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Big advance on simple-sounding math problem was a century in the making
A new proof about prime numbers illuminates the subtle relationship between addition and multiplication — and raises hopes for progress on the famous abc conjecture.
Pasten’s technique also enabled him to make progress on certain cases of the abc conjecture, yet another question that deals with the interplay between addition and multiplication, and one of the most famous — and controversial — unsolved problems in mathematics. In 2001, Stewart and Kunrui Yu of the Hong Kong University of Science and Technology developed a new approach toward studying prime factors in sequences, using an area of mathematics called transcendence theory. Over the years, Pasten developed a new theory involving modular forms and related entities called Shimura curves, which allowed him to tackle many of the questions Murty had given him.
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