Anonymous 4Chan User Proves a 25yr old Math Problem

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In summary: Scandinavians.In summary, an anonymous user on the online bulletin board 4chan proposed a lower bound for the number of episodes required to watch all possible orderings of the cult classic anime series The Melancholy of Haruhi Suzumiya. This proof went unnoticed by the mathematics community for seven years until Australian science fiction writer Greg Egan provided a new upper bound, sparking renewed interest in the problem. The discussion also touched on the declining population of geniuses and the potential impact of technology on intelligence.
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14,737
9,085
https://www.quantamagazine.org/sci-...th-whiz-advance-permutation-problem-20181105/

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. 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. 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?

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. 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. “Please look over [the proof] for any loopholes I might have missed,” the anonymous poster wrote.

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. 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. Egan’s discovery renewed interest in the problem and drew attention to the lower bound posted anonymously in 2011. Both proofs are now being hailed as significant advances on a puzzle mathematicians have been studying for at least 25 years.
 
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  • #2
Would have been interesting to read, whether the problem is also NP-complete and what the lower bound contributes to the NP problem.
(Will say, I haven't put the effort into figure it out myself.)
 
  • #4
Let's invent something here... and... go! :biggrin:
 
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  • #6
Anonymous 4Chan User Proves a 25yr old Math Problem
Not really. They improved a bound a bit. It is a remarkable improvement (it is better than a pattern you might expect from small numbers), but it is not a solution to the problem.
 
  • #7
mfb said:
Not really. They improved a bound a bit. It is a remarkable improvement (it is better than a pattern you might expect from small numbers), but it is not a solution to the problem.
Yes, but given the fact, that lower bounds are much harder to prove than upper, and that it's notoriously difficult to achieve non-linear ones, this is still a remarkable result.
 
  • #8
Greg Bernhardt said:
Let's invent something here... and... go! :biggrin:
That's against the rules! :wink:
 
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  • #9
I think Greg would like a PF user to share their PvNP, or Reimann or Navier Stokes... proof here to be discovered by the Clay foundation. In that way PF would get 10% of the winnings.
 
  • #10
Some Ramanujan-like third world math genius who never afforded formal schooling may actually do that some day.
 
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  • #11
hilbert2 said:
Some Ramanujan-like third world math genius who never afforded formal schooling may actually do that some day.

Very true. We are handicapped by our own technology which weakens our ability to think long and deeply about some topic and to remember what we thought.
 
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  • #12
In some book, written about Richard Feynman I think, there was a mention about how the number of geniuses in the world has not increased at the same rate as the world population. This could in the worst case be a result of some kind of "negative evolution", where the intelligent people get less offspring that others, or a result of the stimulus-rich modern environment making people less thoughtful.

Here in Finland and Sweden we still have a population of significantly less than 20 million people total in both countries together, but we still had many significant mathematicians during the early 20th century, especially in the field of complex analysis. This was because the school system of the time accepted only a very small proportion of young people to senior high school, and the curriculum could be made so tough that they were actually teaching proof techniques to underage students and using things like Euclid's "Elements" as textbooks. That's probably the other method, apart from having a large population, to produce many good mathematicians.
 
  • #13
Haha, there's a funny movie that brings the IQ and population explosion into focus:

https://en.wikipedia.org/wiki/Idiocracy

In 2005, United States Army librarian, Corporal Joe Bauers, is selected for a suspended animation experiment on grounds of average appearance, intelligence, behavior, etc. Lacking a suitable female candidate within the armed forces, they hire Rita, a prostitute whose pimp "Upgrayedd" has been bribed to allow her to take part. The experiment is forgotten when the officer in charge is arrested for having started his own prostitution ring under Upgrayedd's tutelage. Over the next five centuries, the expectations of 21st-century society ensure that the most intelligent humans fail to have children, while the least intelligent reproduce prolifically, which, through the process of natural selection, creates generations that collectively become increasingly dumber and more virile with each passing century. In 2505, Joe and Rita's suspension chambers are unearthed by the collapse of a mountain-sized garbage pile, and Joe's suspension chamber crashes into the apartment of Frito Pendejo, who expels him.

One of the notable events in the film, is the use of Gatorade to water the crops. Its not working but the corporation insists its the right thing to do until the protagonist suggests using water.
 
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  • #14
hilbert2 said:
Here in Finland and Sweden we still have a population of significantly less than 20 million people total in both countries together, but we still had many significant mathematicians during the early 20th century, especially in the field of complex analysis.
I have to include Norway and Marius Sophus Lie, Denmark and Harald August Bohr here. Doesn't change the headcount of Scandinavian population very much, but does to the headcount of geniuses.
 
  • #15
fresh_42 said:
I have to include Norway and Marius Sophus Lie, Denmark and Harald August Bohr here. Doesn't change the headcount of Scandinavian population very much, but does to the headcount of geniuses.

Good point. And there's also Niels Hendrik Abel, the Norwegian group theory genius from a slightly earlier era.
 
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  • #17
jedishrfu said:
Let us not forget Loki. A great genius of another age...
I cancel Loki (bad a..) and raise by two Kaurismäki and a strange Cowboy band!
 
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  • #18
hilbert2 said:
In some book, written about Richard Feynman I think, there was a mention about how the number of geniuses in the world has not increased at the same rate as the world population.
How was that number of geniuses defined and measured?
 
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  • #19
mfb said:
How was that number of geniuses defined and measured?

I couldn't now find the book where I saw that claim. It was not defined in any exact way. If you look at a list of notable historical scientists and artists, it is usually quite weighted towards people who lived before 20th century, but a reason for this may be that all the "easy" scientific discoveries have already been made and art gets more appreciation as it gets old.
 
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  • #20
From the article:
“It took a lot of work to try to figure out whether or not it was correct,” Pantone said, since the key ideas hadn’t been expressed particularly clearly.
I think this is mathematicians' way of saying, "Dang, I wish I'd thought of that!"
 
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  • #21
TeethWhitener said:
From the article:

I think this is mathematicians' way of saying, "Dang, I wish I'd thought of that!"
That's the positive side of the medal. The negative is, that in his next publication the key ideas will be shortened by "it's obvious that" and "clearly we have".
 
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  • #22
fresh_42 said:
That's the positive side of the medal. The negative is, that in his next publication the key ideas will be shortened by "it's obvious that" and "clearly we have".
That reminds me of the old joke that there are two kinds of theorems: trivial and unproven.
 
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  • #23
TeethWhitener said:
That reminds me of the old joke that there are two kinds of theorems: trivial and unproven.
I remember such an "obvious" part in a paper I had to prepare for a seminar. It was about some formulas of complex numbers, and yes, after three days of trying an endless number of ideas, and finally applying three transformations like ##z \mapsto w=\dfrac{1}{x+iy} \, , \, x \mapsto ...## etc. it was indeed trivial.
 
  • #24
I always liked these two phrases

The proof is left to the student...

And

That’s not even wrong - W Pauli
 
  • #25
hilbert2 said:
I couldn't now find the book where I saw that claim. It was not defined in any exact way. If you look at a list of notable historical scientists and artists, it is usually quite weighted towards people who lived before 20th century, but a reason for this may be that all the "easy" scientific discoveries have already been made and art gets more appreciation as it gets old.
It got more difficult to revolutionize a large field of science because the easy things are discovered and more and more collaboration is needed for further advances. At the same time there are simply more scientists everywhere. It is natural that it gets more difficult to be outstanding.
 
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jedishrfu said:
I always liked these two phrases

The proof is left to the student...

And

That’s not even wrong - W Pauli
I'll add: "The generalisation to higher dimensions is trivial." No, it isn't!
 
  • #27
mfb said:
It got more difficult to revolutionize a large field of science because the easy things are discovered and more and more collaboration is needed for further advances. At the same time there are simply more scientists everywhere. It is natural that it gets more difficult to be outstanding.
I tried to find reliable figures for the quantity of geniuses by time. I failed. But what came up was a tremendous number of influences, which affect these figures. Yours in the above quotation is one of them, one which is more related to modern physical projects than to mathematics. Here is another interesting one:
Humanists are genetically unencumbered. In their families, psychoses are no more common than in the social mean. The situation is different with mathematicians: two to three times as many psychoses as expected plague their families.
I found it in a news magazine, so it was unfortunately not referenced. However, under the assumption that it's true, then also our general attitude and reactions to those circumstances play in, and I like to think, that we are nowadays faster in treating them, or at least their symptoms, which may or may not have a feedback reaction - in this case a possibly negative one.

I regularly read Terence Tao's newsletter and he is what we call a "jack of all trades" as well as undoubtedly within the range of a genius. Nevertheless, I couldn't tell any of his achievements to support this opinion. So as long as no one comes up with ##P\neq NP##, ##ERH## or ##Goldbach##, (s)he will probably not be recognized in the counting which led to the statement about the distribution of geniuses, which sounded more to be made by laymen rather than by experts.

So besides the problem of measurement, it also will be extremely difficult to make those figures comparable at all.
 
  • #28
One negative influence is our educational system which has preconceived notions of intelligence and sometimes their policies for keeping students into specific groups impede genius.

One recent case, I read about was Aron Hall who was held back in Algebra. The teacher knew he knew the material but she forced him to retake algebra again the following year because he never turned in any homework. At the time he said he was self studying Calculus having learned Algebra in 5th grade.

His dad was Larry Wall inventor of the Perl scripting language.

Some older cases were Ramanujan who couldn’t advance in school because he didn’t do well in his English courses.
 
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  • #29
hilbert2 said:
Some Ramanujan-like third world math genius who never afforded formal schooling may actually do that some day.
We really need someone like that who hasn't been told that traveling faster than the speed of light is impossible.
 
  • #30
Dr_Zinj said:
We really need someone like that who hasn't been told that traveling faster than the speed of light is impossible.

This reminds me of the story of a grad student who came to class late saw some problems in statistics on the board and assumed they were homework. He worked them out and handed them in.

Later the prof visited him at home saying he wanted to write a foreword to his two proofs and submit them for publication. They were in fact two unproven theorems.

Some time later when he went to see his prof about his PhD research project, the prof said let’s just bundle these two theorems up as your thesis. In that moment, so many grad students became jealous.
 
  • #31
jedishrfu said:
This reminds me of the story of a grad student who came to class late saw some problems in statistics on the board and assumed they were homework. He worked them out and handed them in.

Later the prof visited him at home saying he wanted to write a foreword to his two proofs and submit them for publication. They were in fact two unproven theorems.

Some time later when he went to see his prof about his PhD research project, the prof said let’s just bundle these two theorems up as your thesis. In that moment, so many grad students became jealous.
That was George Dantzig, and he went on to have a very prolific career:
https://en.wikipedia.org/wiki/George_Dantzig
 
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  • #32
Yes, I was writing while traveling and couldn’t remember his name. I especially liked the part about slapping the theorems together and calling it a thesis.
 
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1. What is the 25-year-old math problem that was solved by an anonymous 4Chan user?

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.

2. How did the anonymous 4Chan user solve the problem?

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.

3. Was the solution verified by other mathematicians?

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.

4. Why is this solution significant?

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.

5. What impact does this solution have on the field 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.

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