42 is found to be the sum of three cubes • Hacker News Board

Re: 42 is found to be the sum of three cubes

#61

Post by ocfnash » Fri, Sep 06, 2019, 2:59 PM UTC

rank0 wrote: post #6

I must be missing something. Why is this significant?

Mathematicians are interested in which natural numbers k can be expressed as a sum of three cubes. Prior to this year, it had been established that this is possible for all k 33, 42, 114, 165, 390, 579, 627, 633, 732, 795, 906, 921, 975.

Earlier this year a solution for k=33 was found [1], so 42 was the next unknown value.

[1] Brooker, A., "CRACKING THE PROBLEM WITH 33", https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf

Re: 42 is found to be the sum of three cubes

#62

Post by 98codes » Fri, Sep 06, 2019, 2:59 PM UTC

rdiddly wrote: post #34

It's also the answer to life, the universe and everything. Which is nice.

The ASCII code page index for it anyway.

Re: 42 is found to be the sum of three cubes

#63

Post by zests » Fri, Sep 06, 2019, 2:59 PM UTC

petrikapu wrote: post #25

In Python >>> (-80538738812075974)**3 + 80435758145817515**3 + 12602123297335631**3 42

In dc/shell/bash

       dc -e '_80538738812075974 3 ^ 80435758145817515 3 ^ 12602123297335631 3 ^ + + p'

Re: 42 is found to be the sum of three cubes

#64

Post by dagw » Fri, Sep 06, 2019, 2:59 PM UTC

techolic wrote: post #45

yumraj wrote: post #31

How was this computed? Just brute force ?

(One of) The authors previous finding was for 33, and he had a paper on that, https://arxiv.org/pdf/1903.04284.pdf .

And even with all that optimization it still took 23 core-years to find one solution.

Re: 42 is found to be the sum of three cubes

#65

Post by rawburt » Fri, Sep 06, 2019, 2:59 PM UTC

rdiddly wrote: post #34

It's also the answer to life, the universe and everything. Which is nice.

It's the answer to the ultimate "question" of life, the universe, and everything. This is an important difference. What's the question?

Re: 42 is found to be the sum of three cubes

#66

Post by conjectures » Fri, Sep 06, 2019, 3:00 PM UTC

whitehouse3 wrote: post #39

Why doesn't this evaluate in Excel? =(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 Returns 1.09785E+36

Welcome to numerical computing :D!

Btw:

julia> (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3

42

Re: 42 is found to be the sum of three cubes

#67

Post by rawburt » Fri, Sep 06, 2019, 3:01 PM UTC

binaural wrote: post #60

42 is also the answer to the universe. ;-)

No, it's the answer to the ultimate question of life, the universe, and everything.

Re: 42 is found to be the sum of three cubes

#68

Post by scrungus » Fri, Sep 06, 2019, 3:01 PM UTC

sp332 wrote: post #56

scrungus wrote: post #35

Earlier quoted context omitted.

If you can break up a reasonably-sized table (perhaps 120 or so) of numbers into their respective sums of cubes, breaking many types of encryption is arbitrary.

Guessing you meant "trivial". Do you have some info about how this helps break encryption?

i would show you the proof but it's arbitrary because it only works against the "sum of cubes" encryption system, which only i use.

Re: 42 is found to be the sum of three cubes

#69

Post by nathanm412 » Fri, Sep 06, 2019, 3:02 PM UTC

LandR wrote: post #58

whitehouse3 wrote: post #39

Why doesn't this evaluate in Excel? =(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 Returns 1.09785E+36

same as Google. https://www.google.com/search?sxsrf=ACYBGNQRb1b08L-cU-JY3GHr...

Oddly enough, it works for Bing.

https://www.bing.com/search?q=%3D%28-80538738812075974%29%5E...

Re: 42 is found to be the sum of three cubes

#70

Post by saalweachter » Fri, Sep 06, 2019, 3:02 PM UTC

sp332 wrote: post #56

scrungus wrote: post #35

Earlier quoted context omitted.

If you can break up a reasonably-sized table (perhaps 120 or so) of numbers into their respective sums of cubes, breaking many types of encryption is arbitrary.

Guessing you meant "trivial". Do you have some info about how this helps break encryption?

The math is complicated, but the TL;DR is that you should already be selling your Bitcoins. Dogecoin should last another six months, seven at the outside.