A mathematical puzzle solved by an anonymous anime fans has led to an unexpected breakthrough in combinatorial mathematics, starting with a simple question about binge-watching a 14-episode series in every possible order.
In 2011, an anonymous poster on the 4chan message board wondered about the most efficient way to watch every possible sequence of The Melancholy of Haruhi Suzumiya, a cult anime series designed so episodes could be viewed in any order. What seemed like casual fan speculation turned into a significant mathematical contribution, providing a new formula for calculating the minimum length of "superpermutations" sequences containing all possible orderings of a set of items.
As reported in Scientific American, this anime-inspired discovery caught the attention of mathematician Robin Houston in 2018, who realized its importance. The anonymous fan had derived a formula showing that for n episodes, you need at least "n! +(n – 1)! + (n – 2)! + n – 3" episodes to see every possible sequence. For the 14-episode anime series, this means a minimum of 93,884,313,611 episodes — roughly 4 million years of viewing time.
"A curious situation. The best known lower bound for the minimal length of superpermutations was proven by an anonymous user of a wiki mainly devoted to anime," Houston wrote on Twitter. The discovery was so significant that when mathematicians Houston, Pantone and Vatter formally documented the proof, they credited "Anonymous 4chan Poster" as the first author.
"Outside of 4chan, none of this made any waves. No one seemed to take any notice," notes Scientific American's Manon Bischoff, highlighting how groundbreaking mathematics can emerge from the most unexpected corners of the internet.
Previously:
• Profile of math-inspired 3D printing sculptor Bathsheba Grossman
• How math people look at math, and why it works
• Flatland is one of my favorite Math(ish) books
• Punk math philosophy and podcast
• Is math real?
