In mid-May, Harald Helfgott of the École Normale Supériure in Paris published a proof of the ternary Goldbach conjecture, a longstanding question in number theory.
Of course, making substantial progress on a problem that some of the most brilliant mathematicians of the past century have worked on was not an easy task. “There were several blind alleys-at one point I had to throw away a 50-page manuscript,” Helfgott wrote. “It was difficult to tell down the middle whether the plan would truly succeed. After all, if I had brought C down to 10100, that would still have been larger than the number of subatomic particles in the universe multiplied by the number of seconds since the Big Bang-there would have been no hope of checking things that far!” Helfgott wrote that keeping track of the bounds explicitly was one of the most difficult parts of the work. “One annoying thing about the problem was that it turned out not to be the kind of thing I could work on in my head while at the movies or at a concert (not that I should),” he wrote. “I did get some good ideas in the shower, though.”
Read the full post at Roots of Unity.
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