Arts & Events

FILM REVIEW:Counting from Infinity: It's a Math-erpiece

Gar Smith
Friday May 22, 2015 - 01:11:00 PM

If you are looking for a total break from movies involving wise-cracking action heroes battling it out in Hollywood's latest CGI-fest, you might want to seek out Counting from Infinity—a quiet, simple, and smartly seductive documentary about a humble mathematician named Yitang Zhang.

The film—produced by Oakland-based director George Csicsery and partly shot in Berkeley—was screened at a special one-night event at Berkeley's Elmwood theatre on May 21, with the director and a panel of local mathematicians on hand to celebrate the event.




Thanks to Csicsery (a talented niche-filmmaker who specializes in documentaries celebrating math and mathematicians), we can all share a rare look inside the generally unexplored world of cloistered academics and envelop-pushing thinkers. One stunning realization only dawned after a post-screening conversation. "Did you notice," another reviewer pointed, "on the entire film you never saw a computer or an electronic device." It was true. While you might think mathematicians would be surrounded by keyboards, calculators, screens and hard-drives, the thinkers we meet are more like philosophers, pondering profound mysteries of existence. Or like artists, sketching out parallel universes drawn in meticulous chalk strokes spread across the "canvas" of a whiteboard. 

"Who Is This Guy?" 

It was in April 2013 that Zhang mailed a masterful mathematical thought-piece to the Annals of Mathematics. In his meticulous paper, Zhang claimed to have solved one of the math world's most vexing challenges—the Twin Prime Conjecture. Almost immediately, the publication of "Small Gaps Between Primes" was hailed as a monumental breakthrough in Number Theory. But what really got the world's mathematicians talking was the fact that no one had ever heard of Yitang Zhang. The man behind the breakthrough was an unknown theoretician, working alone, without a fulltime job, and no record of previous publications. 

Zhang, or "Tom," as he likes to be called, is a real life superhero. Like the best superheroes, he comes from a humble and unlikely background. Raised in China during the Cultural Revolution, Tom saw his father, an engineering teacher, persecuted by the government. Tom, along with his mother and siblings, were relocated to a hardscrabble life on a collective farm. After resettling in the US and graduating from Purdue University, Zhang spent seven years working as an accountant at a Subway franchise in Kentucky. Eventually, a friend found him a job as a lecturer in the University of New Hampshire's math department. 

UC Berkley professor Ken Rivet remembers coming across Zhang's paper: "I am deluged with manuscripts in elementary number theory by people who . . . claim typically to have solved simultaneously Fermat's Last Theorem, the Twin Prime Conjecture, Goldbach's Conjecture and usually some unified theory of physics." Many of these papers arrive infused with an air of arrogant condescension, which journal editors generally recognize as a tip-off that the arguments will fail to deliver. Zhang's paper was different. 

A Primer on Primes 

For readers whose high school math may be a bit rusty, primes are those special numbers that are not divisible by any number other than 1—i.e., 1, 3, 5, 7, 11, 13, 17, 19 and on into infinity. This theory goes back along time (Euclid is a prime example). 

But mathematicians have discovered something even more surprising about primes: As far out as you can count, you will find sequential clusters of prime numbers that are separated only by two numerals. Examples: The primes 1 through 7 are all separated by 2 (i.e., 7-5=2). A separation begins with the space between 7 and 11 and the next "twin prime" quickly arrives with 11-13 (13-11=2). The Twin Prime Conjecture proposes that these clusters continue to occur (although with greater and greater separations) endlessly. 

"Theoretically," as UCLA math maven Terence Tao parses it, primes seem to exhibit "some weird conspiracy between them [as if] they have some gentleman's agreement that every time one number decides to be prime, then the number two spaces down will always agree not to be prime…. If the twin primes ever ran out, it would be a huge shock…. We'd have to rethink all of our cryptographic assumptions. We'd have to rethink a lot of number theory." 

The Breakthrough 

While it is one thing to have a theory, it is quite another to offer a proof—and the Twin Prime Conjecture had stumped some of the world's best brains for a very long time. Zhang was also stumped. He recalls how he was frustrated by what seemed like an insurmountable barrier that needed one more new idea. 

It was in July 2012, during the backyard cigarette break at a friend's home in rural Colorado, that Zhang went looking for deer and had a flash of inspiration that carried him over the daunting "square barrier" that had been blocking a solution. 

The world of professional mathematicians was astounded by the insight of this unknown thinker. "He went to the deepest of the deep and he fully understood," said University of Montréal professor Andrew Granville. "His paper establishes him … as one of the top half-dozen people in the world in the field." 

The growing recognition and prizes (including a MacArthur grant) also caught Zhang and his wife, Yaling, by surprise. Yaling was totally unprepared for the news that her modest, self-effacing lifelong companion was somehow, suddenly, an international celebrity. In the documentary, her surprise, pride, and absolute delight, are endearingly palpable. 

Counting from Infinity includes interviews with some of the world's top mathematicians including UCLA's Tao, Britain's James Maynard and local math heavyweights David Eisenbud (from Berkeley's Mathematical Sciences Research Institute) and Daniel Goldston (from San Jose State University). 

The film includes footage shot in New Hampshire, New Jersey and at UC Berkeley's Evans Hall, where Zhang presided over a Colloquium Lecture on September 12, 2013. 

Counting from Infinity offers of a welcome respite from the boom-box bluster of a Hollywood blockbuster. Zhang his wife and his closest friends emanate a sense of quiet and profound contentment. Their daily lives are simple and unassuming while their emotional lives are filled and complete. We watch Zhang as he dons a backpack and walks to a bus stop for a ride to campus. We follow Zhang as he wanders for hours in the woods and pauses by quiet, turtle-stirred ponds, lost in his thoughts, draped in shadows and sunshine. 

George Csicsery admits it can be a challenge to direct a film starring a mathematician like Tom Zhang: "The qualities he embraces—solitude, quiet, concentration—are the opposites of those valued in the media." Fortunately, Csicsery is a master of this scholarly cinematic genre (having made a number of previous documentaries on math prodigies, including Hard Problems and Julia Robinson and Hilbert's Tenth Problem). 

What Csicsery has discovered (and in this film proves) is that you can reveal powerful cinematic truths if you simply take the time to show "a person just sitting with pencil and paper and thinking. The longer the scene, the more you realize that you really can see someone thinking. The human face is very expressive. Give it time and it speaks volumes." 

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