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How Computer Scientists Cracked a 50-Year-Old Math Problem (quantamagazine.org)
An anonymous reader writes: Over the decades, the Kadison-Singer problem had wormed its way into a dozen distant areas of mathematics and engineering, but no one seemed to be able to crack it. The question "defied the best efforts of some of the most talented mathematicians of the last 50 years," wrote Peter Casazza and Janet Tremain of the University of Missouri in Columbia, in a 2014 survey article.
As a computer scientist, Daniel Spielman knew little of quantum mechanics or the Kadison-Singer problem's allied mathematical field, called C*-algebras. But when Gil Kalai, whose main institution is the Hebrew University of Jerusalem, described one of the problem's many equivalent formulations, Spielman realized that he himself might be in the perfect position to solve it. "It seemed so natural, so central to the kinds of things I think about," he said. "I thought, 'I've got to be able to prove that.'" He guessed that the problem might take him a few weeks.
Instead, it took him five years. In 2013, working with his postdoc Adam Marcus, now at Princeton University, and his graduate student Nikhil Srivastava, now at the University of California, Berkeley, Spielman finally succeeded. Word spread quickly through the mathematics community that one of the paramount problems in C*-algebras and a host of other fields had been solved by three outsiders — computer scientists who had barely a nodding acquaintance with the disciplines at the heart of the problem.
As a computer scientist, Daniel Spielman knew little of quantum mechanics or the Kadison-Singer problem's allied mathematical field, called C*-algebras. But when Gil Kalai, whose main institution is the Hebrew University of Jerusalem, described one of the problem's many equivalent formulations, Spielman realized that he himself might be in the perfect position to solve it. "It seemed so natural, so central to the kinds of things I think about," he said. "I thought, 'I've got to be able to prove that.'" He guessed that the problem might take him a few weeks.
Instead, it took him five years. In 2013, working with his postdoc Adam Marcus, now at Princeton University, and his graduate student Nikhil Srivastava, now at the University of California, Berkeley, Spielman finally succeeded. Word spread quickly through the mathematics community that one of the paramount problems in C*-algebras and a host of other fields had been solved by three outsiders — computer scientists who had barely a nodding acquaintance with the disciplines at the heart of the problem.
By injecting its SQL
Table-ized A.I.
Dude, we get the first story reminiscent of the Old Slashdot in freaking forever... and you're asking for practical applications?
#DeleteChrome
I'd like a car analogy.
You are all klein group. The klein group is Trivial! Trivial Cows Trivial! Mooo! Mooo! Mooo say the Cows. YOU NEUTRAL ELEMENTS!!!
No one has a sense of humor anymore, especially when ti comes to algorithms proven by boundary equations.
---- Teach Peace. It's Cheaper Than War.
What are you doing here? Where are your parents!?
Inheritance is the sincerest form of nepotism.
The difference in the way of thinking is simple.
Mathematician: "This is too complex for my brain. I can grasp the outer layer of the problem, but the underlying thing is beyond any human's capacity."
CompSci guy: "Oh, I can write a program that handles the outer layer of this problem; I have no clue what that underlying thing is but I bet it can be brute-forced."
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