4 highlights
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Occasionally, a scientific result is so important, multiple disciplines are forced to take notice. Such was the case in January with a landmark proof simply titled “MIP* = RE.” Written by five computer scientists, the paper establishes that quantum computers calculating with entangled qubits can theoretically verify the answers to an enormous set of problems.
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Computer scientists also triumphed this year in dealing with the famous traveling salesperson problem, which concerns how to find the shortest round trip for any collection of cities. In July, three computer scientists used a mathematical discipline called the geometry of polynomials to show that a modern algorithm is guaranteed to be at least infinitesimally more efficient than the long-standing best method.
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The proof of Fermat’s Last Theorem nearly three decades ago was lauded by math journals and newspapers around the world. But it was also just the beginning of a larger effort.
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The theorem established a kind of bridge between distant mathematical continents, with certain algebraic equations on one side and a kind of symmetric organization of geometric tilings on the other. Known as the Langlands correspondence, this bridge received major upgrades when two papers dramatically expanded the kinds of equations and tilings that are now connected and eliminated long-standing barriers to further expansions.