‘Remarkable’ Mathematical Proof Describes How to Solve Seemingly Impossible Computing Problem

Ryan F. Mandelbaum @ Gizmodo

Complexity classes diagram

You enter a cave. At the end of a dark corridor, you encounter a pair of sealed chambers. Inside each chamber is an all-knowing wizard. The prophecy says that with these oracles’ help, you can learn the answers to unanswerable problems. But there’s a catch: The oracles don’t always tell the truth. And though they cannot communicate with each other, their seemingly random responses to your questions are actually connected by the very fabric of the universe. To get the answer you seek, you must first devise… the questions.

Computer scientists are buzzing about a new mathematical proof that proposes a quantum-entangled system sort of like the one described above. It seems to disprove a 44-year-old conjecture and details a theoretical machine capable of solving the famous halting problem, which says a computer cannot determine whether it will ever be able to solve a problem it’s currently trying to solve.

The 150-page proof, titled simply “MIP*=RE,” deals in the esoteric subject of computational complexity. If it holds under scrutiny, it demonstrates a profound connection between quantum physics, computation, and mathematics. It shows that a theoretical class of computing devices—a verifier interrogating the quantum-entangled oracles—can check some of the most complex computer problems imaginable. And it has important implications for quantum physicists.

Read the rest at Gizmodo.com

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