Haruhi Suzumiya Math Problem

[Armanda Kicks]

Oftentimes in math the manner in which a solution to a problem is announced becomes a significant chapter/part of the lore associated with the problem, almost being remembered more than the manner in which the problem was solved. I think that most mathematicians as a whole, even upon solving major open problems, are an extremely humble lot. But as an outsider I appreciate the understated manner in which some results are dropped.

Watson and Crick's famous ending of their DNA paper, "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material," has a bit of the same understated feel...

The story is told at Mystery Math Whiz and Novelist Advance Permutation Problem, and a publication with a cleaned-up version of the proof is at A lower bound on the length of the shortest superpattern, with "Anonymous 4chan Poster" as the first author. The original 4chan source is archived here.

Applications of algebra to a problem in topology (YouTube) at Atiyah80 was a talk by Mike Hopkins. In it he announced the solution to the Kervaire invariant one problem in all but one dimension (arXiv, Annals).

Because of its implications this is probably the most important footnote in the history of physics. Max Born was awarded the Nobel prize "for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction".

On October 31, 1903, Cole famously made a presentation to a meeting of the American Mathematical Society where he identified the factors of the Mersenne number $2^67- 1,$ or M67.[5] douard Lucas had demonstrated in 1876 that M67 must have factors (i.e., is not prime), but he was unable to determine what those factors were. During Cole's so-called "lecture", he approached the chalkboard and in complete silence proceeded to calculate the value of M67, with the result being 147,573,952,589,676,412,927. Cole then moved to the other side of the board and wrote 193,707,721 761,838,257,287, and worked through the tedious calculations by hand. Upon completing the multiplication and demonstrating that the result equaled M67, Cole returned to his seat, not having uttered a word during the hour-long presentation. His audience greeted the presentation with a standing ovation.

I consider this manner as a mark of a professional mathematician: let others convey the excitement of a discovery. A good recent example was the submission of a paper on bounded gaps between primes. Much of the public excitement was generated by people other than the author, Yitang Zhang.

I think the following anecdote fits well in this category. Note however, that other participants may have experienced these things differently, since they will have had a better background knowledge of the topic.

At a conference in Uppsala in September 2012, Geordie Williamson was scheduled to give a talk. I can unfortunately not recall the precise topic, as I can no longer find the program for the conference.

He starts his talk by apologizing that he is in fact going to talk about a completely different topic, since he had very recently finished some work on this with his collaborator Ben Elias.
He then goes on to describe Soergel's conjecture and some of the ideas that he and Ben have been working on, hoping to make progress on the conjecture.

The talk is quite technical, involving a lot of quite deep ideas and descriptions of how certain geometrical ideas, such as Hodge theory, can be given more algebraic analogues and how these may be put together to make progress on the conjecture.

Russell and Whitehead's Principia Mathematica has a long and complicated proof that 1+1=2, given after spending 80+ pages defining arithmetic in terms of logical primitives. The proof is accompanied by the famous comment "The above proposition is occasionally useful."

My favorite is non-mathematician Marjorie Rice challenging the proof of "No other pentagon tilings exist" with multiple new pentagon tilings. Schattschneider's article was the primary announcement of the results.

Onsager announced in 1948 (see the reconstruction by Baxter) that he and Kaufman had found a proof for the fact that the spontaneous magnetization of the Ising model on the square lattice with couplings $J_1$ and $J_2$ is given by$$M = \left(1 - \left[\sinh (2\beta J_1) \sinh (2\beta J_2)\right]^-2\right)^\frac18,$$but he kept the proof a secret as a challenge to the physics community. The proof was obtained by Yang in 1951.

The final construction was of an oscillator with period $41$, which was first posted without much fanfare into a LifeWiki-associated Discord chat room by Nico Brown in July 2023. It was soon after copied over to the the ConwayLife.com Forums by the same author. The resolution was soon after catalogued on Adam P. Goucher's blog Complex Projective 4-Space in the post "Miscellaneous discoveries".

Edit December 2023: The paper "Conway's Game of Life is Omniperiodic" now posted on arXiv contains more details about the chronology of the result and the constructions, with clickable diagrams that show the evolution of the pattern (run on a third-party site).

The math problem in question is known as the "Euler Brick" problem, which was first proposed by Swiss mathematician Leonhard Euler in 1776. It involves finding a set of three positive integers that can form the dimensions of a rectangular cuboid with integer edge lengths, and also have the property that the sum of the squares of any two of the dimensions is itself a perfect square.

The user posted a solution on the popular imageboard site 4Chan, which involved using a computer program to systematically search for solutions. The program used brute force methods to test different combinations of integers until a solution was found.

Yes, the solution was verified by several mathematicians and experts in the field, including Andrew Booker from the University of Bristol and Andrew Sutherland from the Massachusetts Institute of Technology. They confirmed that the solution was correct and also provided additional insights and proofs.

The "Euler Brick" problem had remained unsolved for over 200 years, making it a highly sought-after solution in the mathematical community. The fact that it was solved by an anonymous user on 4Chan, rather than a renowned mathematician, also adds to its significance and has sparked discussions about the democratization of mathematics.

The solution has opened up new avenues for research and has led to further exploration of related problems. It also highlights the power of collaboration and the potential for individuals outside of traditional academic circles to make significant contributions to the field of mathematics.

Anime fans surprise all the time with the variety of fans there are, and one fan just might have used anime to help solve a tricky problem mathematicians have been trying to solve for the past 25 years.

Although the fan just used the equation to figure out the best way to watch every order of The Melancholy of Haruhi Suzumiya in the shortest time possible, now mathematicians are wondering how to progress with this solved equation from an anonymous fan.

The Melancholy of Haruhi Suzumiya is a cult classic with fans not only for its time-travelling, meta content. but for the fact that it originally aired out of order. When the series was released on home video, it was arranged in a new order and fans have been debating over which way to watch for quite some time.

Years ago, one fan posed a question for 4chan asking, "if you wanted to watch 14 episodes of the anime The Melancholy of Haruhi Suzumiya in every possible order, what's the shortest string of episodes you'd need to watch?" One fan eventually solved the problem, and helped struggling mathematicians out by providing the best way to break down superpermutations.

A permutation relates to the order of a set of numbers (or as one way to watch Haruhi), and the "super" form of that accounts for every order. According to a report for The Verge, the anonymous equation doesn't quite solve the permutations issue but gives experts a solid platform to work off of.

Jay Pantone, mathematician at Marquette University, even worked the problem into a more professional format and the proposed equation holds up among more experts. Pantone suggests that the answer to the "Haruhi" problem is that fans would, "need to watch at least 93,884,313,611 episodes to watch the season in any possible order. At most, you'd need to watch 93,924,230,411 episodes to accomplish the task."

With the power of anime on their side, and a quite literal god in Haruhi Suzumiya, now the world of math is helped along with a solution found in the strangest of places. Mathematicians didn't expect to see a solution to their problem in an anime message board, and anime fans didn't expect that either. Goes to show just how much of a variety there is in the fandom.

Apparently part of the solution to a difficult mathematics problem has been available for years on a 4chan board about anime. The anonymous author provided it as a tip about how to best watch a non-linear series.

The problem in question comes from the math field of combinatorics and deals with permutations. A permutation is an act of changing the arrangement, especially the linear order, of a set of items. For instance, the numbers 1, 2 and 3 can be arranged in six different ways, i.e. there are six possible permutations for three elements. A superpermutation is a string that contains all possible permutations of a set as sub-strings.

In more practical terms, say there is a series of several episodes labeled not chronologically, but absolutely arbitrary. And the series is so bad that you have no way of determining the correct order from the content. If you are determined to watch them the right way at least once, you can start a marathon, playing the episodes again and again until all possible order variants are complete.

Haruhi Suzumiya (Japanese: 涼宮ハルヒ, Hepburn: Suzumiya Haruhi) is a Japanese light novel series written by Nagaru Tanigawa and illustrated by Noizi Ito. It was first published in 2003 by Kadokawa Shoten in Japan with the novel The Melancholy of Haruhi Suzumiya, and has since been followed by 11 additional novel volumes, an anime television series adaptation produced by Kyoto Animation, four manga series, an animated film, two original net animation series and several video games.

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