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In order to teach robots how to move and computers how to see, mathematicians have to reconsider one of their most ancient challenges: how to find the zeroes (or "roots") of a polynomial. The computer has re-invigorated the field by enabling mathematicians to use approximate methods, zeroeing in on the zeroes with high speed and precision. New algorithms developed by the author and colleagues make it possible, in principle, to solve a polynomial equation almost as fast as it can be written down.
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