My file is open...'  *
A h/t to Nicholas Christakis for passing along the below article (via Twitter):

For years, the FBI maintained a surveillance file on eccentric, peripatetic genius Paul Erdös -- because, as you know, he was such a dangerous, menacing presence... in fact here he is in 1985, inculcating impressionable American youth** with heady (perhaps subversive) formulations and sly propaganda (notice too his frumpy apparel and deceptively simple-looking trademark coffee cup, all designed to lend Paul an innocent, innocuous appearance to the untrained eye):

Anyways, read the article below, which at the end actually links to Erdös' full, boring file:

http://www.atlasobscura.com/articles/the-fbi-files-of-one-of-the-most-prolific-mathematicians-ever

Of course little of significance was ever found in tracking the incredible Erdös (...yo, FBI, you feel obliged to start a file? ...fill one on Mitch McConnell, Jeff Sessions, Karl Rove, Clarence Thomas, or other real dangers to democracy and the American way).

Perhaps J. Edgar Hoover's only true goal was to claim an Erdös number of 1: The final sentence of the piece reads, "His FBI surveillance, then, appears little more than a clever way to get J. Edgar Hoover's name on a paper with Paul Erdős."  (...yes, J. Edgar was a clever one... and, according to some, looked better in a dress than Paul ever would have! ...not that anyone even wants to imagine that).

The non-seditionary parts of Erdös' life (i.e., his entire life) have been well-chronicled in two biographies:
"The Man Who Loved Only Numbers" by Paul Hoffman
"My Brain Is Open" by Bruce Schecter


p.s...:  this coming Saturday would have been Erdös' 103rd birthday, so in case you're looking for a reason to party this weekend (now that your March Madness bracket is in a shambles) there you are! Have some coffee, dream up some theorems, and party hard.

p.p.s...:  I can only imagine what the FBI's file on Keith Devlin must look like by now ;-)


      *  a take-off on Erdös' signature phrase, "My brain is open" (or, more likely, "My  
          br-r-r-r-a-ain eeez o-o-open).

     **  lest anyone not be familiar with it, Paul Erdös pictured with 10-year-old Terence Tao,
         via Wikipedia.

Paul Erdös For the Holidays?

"The Boy Who Loved Math: The Improbable Life of Paul Erdös," is a children's picture book that has been out for a couple of years... oddly enough, about the life of Paul Erdös ;-) ...no really, it is a bit odd that someone (Deborah Heiligman and LeUyen Pham) thought to make a children's book based on the eccentric life of a great mathematician.
Anyway, James Propp has a fabulous new and extended review of the volume (great job covering the book and some of the key ideas Erdös worked on as well):

https://mathenchant.wordpress.com/2015/11/11/erdos-for-epsilons-the-boy-who-loved-math/

Not too early to be thinking of stocking stuffers for any math-inclined younguns on your Holiday list. And even if you don't have children or an interest in children's books, the above piece from Propp is a VERY worthwhile read for the included mathematics.

Perhaps worth noting also that there are two wonderful, older bios of Erdös for the adults on your shopping list as well (no one would believe Erdös' life if someone wrote him up as a character in a work of fiction... YET he was REAL!):

Paul Hoffman's "The Man Who Loved Only Numbers"
Bruce Schecter's "My Brain Is Open"

p.s. ...don't spend all your money at once; I'll be posting my choices for best popular math books of the year before the end of the month.

Sunday Reflection

A conjecture both deep and profound
Is whether the circle is round.
In a paper of Erdös
Written in Kurdish
A counterexample is found.
      -- by a colleague of Paul Erdös


This Sunday I've been thinking about that worshiper of the Supreme Fascist, Paul Erdös…

I often recall Doug Hofstadter's words in tribute to Martin Gardner, noting how peculiar it was that someone who wrote such a large, excellent body of work as Martin, and had such a devoted following, was nonetheless unknown to the vast majority of Americans. Although they were widely different individuals, the same could be said of Paul Erdös, who I suspect is unknown to 99% of Americans. Even if his contributions to mathematics were more average (instead of being the most prolific math paper author in history), he ought be better known for the sheer entertaining eccentricity of his life. A novelist couldn't invent Paul Erdös and have him be a believable figure, so odd/unique a character was he.

The classic popular work on his life is Paul Hoffman's "The Man Who Loved Only Numbers," a volume every math buff should read.
There is also a more recent award-winning volume geared especially to young people entitled, "The Boy Who Loved Math: the improbable life of Paul Erdös" by Deborah Heiligman.

Anyway, just a few reflective quotes from Paul for this Sunday morn:

"God may not play dice with the universe, but something strange is going on with the prime numbers."

"Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is."

"The purpose of life is to prove and to conjecture."

By the way, the epitaph Erdös purportedly suggested for his grave was, "I've finally stopped getting dumber" -- now, ya gotta love that! [...can't you just imagine that as the new American euphemism for dying... instead of the NY Times reporting that "So-and-So passed away last week at the age of...." it would be "So-and-So stopped getting dumber last week at the age of...."]

For all his brilliance, Erdös was also one of those famous mathematicians who had difficulty with the "Monty Hall puzzle" when it first hit the scene, believing Marilyn vos Savant had blown the answer. It took computer simulations to finally convince him of her answer's correctness.

Erdős was also known for his own idiosyncratic terminology which included the following:

Children were "epsilons"
Women were "bosses"
Men were "slaves"
(...ahhh, so bosses and slaves sometimes had epsilons together)
People who stopped doing mathematics had "died"
Music (other than classical) was "noise"
People who married were "captured"
People who divorced were "liberated"
Giving a mathematics lecture was "preaching"
And, as indicated above, God was "the Supreme Fascist" who retained "the BOOK" of great math proofs (Erdös was actually an agnostic-atheist)

As we celebrate the Centennial of Martin Gardner's birth this year, worth noting that a little over a year ago was the centennial of Erdös' birth (he died in 1996... and no doubt by now has peeked at, and committed to memory, all chapters of the BOOK ;-).

Lastly, here's a 10-min. clip from an Erdös documentary:




[p.s… I tend to just stumble across topics I use here for Sunday "meditations" or "reflections"… But if YOU have a favorite passage, quotation, or subject to share that you think mathematics lovers might enjoy contemplating on a Sunday morning please send it along to me (sheckyr@gmail.com) for consideration, and if used, I'll note the contributor.]

quick ADDENDUM: Fawn Nguyen just passed along to me mention of a second Erdös biography that I was unaware of, but looks great: "My Brain Is Open" by Bruce Schecter (title coming from a famous phrase of Erdös).

Friday Fun

Seeing is.... be-fuddling. . . .

Recently highlighted at Grey Matters Blog this version (known as the Winston Freer tile puzzle) of a classic geometry-type puzzle:




On a side-note, KW Regan posted this entry yesterday in honor of the recent Paul Erdös anniversary (with many wonderful links):

https://rjlipton.wordpress.com/2013/03/28/happy-100th-birthday-paul-erdos/

Two-ooo Wonderful!

H/T to Patrick Honner who tweeted this delightful photo of a 72-yr.-old Paul Erdös with a 10-yr.-old Terence Tao (from Terry Tao's Google+ account):

https://plus.google.com/u/0/114134834346472219368/posts/fiZbgKv4Yew

(so great, made my day!... love the two right arms, in synchrony and thought, held to chins)

Turning Coffee Into Theorems...

Today would be Paul Erdos' 100th birthday!
In his honor, check out this endearing, heartwarming video of one of the most odd, curious, and prolific mathematicians of all time (...it's an hour long, but if you've never seen it, I truly recommend you find time to watch!):

http://www.youtube.com/watch?v=pnCrUroeVlI 
--> Addendum: sorry, taken down apparently due to copyright violation :-(

And here's a wonderful piece just done for the NY Times on Erdös:

http://tinyurl.com/cdv6zzl

 (ohhh, and get your In-honor-of-Erdos coffee mugs here or here.)

Paul Erdos... Still Publishing After All These Years

 

“A mathematician is a device for turning coffee into theorems.” --Paul Erdos

(via kmhkmh at WikimediaCommons)

John Cook notes at his blog that Paul Erdos, the most prolific mathematician of all time (who died in 1996), is STILL publishing an occasional paper now and then, because of all the collaborators who started papers with him way back when, that were put aside, and are only now being completed. John's short post here:

http://www.johndcook.com/blog/2012/10/23/dead-man-writing/

The above leads in turn to a fresh hour-long podcast (from "Relatively Prime") on Erdos here:

https://itunes.apple.com/us/podcast/relatively-prime/id560923828

...Several of the personal stories told therein are quite wonderful.

And some more Erdos reminiscences here:

http://www.maa.org/features/erdos.html

Finally, Paul Hoffman's classic biography of Erdos, "The Man Who Loved Only Numbers" remains a great read.

Paul Erdos

Image via Wikipedia

A documentary portrait of the amazing Paul Erdos (1913-1996) via YouTube clips here:

http://tinyurl.com/2f2776n

To this day Erdos is the most published mathematician of all time. He was well-known as a traveling math vagabond who would simply hang out with colleagues he had all over the world, after showing up on their doorstep and announcing, "My brain is open," essentially meaning 'hey, let's do some math!' And yet despite many award-winning accomplishments in several math fields he was initially flummoxed by the well-known 'Monty Hall problem.' A fascinating character, whose likes we may never see again.