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Friday, August 02, 2019

This Mathematician's 'Mysterious' New Method Just Solved a 30-Year-Old Problem | Tech - Live Science

Rafi Letzter, Staff Writer at Live Science reports, The proof took 30 years to be solved, but it's so simple and elegant that you can summarize it in a single tweet. 

Hao Huang
Photo: Emory University
A mathematician has solved a 30-year-old problem at the boundary between mathematics and computer science. He used an innovative, elegant proof that has his colleagues marveling at its simplicity.

Hao Huang, an assistant professor of mathematics at Emory University in Atlanta, proved a mathematical idea called the sensitivity conjecture, which, in incredibly rough terms, makes a claim about how much you can change the input to a function without changing the output (this is its sensitivity).

In the decades since mathematicians first proposed the sensitivity conjecture (without proving it), theoretical computer scientists realized that it has huge implications for determining the most efficient ways to process information. [5 Seriously Mind-Boggling Math Facts]

What's remarkable about Huang's proof, according to other experts in the field, isn't just that Huang pulled it off, but also the elegant and straightforward way in which he did it... 

Huang "took this matrix, and he modified it in a very ingenious and mysterious way," Kalai said. "It's like you have an orchestra and they play some music, and then you let some of the players, I don't know, stand on their head, and the music becomes completely different — something like that."

That different music turned out to be the key to proving the conjecture, Kalai said. It's mysterious, he said, because even though mathematicians understand why the method worked in this case, they don't fully understand this new "music" or in what other cases it might be useful or interesting.
Read more... 

Source: Live Science