Then Robin Houston, a mathematician at the data visualization firm Kiln, and Jay Pantone of Marquette University in Milwaukee independently verified the work of the anonymous 4chan poster. Mathematicians quickly verified Egan’s upper bound, which, like the lower bound, applies to series of any length. Both proofs are now being hailed as significant advances on a puzzle mathematicians have been studying for at least 25 years. Egan’s discovery renewed interest in the problem and drew attention to the lower bound posted anonymously in 2011. But in a plot twist last month, the Australian science fiction novelist Greg Egan proved a new upper bound on the number of episodes required. The proof slipped under the radar of the mathematics community for seven years - apparently only one professional mathematician spotted it at the time, and he didn’t check it carefully. “Please look over for any loopholes I might have missed,” the anonymous poster wrote. The argument, which covered series with any number of episodes, showed that for the 14-episode first season of Haruhi, viewers would have to watch at least 93,884,313,611 episodes to see all possible orderings. In less than an hour, an anonymous person offered an answer - not a complete solution, but a lower bound on the number of episodes required. Fans were arguing online about the best order to watch the episodes, and the 4chan poster wondered: If viewers wanted to see the series in every possible order, what is the shortest list of episodes they’d have to watch? Season one of the show, which involves time travel, had originally aired in nonchronological order, and a re-broadcast and a DVD version had each further rearranged the episodes. On September 16, 2011, an anime fan posted a math question to the online bulletin board 4chan about the cult classic television series The Melancholy of Haruhi Suzumiya.

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