I think all this proves is that some mice inserted the number 42 into Douglas Adams' head all those years ago. Now I am wondering when the program will stop running.
Finally! A solution to 42 – the Answer to the Ultimate Question of Life, The Universe, and Everything
Mathematicians have finally cracked the sum-of-three-cubes problem for the geek-friendly number 42. The puzzle, set more than half a century ago in 1954, challenges you to solve the equation x3 + y3 + z3 = k, where x, y, z are integers and k is an integer from 1 to 100. Some values of k are impossible to solve, and the …
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Saturday 7th September 2019 22:45 GMT Bill Gray
1729 = 12^3+1^3 = 10^3+9^3, making 1729 the first "taxicab number."
https://en.wikipedia.org/wiki/Taxicab_number
From the above :
The name is derived from a conversation in about 1919 involving mathematicians G. H. Hardy and Srinivasa Ramanujan. As told by Hardy:
“I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. 'No,' he replied, 'it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways.'"
Somebody (don't remember who) once said of Ramanujan that it seemed as if every integer was a personal friend of his. So it's not too surprising that Ramanujan noticed this right away.
Unfortunately, Ramanujan died the next year, so the "favourable omen" bit didn't pan out.
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Saturday 7th September 2019 08:11 GMT Muscleguy
Re: Disturbing
Autumn is closing in, the mice, currently largely outside will come in and make themselves known to you. I must bait and reset my traps. I only caught three last Autumn.
Of course white mice are almost all housed with ad libitum food and water and a constant warm climate in labs all over the world. They can also sometimes be found in pet shops.
Personally despite having spent my working life working on mice I would prefer rats as pets. Rats have more smarts and personality. They can also be trained to be less likely to piss and poo and you.
It might have something to do with pet rats and lab rats being much less inbred than most of the mice. Because we have a strongly established genetics for mice and not for rats. Which means inbred lines. Outbred mouse mothers will collect the faeces of her and her offspring and push them up into the cage bars wth the sawdust keeping the nest clean. Inbred mothers do not.
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Saturday 7th September 2019 08:31 GMT Spamfast
“The computation on each PC runs in the background so the owner can still use their PC for its usual tasks,” Sutherland told The Register.
Yet another pointless waste of energy keeping the CPU at high clock and the drives spinning just like the distributed Mersenne prime software. And it encourages people to leave their PCs runnng where they previously might have turned them off. These mathematical curiosities are of no theoretical or practical value even within the field of mathematics let alone outside it.
If you must run something in the background, do something useful like Folding@home. Or turn the computer off, got for a walk and do flora & fauna surveys for the RSPB or whoever. Who knows, you might discover a new species of insect or plant. Wouldn't that be more satisfying than some pointless string of digits?
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Saturday 7th September 2019 09:26 GMT GrumpenKraut
Where to start?
Just one point: the techniques used in such HPC tasks have a tendency to be useful for other tasks. Say, for the computer algebra system you are using.
OK, another one: the proudly non-applied field of number theory turned (many decades later) out to be the guts of error-correcting codes and cryptography. Useful for computer-y stuff, you know?
Of course the alternatives like protein folding (and tons others) are exciting as well.
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Sunday 8th September 2019 11:08 GMT Spamfast
I'm all for pure research and the unexpected spin-offs it generates.
But mathematicians themselves say that these sorts of brute force searches are pointless. Explain to me how knowing the answer for 42 or finding the largest Mersenne prime advances any field in mathematics. It's all stamp collecting. Real mathematics is done by mathematicians not computers.
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Monday 9th September 2019 06:34 GMT GrumpenKraut
> ...these sorts of brute force searches are pointless.
Number crunching is not mathematics, sure. But brute force computations are useful, for example, for ...
Finding solutions for Diophantine equations when you don't have stronger theorems, possibly helping you to find theorems (yes, you must prove them).
Verifying or falsifying conjectures. In discrete mathematics (e.g., number theory, coding theory, combinatorics, ...) this is done all the time.
Numerically solving problems that are outright impossible to do by hand. Nonlinear differential equations are a good example (think solitons).
It is routine to use computers to observe properies and make conjectures. A certain Gauss did this all the time.
Not every mathematician works this way, but a lot of them do. So...
> Real mathematics is done by mathematicians not computers.
...implies that dozens of mathematicians I happen to know are not actually mathematicians. I refuse to to believe that.
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Monday 9th September 2019 08:26 GMT JetSetJim
As an individual result it may not really help all that much, but I'd posit that at the very least:
a) an algorithm was developed to help search the solution space - perhaps a nice undergrad project, possibly even a masters element
b) existing theorem's/hypotheses are present that help filter out bits of the solution space as a waste of search time - having this result will help validate them or even extend them, even if it can't prove a general case
c) it may perhaps inspire others to come up with a general purpose proof that these things exist, much like Andrew Wiles' proof of Fermat's theorem - I suspect this is more in line with the end game.
An example of an instance where the equation holds true isn't proof that the equation is true for all values - the two problems are approached in a very different way, and both pose challenges in implementation, and (for some) are fun to play with.
Let the maths-bods have some fun, and that includes the ones donating CPU to the project.
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Monday 9th September 2019 13:26 GMT JDX
re:Real mathematics is done by mathematicians not computers.
That's just hopelessly out of date. Many proofs are computer-aided now. Figuring out how to use computers to find proofs that cannot ever be done unaided is a part of modern mathematics.
Quite old now, but Fermat's last theorem is a good example.
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Monday 9th September 2019 16:11 GMT Lee D
Four colour theorem.
It's about using a tool appropriate to the job to do the boring parts, rather than having the computer hypothesise new theories (which they can't do anyway).
And Mersenne primes are incredibly important.
Sorry, but that's just a staggering amount of ignorance you're showing.
And I'm a mathematician, and a computer science guy.
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Tuesday 10th September 2019 12:01 GMT Lee D
Mersenne Primes are forming the basis of some ECC curves because of their special properties, as well as random number generators, not to mention being an integral part of some post-quantum cryptography candidates (e.g. Mersenne-756839).
Every time you say to a mathematician "Well what's the point of that?", I guarantee you that it's *already* in use somewhere for some purpose that will end up in something you use every day and rely on.
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Friday 13th September 2019 16:51 GMT Charles 9
I withdrew my earlier post because it hadn't been made clear that "Mersenne number" (n = 2^p - 1 where p is prime) and "Mersenne prime" (n = 2^p - 1 where p is prime) are actually the same thing (2^p - 1 being prime -> p is also prime). That said, I'll believe their practicality when I see them in action.
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Sunday 8th September 2019 23:03 GMT doublelayer
Let's really think about this. I don't mind if people want to donate cycles to finding this answer. But why do we care about it? I really like lots of abstract math problems, but they didn't find and execute a new algorithm that can solve these things; they brute forced a bunch of options and found one. If we should need to solve this problem for some reason in the future, and I'm willing to assume we've found one even though I haven't a clue what that would be, does this program give us a new, faster, or organized way of solving for it? From what I've seen, it does not, and we'd have to put more resources into a brute force search. So let's not give it the kind of credit that you've implied. The examples you provide gave us new algorithms, and they turned out to be useful later on. All we got from this are three big numbers.
Computing resources can be quite cheap in cases like these. If that's the way people choose to use them, then that's fine. But let's not give this more credit than it deserves.
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Saturday 7th September 2019 12:40 GMT Martin Gregorie
Yet another pointless waste of energy keeping the CPU at high clock
Not all BOINC projects are a waste of energy.
That said, I used to be a supporter back when a PC's clockspeed was fixed, but once my house server, which runs 24/7, had its old hardware replaced with a variable clock speed dual Athlon box and I'd had to listen to the poor thing howling continuously at maxed-out clock speed and full-throttle fans, BOINC got the chop and has never been reinstalled.
Bottom line: I'm happy to donate unused cycles to worthwhile projects, but these were not unused cycles: they would not have existed if BOINC hadn't stomped the PC's pedal to the metal and held it there.
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Wednesday 11th September 2019 12:02 GMT Spamfast
Re: PC's pedal to the metal
It's still going to consume resources that it needn't if it were switched off or put into deep sleep until an external event woke it up to do useful work.
Despite all the protests to the contrary in this thread, finding huge Mersenne primes and sum-of-cubes triples using existing algorithms doesn't achieve anything for mathematics, HPC or cryptography.
If someone designs/discovers a new, better algorithm that then might be useful elsewhere I agree.
But that doesn't justify consuming power to run an existing algorithm - that achieves diddley-squat, other than smugness if it happens to be one of 'your' computers that finds a larger/harder solution.
And quite often its academic BOFHs who install this nonsense on all the computers under their control and it's the students or the taxpayers who end up paying for the juice to power & cool it & the extra spinning-rust wear-and-tear, let alone the environmental damage.
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Tuesday 24th September 2019 21:38 GMT Eclectic Man
Art
If you object to computers being used for pure, in this case Diophantine, mathematics, what is your position on using resources for art?
I often find the entries to the Turner Prize to be baffling, and the artists have certainly used lots of resources to make them.
I do mathematics, and I'm currently researching some diophantine mathematics myself, although my numbers are somewhat larger (2578 decimal digits), but only use squares, not cubes.
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Saturday 7th September 2019 09:59 GMT Anonymous Coward
Re: Nice.
Fermat's Last Theorem required a and b (and therefore c) to be positive integers greater than zero, and n to be greater than two.
I realised some years ago that the general theorem which states that the following has no solution:
a^n + b^n = c^n
can be simplified to the following true algorithm:
(a-1)^n + a^n < (a+1)^n
for all n greater than two.
Which I would assume (I'm no mathematician) is easier to prove in a mathematical sense than the original theorem. Which would then also prove Fermat.
(I like to think this is the simple proof Fermat alluded to in his infamous margin, but I guess we'll never know.)
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Tuesday 24th September 2019 21:42 GMT Eclectic Man
Re: Nice.
Now then do not confuse symbolic mathematics with all mathematics. Rational thought is mathematics, so if you do deductions, derivations etc., you are a mathematician. Consider that someone can be illiterate, yet still be a brilliant orator. Would you say that person was 'no good' at English?
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Sunday 8th September 2019 00:06 GMT Carpet Deal 'em
Re: Nice.
It's highly doubtful that Fermat actually had a proof. First, he never wrote about it again for the thirty or so years he lived after the famous scribble(despite posing specific exponent versions as challenges to other mathematicians of the day); second, the actual proof was over a hundred pages and relied on recently invented techniques(which would mean a proof based solely on early/mid 1600s math would probably be well over a thousand pages - a magnitude that would warrant language stronger than "this margin is too narrow to contain").
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Monday 9th September 2019 05:12 GMT brotherelf
Re: Nice.
> Nobody I ever met believes that Fermat really had a proof.
I'm not much of a believer in afterlife, but I get a chuckle out of the idea that Fermat's corner of hell, for whatever reasons, is everybody recognizing him, looking at his proof in the margin, and going "you forgot a minus at the beginning there, mate".
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Monday 9th September 2019 08:42 GMT Mr Humbug
If you're referring to Arthur's use of teh scrabble tiles to divine the question (what do you get if you multiply six by nine) then I think you mean 54.
But the programme that ended with Arthur's result was corrupted by the Golgafrincham B Ark, which is why he produced the wrong question.
</pedant>
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Monday 9th September 2019 06:34 GMT MacroRodent
Checked it
On Fedora Linux
$ bc
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'.
x=-80538738812075974
y=80435758145817515
z=12602123297335631
x^3+y^3+z^3
42
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Biting the hand that feeds IT
