6 ms·

The Shortest Research Paper Ever Published

34 points by PLenz 7y ago

flywithdolp 7y ago
It's probably about what we did to stop the global warming so far
megalawn 7y ago
Numberphile did a video on short papers: https://www.youtube.com/watch?v=QvvkJT8myeI https://www.youtube.com/watch?v=QvvkJT8myeI
Someone 7y ago
”Euler proposed that the equation, a^n + b^n = c^n doesn’t hold true if the value of “n” is greater than “2”. Then in 1966, two mathematicians L.J. Lander and T.R. Parkin came along and swiftly overturned his claim with a counterexample: 27^5 + 84^5 + 110^5 + 133^5 = 144^5” That’s mixing Euler’s claim that you need to sum at least n n-th powers to get another n-th power (https://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjecture https://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjec...) with the (less general) Fermat’s last theorem (https://en.wikipedia.org/wiki/Fermat%27s_last_theorem https://en.wikipedia.org/wiki/Fermat%27s_last_theorem) The example in the paper disproved Euler’s conjecture, but did nothing about Fermat’s.
astazangasta 7y ago
>Euler proposed that the equation, an + bn = cn doesn’t hold true if the value of “n” is greater than “2”. This is wrong. That is Fermat's last theorem, which is true. Euler's conjecture is related but more general: >for all integers n and k greater than 1, if the sum of n kth powers of positive integers is itself a kth power, then n is greater than or equal to k: a1k + a2k + ... + ank = bk ⇒ n ≥ k
hervature 7y ago
Link to a previous post that talks about short papers - including this one. https://news.ycombinator.com/item?id=15737611 https://news.ycombinator.com/item?id=15737611
hprotagonist 7y ago
See also Conway and Soifer, “ Can n^2+ 1 unit equilateral triangles cover an equilateral triangle of side > n,say n + ε?” American Mathematical Monthly (2005). which is two words and two figures. Annotated so that it’s understandable: https://fermatslibrary.com/s/shortest-paper-ever-published-in-a-serious-math-journal-john-conway-alexander-soifer https://fermatslibrary.com/s/shortest-paper-ever-published-i...
andrepd 7y ago
Euler proposed that the equation, a^n + b^n = c^n doesn’t hold true if the value of “n” is greater than “2”. Then two mathematicians came along and overturned his claim with a counterexample: 27^5 + 84^5 + 110^5 + 133^5 = 144^5 Is it me or there's something wrong with that paragraph? x)
elcomet 7y ago
It's fun but not very interesting. A real research paper would explain the method they used to find this examples. Even only a few lines if the method is already known.
- dahart 7y ago
  “A direct search on the CDC 6600 yielded” That’s probably enough description of methodology for many people here to reproduce the results, right? :)
  - mikeash 7y ago
    I wouldn’t even know where to start looking for a working CDC 6600.
    - jfk13 7y ago
      Someone's probably written an emulator in JavaScript, so you can just run it in your browser. :)
      - pinewurst 7y ago
        http://members.iinet.net.au/~tom-hunter/ http://members.iinet.net.au/~tom-hunter/ There's a C one. Truly though, it wouldn't be hard to just write a brute force checker for this in some reasonably efficient compiled language.
    - dahart 7y ago
      I wouldn’t either. But I guess I don’t consider a CDC 6600 specifically to be critical to the methodology. I just meant that a lot of people around here could certainly write a computer program for direct search of the sum of four fourth power integers. It seems like this might even be one of the problems on Project Euler...?
      - mikeash 7y ago
        I was just pretending to misunderstand as a joke. You did make me curious, though. The numbers are fairly small. I implemented the dumbest possible brute force search for all combinations of numbers 1-255. On my laptop, it found 133^5 + 110^5 + 84^5 + 27^5 = 144^5 in about 50 minutes. I'd guess that this laptop is something like 100,000 times faster than the CDC 6600, so that dumb search would have taken about a decade. However, you can get at least a couple orders of magnitude improvement with some simple improvements.
sys_64738 7y ago
How do you discover these number in 1966?
radioactivist 7y ago
There is a story in a similar spirit about showing that one of the supposed Mersenne primes (2^67-1) was in fact composite -- (probably apocryphally) by simply doing the arithmetic by hand on a blackboard during a talk. For more details, see: - https://en.wikipedia.org/wiki/Mersenne_prime https://en.wikipedia.org/wiki/Mersenne_prime - https://hsm.stackexchange.com/questions/2105/whats-the-famous-story-about-a-mathematician-who-gave-a-talk-without-saying-a-w/2106 https://hsm.stackexchange.com/questions/2105/whats-the-famou... - https://mathoverflow.net/questions/207321/how-did-cole-factor-267-1-in-1903 https://mathoverflow.net/questions/207321/how-did-cole-facto...
Upvoter33 7y ago
sure, but the paper could have included the code ... :)
jamesb93 7y ago
That's just poor research.
selimthegrim 7y ago
Surprised no one linked to this well-known preprint by Asher Peres. https://arxiv.org/abs/quant-ph/0310035 https://arxiv.org/abs/quant-ph/0310035
marttt 7y ago
Here's an even shorter one: Upper, Dennis. "The unsuccessful self-treatment of a case of “writer's block”." Journal of Applied Behavior Analysis 7.3 (1974): 497. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1311997/pdf/jaba00061-0143a.pdf https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1311997/pdf/jab...
- frosted-flakes 7y ago
  The reviewer comment is hilarious: > COMMENTS BY REVIEWER A > I have studied this manuscript very carefully with lemon juice and X-rays and have not detected a single flaw in either design or writing style. I suggest it be published without revision. Clearly it is the most concise manuscript I have ever seen—yet it contains sufficient detail to allow other investigators to replicate Dr. Upper's failure. In comparison with the other manuscripts I get from you containing all that complicated detail, this one was a pleasure to examine. Surely we can find a place for this paper in the Journal—perhaps on the edge of a blank page.

34 points by PLenz 7y ago

It's probably about what we did to stop the global warming so far

Numberphile did a video on short papers: https://www.youtube.com/watch?v=QvvkJT8myeI https://www.youtube.com/watch?v=QvvkJT8myeI

Someone 7y ago

”Euler proposed that the equation, a^n + b^n = c^n doesn’t hold true if the value of “n” is greater than “2”. Then in 1966, two mathematicians L.J. Lander and T.R. Parkin came along and swiftly overturned his claim with a counterexample: 27^5 + 84^5 + 110^5 + 133^5 = 144^5” That’s mixing Euler’s claim that you need to sum at least n n-th powers to get another n-th power (https://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjecture https://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjec...) with the (less general) Fermat’s last theorem (https://en.wikipedia.org/wiki/Fermat%27s_last_theorem https://en.wikipedia.org/wiki/Fermat%27s_last_theorem) The example in the paper disproved Euler’s conjecture, but did nothing about Fermat’s.

astazangasta 7y ago

>Euler proposed that the equation, an + bn = cn doesn’t hold true if the value of “n” is greater than “2”. This is wrong. That is Fermat's last theorem, which is true. Euler's conjecture is related but more general: >for all integers n and k greater than 1, if the sum of n kth powers of positive integers is itself a kth power, then n is greater than or equal to k: a1k + a2k + ... + ank = bk ⇒ n ≥ k

hervature 7y ago

Link to a previous post that talks about short papers - including this one. https://news.ycombinator.com/item?id=15737611 https://news.ycombinator.com/item?id=15737611

hprotagonist 7y ago

See also Conway and Soifer, “ Can n^2+ 1 unit equilateral triangles cover an equilateral triangle of side > n,say n + ε?” American Mathematical Monthly (2005). which is two words and two figures. Annotated so that it’s understandable: https://fermatslibrary.com/s/shortest-paper-ever-published-in-a-serious-math-journal-john-conway-alexander-soifer https://fermatslibrary.com/s/shortest-paper-ever-published-i...

andrepd 7y ago

Euler proposed that the equation, a^n + b^n = c^n doesn’t hold true if the value of “n” is greater than “2”. Then two mathematicians came along and overturned his claim with a counterexample: 27^5 + 84^5 + 110^5 + 133^5 = 144^5 Is it me or there's something wrong with that paragraph? x)

elcomet 7y ago

It's fun but not very interesting. A real research paper would explain the method they used to find this examples. Even only a few lines if the method is already known.

dahart 7y ago
“A direct search on the CDC 6600 yielded” That’s probably enough description of methodology for many people here to reproduce the results, right? :)
- mikeash 7y ago
  I wouldn’t even know where to start looking for a working CDC 6600.
  - jfk13 7y ago
    Someone's probably written an emulator in JavaScript, so you can just run it in your browser. :)
    - pinewurst 7y ago
      http://members.iinet.net.au/~tom-hunter/ http://members.iinet.net.au/~tom-hunter/ There's a C one. Truly though, it wouldn't be hard to just write a brute force checker for this in some reasonably efficient compiled language.
  - dahart 7y ago
    I wouldn’t either. But I guess I don’t consider a CDC 6600 specifically to be critical to the methodology. I just meant that a lot of people around here could certainly write a computer program for direct search of the sum of four fourth power integers. It seems like this might even be one of the problems on Project Euler...?
    - mikeash 7y ago
      I was just pretending to misunderstand as a joke. You did make me curious, though. The numbers are fairly small. I implemented the dumbest possible brute force search for all combinations of numbers 1-255. On my laptop, it found 133^5 + 110^5 + 84^5 + 27^5 = 144^5 in about 50 minutes. I'd guess that this laptop is something like 100,000 times faster than the CDC 6600, so that dumb search would have taken about a decade. However, you can get at least a couple orders of magnitude improvement with some simple improvements.

sys_64738 7y ago

How do you discover these number in 1966?

radioactivist 7y ago

There is a story in a similar spirit about showing that one of the supposed Mersenne primes (2^67-1) was in fact composite -- (probably apocryphally) by simply doing the arithmetic by hand on a blackboard during a talk. For more details, see: - https://en.wikipedia.org/wiki/Mersenne_prime https://en.wikipedia.org/wiki/Mersenne_prime - https://hsm.stackexchange.com/questions/2105/whats-the-famous-story-about-a-mathematician-who-gave-a-talk-without-saying-a-w/2106 https://hsm.stackexchange.com/questions/2105/whats-the-famou... - https://mathoverflow.net/questions/207321/how-did-cole-factor-267-1-in-1903 https://mathoverflow.net/questions/207321/how-did-cole-facto...

Upvoter33 7y ago

sure, but the paper could have included the code ... :)

jamesb93 7y ago

That's just poor research.

selimthegrim 7y ago

Surprised no one linked to this well-known preprint by Asher Peres. https://arxiv.org/abs/quant-ph/0310035 https://arxiv.org/abs/quant-ph/0310035

marttt 7y ago

Here's an even shorter one: Upper, Dennis. "The unsuccessful self-treatment of a case of “writer's block”." Journal of Applied Behavior Analysis 7.3 (1974): 497. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1311997/pdf/jaba00061-0143a.pdf https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1311997/pdf/jab...

frosted-flakes 7y ago
The reviewer comment is hilarious: > COMMENTS BY REVIEWER A > I have studied this manuscript very carefully with lemon juice and X-rays and have not detected a single flaw in either design or writing style. I suggest it be published without revision. Clearly it is the most concise manuscript I have ever seen—yet it contains sufficient detail to allow other investigators to replicate Dr. Upper's failure. In comparison with the other manuscripts I get from you containing all that complicated detail, this one was a pleasure to examine. Surely we can find a place for this paper in the Journal—perhaps on the edge of a blank page.