A Chinese mathematician Hao Huang has tackled a 30-year-old mathematical issue at the limit between mathematics and computer science by utilizing an inventive, elegant proof that has his associates wondering about its simplicity.
Hao, an associate teacher of arithmetic at Emory University in Atlanta, proved a mathematical idea called the sensitivity conjecture, which, in inconceivably 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 initially proposed the sensitivity conjecture (without proving it), hypothetical PC researchers understood that it has huge implications for determining the most efficient ways to process information.
What’s surprising about Hao’s confirmation, as per different specialists in the field, isn’t only that Hao pulled it off, but also the elegant and straightforward way in which he did it. His proof hasn’t been officially peer-reviewed or published in any math journal. In any case, not long after Hao put it online July 1, his associates immediately acknowledged it as fact.
“Whenever there’s an announcement like this,” University of Texas at Austin theoretical computer scientist Scott Aaronson wrote on his blog, “~99% of the time either the proof is wrong, or at any rate it’s way too complicated for outsiders to evaluate it quickly. This is one of the remaining 1% of cases. I’m rather confident that the proof is right. Why? Because I read and understood it. It took me about half an hour.”
Ryan O’Donnell, a software engineering professor who studies number theory at Carnegie Mellon University in Pittsburgh, pointed out that Hao’s proof can be summed up in a single tweet:
Hao Huang@Emory:
Ex.1: ∃edge-signing of n-cube with 2^{n-1} eigs each of +/-sqrt(n)
Interlacing=>Any induced subgraph with >2^{n-1} vtcs has max eig >= sqrt(n)
Ex.2: In subgraph, max eig = sqrt(deg(f))
Hao is a tenure-track Assistant Professor in the Math and Computer Science Department at Emory University. After completing B.S. degree in School of Mathematical Sciences, Peking University back in 2007, he received the Ph.D degree in Jun, 2012, from Department of Mathematics, UCLA.
As indicated by the data he posted on his homepage, Hao’s research interests include extremal combinatorics, probabilistic/algebraic methods, spectral graph theory, structural graph theory, and theoretical computer science.
livescience.com
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