42 solved

[Michael 345]

Mathematicians Solve '42' Problem With Planetary Supercomputer

Yes there is a nod to Douglas Adams

https://www-sciencealert-com.cdn.am...of-three-cubes-problem-has-been-solved-for-42

 

[Gawdzilla Sama]

42 was the answer, not the problem.

 

[Michael 345]

42 was the answer, not the problem.

Good point but not correct in terms of the article

Which was
***
Mathematicians have finally figured out the three cubed numbers that add up to 42. This has settled a problem that has been pondered for 65 years: namely, can each of the natural numbers below 100 be expressed as the sum of three cubes?
*****
And THAT answer is/was
*****
(-80538738812075974)3 + 804357581458175153 + 126021232973356313 = 42.
*****
My highlights pertinent parts

YES 42 WAS Douglas Adams answer but not the mathematicians answer

 

[James R]

I haven't looked into this, but for me the interesting part would be the search algorithms that are used to narrow down the possible solutions. Obviously, this solution wasn't found merely by brute-force search.

The question that follows is then: is there a pattern here that we have some glimpse of, but not a complete solution for?

And the other, obvious question that I assume mathematicians would really like an answer to is:

Can every integer be expressed as the sum of three integer cubes?
​

Does this problem has a name? Is there a conjecture? How is progress going towards a proof, either way?

 

[Michael 345]

Can every integer be expressed as the sum of three integer cubes?

From what I understand they have solved 1 to 100 and now looking at numbers above 100.
Something about using private computers when not being used (like SETI)

 

[Gawdzilla Sama]

YES 42 WAS Douglas Adams answer but not the mathematicians answer

And we know which answer was most important, now don't we?

 

[Michael 345]

And we know which answer was most important, now don't we?

Yes

Nothing more important than Life, the Universe, and Everything

 

[TheFrogger]

The solution should be simple using brute force computing:

(-10³<x<10³)+(-10³<y<10³)+(-10³<z<10³)

Of course you may have to extend the range of x,y and z, but I do not see why the solution involved such massive computer power.

 

[James R]

The solution should be simple using brute force computing:

(-10³<x<10³)+(-10³<y<10³)+(-10³<z<10³)

According to what you have written here, that involves a brute-force check of 8 billion possibilities, and you're only checking numbers between -1000 and 1000 there.

Now, look at the actual answer for 42. One of the numbers there was 126021232973356313. That's $1.26\times 10^{17}$. To find that number by the same kind of brute-force search you suggest would require a check of $10^{36}$ possibilities, which is about 1 billion billion billion billion.

Are you still puzzled as to why massive computing power would be necessary? The actual problem is only about a billion billion billion times more complicated that you thought it was.

 

[TheFrogger]

Ahhh, okay JamesR. I see.