A Simple and Clear-Cut Constellation

The New Yorker, Feb 2, 2015

from Alec Wilkinson's profile of Yitang Zhang "The Pursuit of Beauty":

The British mathematician G. H. Hardy wrote in 1940 that mathematics is, of "all the arts and sciences, the most austere and the most remote." Bertrand Russell called it a refuge from "the dreary exile of the actual world." Hardy believed emphatically in the precise essence of math. A mathematical proof, such as Zhang produced, "should resemble a simple and clear-cut constellation," he wrote, "not a scattered cluster in the Milky Way." 
 *
The books on his shelves have titles such as "An Introduction to Hilbert Space" and "Elliptical Curves, Modular Forms, and Fermat's Last Theorem." There are also books on modern history and on Napoleon, who fascinates him, and copies of Shakespeare, which he reads in Chinese, because it's easier than Elizabethan English.
* 
"Bounded Gaps Between Primes" is a back-door attack on the twin-prime conjecture, which was proposed in the nineteenth century, and says that, no matter how far you travel on the number line, even as the gap widens between primes you will always encounter a pair of primes that are separated by two. The twin-prime conjecture is still unsolved. Euclid's proof established that there will always be primes, but it says nothing about how far apart any two might be. Zhang established that there is a distance within which, on an infinite number of occasions, there will always be two primes.
"You have to imagine this coming from nothing," Eric Grinberg said. "We simply didn't know. It is like thinking that the universe is infinite, unbounded, and finding it has an end somewhere."... 
* 
When we reached Zhang's office, I asked him how he had found the door into the problem. On a whiteboard, he wrote, "Goldston-Pintz-Yildirim" and "Bombieri-Friedlander-Iwaniec." He said, "The first paper is on bounded gaps, and the second is on the distribution of prime numbers in arithmatic progression. I compare these two together, plus my own innovations, based on the years of reading in the library." 
* 
"Many people have tried that problem," Iwaniec said. "He's a private guy. Nothing is rushed. If it takes him another ten years, that's fine with him. Unless you tackle a problem that's already solved, which is boring, or one whose solution is clear from the beginning, mostly you are stuck. But Zhang is willing to be stuck much longer." 
* 
"I think what he did was brilliant," Deane Yang told me. "If you became a good calculus teacher, a school can become very depended on you. You're cheap and reliable, and there's no reason to fire you. After you've done that a couple of years, you can do it on autopilot; you have a lot of free time to think, as long as you're willing to live modestly...."


Comments

Post a Comment

Popular posts from this blog

Goh Chok Tong's Visit to FCBC

Image
I am surprised by how much this incident is affecting me. I thought I have moved past my former religious life, left it behind in Singapore, but like tin cans tied to a dog it has followed me and is rattling me. I am posting the incident, and my response to it, here on this blog, because I want to remember that the past is not yet past. When Emeritus Senior Minister of Singapore Goh Chok Tong visited Faith Community Baptist Church on 13 January during a Sunday service, Senior Pastor Lawrence Khong took the opportunity to deliver a hateful anti-gay message . Among other things, he said: We affirm that the family unit comprises a man as Father, a woman as Mother, and Children. This is the basic building block of society, a value foundational for a secure future, a premise fundamental to nation-building. and warned ominously that We see a looming threat to this basic building block by homosexual activists seeking to repeal Section 377A of the Penal Code.   Example...
Read more

Wallace Stevens' "The Noble Rider and the Sound of Words"

Just read three essays from the "Poetics" section at the back of Volume One of The Norton Anthology of Modern and Contemporary Poetry : "The Poetry and the Present" by D.H. Lawrence (1919); "The Negro Artist and the Racial Mountain" by Langston Hughes (1926); and "The Noble Rider and the Sound of Words" by Wallace Stevens (1942). The first is an artful polemic for free verse in contact with the "insurgent naked throb of the instant moment." The second is a spirited rejoinder to a young Negro poet who wanted to "write like a poet--not a Negro poet." The third, my favorite, is a wide-ranging meditation on the nature of poetry and the role of the poet. So many grand things said but I will only quote a few passages: I am interested in the nature of poetry and I have stated its nature, from one of many points of view from which it is possible to state it. It is an interdependence of the imagination and reality as equals. This is...
Read more

Steven Cantor's "What Remains: the Life and Work of Sally Mann"

Image
Sally Mann, The Perfect Tomato , 199 0 Since it is moving pictures, a film necessarily captures--produces--a process. It turns photographs into the making of photographs. It joins moments ("spots of time") into a Life. This I expected watching Cantor's documentary on Sally Mann's creation of the exhibit "What Remains." So photographs of a long-dead beloved greyhound "lead" to photographs of the Civil War battlefield of Antietam, to photographs of Mann's Virginian farm bloodied by the police killing of a runaway convict, to photographs of decomposing bodies in a forensic study site, as if each group of pictures forms an independent yet preparatory stage in the creative process. What I did not expect to see is the influence of the film-making on the photography itself. Mann begins to think of her exhibit as a "narrative," and wants the narrative of death to end on a more uplifting note. With such an idea in mind, she takes close-up pic...
Read more