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42 is found to be the sum of three cubes

552 pointsby techolicover 5 years ago

38 comments

isotropyover 5 years ago
For context, 42 was the only remaining number below 100 where it wasn’t known if this was possible. The general problem of exactly which numbers are the sum of three cubes is unsolved.<p><a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Sums_of_three_cubes" rel="nofollow">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Sums_of_three_cubes</a>
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robinhoustonover 5 years ago
I’ve just seen that my tweet is here!<p>If anyone wants more details, I wrote a more detailed account, which has just been published at <a href="https:&#x2F;&#x2F;aperiodical.com&#x2F;2019&#x2F;09&#x2F;42-is-the-answer-to-the-question-what-is-80538738812075974%c2%b3-80435758145817515%c2%b3-12602123297335631%c2%b3&#x2F;" rel="nofollow">https:&#x2F;&#x2F;aperiodical.com&#x2F;2019&#x2F;09&#x2F;42-is-the-answer-to-the-ques...</a>
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techolicover 5 years ago
See also <a href="https:&#x2F;&#x2F;twitter.com&#x2F;robinhouston&#x2F;status&#x2F;1169877007045296128" rel="nofollow">https:&#x2F;&#x2F;twitter.com&#x2F;robinhouston&#x2F;status&#x2F;1169877007045296128</a>. I was prompted the twitter link has been submitted but wasn&#x27;t able to find it.<p>Edit: And apologies for using unicode ㊷ in the title, the ascii 42 was removed from the title after initial submission.
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intuitionistover 5 years ago
This is a great announcement; it reminds me of the legendary story of Frank Nelson Cole wordlessly announcing his factorization of 2^67 - 1: <a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Frank_Nelson_Cole" rel="nofollow">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Frank_Nelson_Cole</a>
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thekyleover 5 years ago
Could someone elaborate on why this is interesting? The linked page doesn&#x27;t have much context.
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federicoponziover 5 years ago
document.body.innerHTML = document.body.innerHTML.replace(&quot;&lt;!--&quot;, &quot;&quot;);
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ivan_ahover 5 years ago
We can easily verify using SymPy on live.sympy.org:<p><a href="https:&#x2F;&#x2F;live.sympy.org&#x2F;?evaluate=(-80538738812075974)**3%20%2B%2080435758145817515**3%20%2B%2012602123297335631**3%0A%23--%0A" rel="nofollow">https:&#x2F;&#x2F;live.sympy.org&#x2F;?evaluate=(-80538738812075974)**3%20%...</a>
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whitehouse3over 5 years ago
Why doesn&#x27;t this evaluate in Excel?<p>=(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3<p>Returns 1.09785E+36
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jacquesmover 5 years ago
That&#x27;s got to be the shortest article on HN ever to make the homepage.
alejohausnerover 5 years ago
What about zero? Can zero be the sum of three cubes? Actually, I read that somebody proved it can&#x27;t be done, but the proof is too long to fit in this comment. ;-)
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alskdj21over 5 years ago
Here&#x27;s a Numberphile video about this news. <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=zyG8Vlw5aAw" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=zyG8Vlw5aAw</a>
Lioover 5 years ago
_randomly pulling letters out of a scrabble bag_<p>(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 is 42?<p>42?!<p>I always said there was something fundamentally wrong with the universe.
chrisauover 5 years ago
Ignoring the century in the year, I love the coincidence that this question was first asked in the year &#x27;54 and in &quot;Hitchhiker&#x27;s&quot;, it&#x27;s said that 6x9 and 42 are the same. In fact they are if 6x9 is base 10 (6x9=54), and 42 is base 13 (4x13+2 = 54).<p>So, we get three coincidences: This question was asked in &#x27;54 ; &quot;Hitchhiker&#x27;s&quot; said the answer to the meaning of life is 54 (6x9, 42 base 13); and best of all, 42 was the last number solved. And if you want to add one more coincidence, this was solved in the year &#x27;19 (connecting 19 and 54).<p>All irrelevant coincidences applied with hindsight, but fun.<p>(Douglas Adams claimed that 42 was a randomly chosen number, but I&#x27;d argue his subconscious had been processing the idea for a while and gave him a number with a meaning. We just don&#x27;t know which is the correct meaning.)
artie_effimover 5 years ago
checks out <a href="https:&#x2F;&#x2F;www.wolframalpha.com&#x2F;input&#x2F;?i=%28-80538738812075974%29%5E3+%2B+80435758145817515%5E3+%2B+12602123297335631%5E3+" rel="nofollow">https:&#x2F;&#x2F;www.wolframalpha.com&#x2F;input&#x2F;?i=%28-80538738812075974%...</a>
jliptzinover 5 years ago
Any writeup for how this was found? Any interesting algorithm or was it just brute forced?
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CharityEngineover 5 years ago
Hey guys, Mark from Charity Engine here.<p>If anyone else could use planetary-scale computing (potentially for free, if your project is really cool), then come and talk to us.<p>The CE grid has over 2 million CPU cores, 600k+ unique IP addresses, can run anything in a Docker container and has integration with Ethereum. Adding Kubernetes and GPU support as we speak.<p>You can fire it up with 8 clicks, easier than AWS. This is literally a fully-functional worldwide computer.<p>PS. It&#x27;s not just ridiculously huge, it is also ridiculously cheap :)
rank0over 5 years ago
I must be missing something. Why is this significant?
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raghavkhannaover 5 years ago
Here&#x27;s a great video by numberphile on the subject <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=ASoz_NuIvP0" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=ASoz_NuIvP0</a>
densetsuover 5 years ago
Hitchhikers rejoice!
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djyaz1200over 5 years ago
<a href="http:&#x2F;&#x2F;youtu.be&#x2F;8190ziL5v-k" rel="nofollow">http:&#x2F;&#x2F;youtu.be&#x2F;8190ziL5v-k</a>
yumrajover 5 years ago
How was this computed? Just brute force ?
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petrikapuover 5 years ago
In Python<p><pre><code> &gt;&gt;&gt; (-80538738812075974)**3 + 80435758145817515**3 + 12602123297335631**3 42</code></pre>
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brokenmachineover 5 years ago
I understand that it is interesting, but can someone ELI5 what this might be useful for in real life?
sidcoolover 5 years ago
Any idea what algorithm was used? Was it brute forcing through all combinations?
dustinmrover 5 years ago
Now that we have the answer, I wonder what the question was?<p>And why is that mouse looking at me?
t_minus_3over 5 years ago
dumb question: What is the practical application of this conjecture?
JustSomeNobodyover 5 years ago
So, does this mean life, the universe, and everything are all cubes?
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countryqt30over 5 years ago
If I copy and paste this formula to Google, I get a different result
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CharityEngineover 5 years ago
Any questions about the platform they used, feel free to ask :)
arthurcolleover 5 years ago
Was the author so excited by this finding that he replaced his academic page with just this expression?<p>Very interesting finding in any case!
airockerover 5 years ago
Can this be used instead of RSA?
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AstralStormover 5 years ago
And the universe turned slightly weirder again.
archie2over 5 years ago
Why should I care?
rdiddlyover 5 years ago
It&#x27;s also the answer to life, the universe and everything. Which is nice.
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Scoobertover 5 years ago
Clicked hoping for Douglas Adams, got Numberwang
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sabujpover 5 years ago
i love bc, just to verify :<p>bc 1.07.1 Copyright 1991-1994, 1997, 1998, 2000, 2004, 2006, 2008, 2012-2017 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty&#x27;.<p>(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3<p>42
binauralover 5 years ago
42 is also the answer to the universe. ;-)
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gunnihinnover 5 years ago
As a mathematician and long-time sufferer of that Douglas Adams meme:<p>GIVE A FUCK?