News & AnalysisMathematics

Two Proofs Spark a Prime Week for Number Theory

Science  24 May 2013:
Vol. 340, Issue 6135, pp. 913
DOI: 10.1126/science.340.6135.913

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Summary

Last week, in a remarkable game of intercontinental "can you top this," number theorists announced breakthroughs on two of the oldest unsolved problems in their subject. Although neither problem is close to being fully solved, the most dramatic progress in decades galvanized mathematical chat boards and provided instant fodder for seminars around the world. Mathematicians think that the twin prime conjecture and Goldbach's conjecture are almost certainly true, but in more than a century and a half of trying, no one has come close to proving either one. Then, on 13 May, Harald Helfgott posted a preprint with a proof of the ternary (three-prime) part of Goldbach's conjecture, and Yitang (Tom) Zhang presented in a lecture a proof showing that there are infinitely many prime numbers separated by less than 70 million.

  • * Dana Mackenzie is a writer in Santa Cruz, California.