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MathFest Highlight: Daniel Goldston and the Revenge of the Twin Prime Conjecture (175 words) |
 | Two years ago, Daniel Goldston and his collaborators proved that there always exist primes that are very close together. |
| With that success, Goldston hoped that their method would soon lead to a proof that there are infinitely often pairs of primes closer than some fixed bounded distance. |
| Goldston comes to MathFest to discuss the methods that he and his colleagues used and to talk about why further progress towards a proof of the twin prime conjecture may be more difficult than he had originally thought. |
| When is a proof? (2570 words) |
| Granville and Soundarajan took Goldston and Yildirim's argument and extended it to show that there are infinitely many pairs of primes differing by no more than 12. |
| Not believing their result, the two decided to look again at Goldston and Yildirim's core lemmas to see if there was some crucial detail that was being too easily glossed over. |
| Goldston and Yildirim's core lemmas had a familiar flavor and their conclusions were very believable, so everyone believed them. |
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