Today, a 4chan poster solved a 25-year old math problem that the nation’s top mathematicians haven’t been able to crack. The 4chan user was on a hunt for a more efficient way to view a nonlinear anime series, but he ended up garnering massive interest in the world of mathematics. No one has any idea how to identify the anonymous (genius) user.
Just yesterday, a computer scientist/mathematician named Robin Houston released a tweet discussing the strange bed fall between 4chan and complex math. Intentionally or not, large swaths of the public were suddenly enthralled with the story.
A curious situation. The best known lower bound for the minimal length of superpermutations was proved by an anonymous user of a wiki mainly devoted to anime. https://t.co/z3wVAcUJl1
— Robin Houston (@robinhouston) October 23, 2018
Within hours of the tweet, Houston’s phone started to continuously vibrate. “It started to go mad,” said Houston. “My phone started going crazy.”
The 4chan aspect of these events began in September 2011, when a user posted a question: if you watched the 14 episodes of the anime The Melancholy of Haruhi Suzumiya in every possible order, what’s the shortest string of episodes you need to watch?
There are 14 episodes in Haruhi’s first season. The episodes are often chronologically challenging for the viewer and aired in a nonlinear order. When the series was released on DVD, the episodes were rearranged, so many of these anime aficionados rewatched the series again and again in different orders each time.
One of the anonymous posters found a way to solve this dilemma through a complex mathematical formula. In the process, this user just happened to figure out an issue that mathematicians have been working on since 1993. The 4chan proof, recently reposted on a Fandom wiki, is the most elegant solution to a mathematical dilemma known as superpermutation.
A permutation is the order of a set of numbers. If one were to refer to anime, one permutation of Haruhi would be equivalent to watching all 14 episodes in the order they are aired. However, if you’re a Haruhi superfan you may want to watch the show over and over again. In this case, you may want to view all the possible permutations of a set put together, i.e. a superpermutation. For a 4chan user, this was almost like an ultimate Haruhi marathon.
The field of math that studies permutations is called combinatorics. Unlike other mathematical field, combinatorics is more accessible to amateurs and casual math enthusiasts. Because of this, the poster’s anonymous identity does not denigrate his solution’s validity.
According to Jay Pantone, a mathematician at Marquette University, “What’s beautiful about mathematics is that it’s a proof that starts with your hypothesis and leads to your conclusion. You have to convince a skeptical reader that you’re correct. That doesn’t rely on your identity being known.”
Pantone had his doubts about the 4chan proof, and last week he translated the 4chan user’s work into a more formal layout. According to his analysis, the 4chan proof has zero flaws.
With regards to the Haruhi conundrum, 4channers were searching for the shortest possible superpermutation for the 14-episode set. This formula had never been found though. The original 1993 paper suggested part of the solution. However, after Houston analyzed it in 2014, he found that the mathematics in the 1993 problem didn’t work for sets containing over 6 numbers. Houston’s discovery excited the mathematical world which thought that this problem had been put to rest. Since the 4chan proof was discovered, everything from the problem set has fallen into place.
The 4chan proof shows how to find the smallest number of episodes for the solution. But it doesn’t quite solve the entire superpermutational dilemma. An even bigger discovery was made earlier this month when sci-fi author Greg Egan wrote a proof that outlined how to find the largest number for any given superpermutation problem.
According to tech site The Verge, one would need to view at least 93,884,313,611 to watch the season in any given order. At the very most, they would need to see 93,924,230,411 to do so. There still is a way to go to narrow down the answer, but they are on their way.
Through 4chan’s ingenious user, mathematicians now have a way of determining the range of possible answers. A group of them are also working to merge Egan’s work with the 4chan proof to determine a conclusive formula.
“It might be possible to crack it open.”
At the moment, there are no known applications for the formula before answering niche-based anime inquiries. Pantone claims it takes a long time before pure mathematical proofs can be applied to the real world. However, the 4chan discovery does show that math is a field accessible to any enthusiast, not just academic elites.