Submitted via IRC for chopchop1
The problem of 42 — at least as it relates to whether the number could be considered the sum of three cubes — has finally been solved. The question of whether every number under 100 could be expressed in this fashion has been a long-standing puzzle in the world of mathematics. Now, two mathematicians, Andrew Sutherland of MIT and Andrew Booker of Bristol, have jointly proven that 42 is indeed the sum of three cubes.
In the equation x3+y3+z3 = k, let x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631. Plug it all in, and you get (-80538738812075974)3 + 804357581458175153 + 126021232973356313 = 42.
(Score: 3, Touché) by DannyB on Friday September 13 2019, @09:16PM (15 children)
Gaslighted?
While 42 was a good joke, the sum of three cubes is not. Why didn't the summary simply include the three cubes? Even within a spoiler tag.
People today are educated enough to repeat what they are taught but not to question what they are taught.
(Score: 0) by Anonymous Coward on Friday September 13 2019, @09:28PM (4 children)
"the sum of three cubes is not"
What's the point? With the modern computing power, you can brute-force it. But whatever, Did it actually reveal something more profound?
(Score: 2, Insightful) by Anonymous Coward on Friday September 13 2019, @09:30PM (1 child)
If you don't pay mathematicians to work on problems like these, they'll help the NSA break encryption instead.
(Score: 0) by Anonymous Coward on Friday September 13 2019, @10:10PM
If you round X&Y and plug it in a GPS you get Antarctica. If Z is altitude... Oh shit!
(Score: 4, Insightful) by FatPhil on Friday September 13 2019, @11:19PM (1 child)
Nope. That's the most idiotic thing I've seen since 42 Jump Street[*]. The search space is the square of the middle number, for pity's sake. Naive residue filters will reduce the search space by a small constant factor.
Mathematicians in several different fields (number theory and computability) are interested in concepts such as whether Z^3+Z^3+Z^3 covers all admissible values (some are simply impossible, so are uninteresting), so removing a known absentee in the list is an interesting thing, as it reduces the space where non-solutions may hide. Yes, Heath-Brown was one of my lecturers. And you don't even know who he is, or why he's relevant, so just go away, troll.
[* Ballet School?]
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: -1, Flamebait) by Anonymous Coward on Friday September 13 2019, @11:56PM
Oh, wow, we're so impressed.
(Score: 2) by legont on Saturday September 14 2019, @12:40AM (1 child)
Because they could not figure out how to express it in football fields or libraries of Congress.
But seriously, we need the answer for 74,088.
"Wealth is the relentless enemy of understanding" - John Kenneth Galbraith.
(Score: 2) by Mer on Saturday September 14 2019, @07:07AM
How many parsecs is a football field?
Shut up!, he explained.
(Score: 2) by captain normal on Saturday September 14 2019, @04:35AM (2 children)
Is a negative number really a cube?
When life isn't going right, go left.
(Score: 3, Informative) by martyb on Saturday September 14 2019, @09:54AM
Why not?
A cube is a number that has been multiplied with itself 3 times, just as a square is a number that has been multiplied with itself 2 times.
so, just as the square of 5 is 5x5 (i.e. 25), the cube of 5 is 5x5x5 (i.e. 125), and the cube of -5 is (-5)x(-5)x(-5) which is -125
Example 1: take one cube that is 10 units on a side and another cube that is 5 units on a side. Let's assume each cubes is made of lead. Now imagine a bucket that is 30 units in diameter and 20 units tall, filled with water. I place both blocks in the bucket. How much water is displaced?
(10^3) + (5^3) = (1000) + (125) = 1125 cubic units of water are displaced. We have simply combined the volumes of each of these cubes.
Example 2: Imagine another pair of cubes. Like before, we start with a cube that is 10 units on a side. Now we remove a chunk of that cube by measuring 5 units in from a corner. We now place this single (reduced-in-size) cube into a fresh bucket filled with water. How much water is displaced?
(10^3) + (-5^3) = (1000) + (-125) = 875 cubic units would be displaced. The removed 5x5x5 chunk could be considered to have negative volume when compared to the original 10x10x10 cube.
Wit is intellect, dancing.
(Score: 0) by Anonymous Coward on Saturday September 14 2019, @11:54AM
Never been inside a TARDIS have you?
(Score: 3, Funny) by martyb on Saturday September 14 2019, @09:24AM
Because it was left as an exercise for the reader!
=)
Wit is intellect, dancing.
(Score: 3, Interesting) by martyb on Saturday September 14 2019, @10:06AM
Although my previous reply was somewhat facetious, it wasn't entirely. Using the arbitrary precision Unix dc "Desk Calculator" utility that employs postfix notation (aka RPN: Reverse-Polish Notation), and specifying 60 significant digits
Wit is intellect, dancing.
(Score: 3, Informative) by janrinok on Saturday September 14 2019, @11:02AM (2 children)
I guess you didn't read TFS then....
So, this isn't a joke. The numbers 33 and 42 have been causing a problem for quite some time. Another comment said that the answers could be easily brute forced - but for some reason they weren't. So perhaps this wasn't as simple to solve as many seem to thing it was.
(Score: 2) by janrinok on Saturday September 14 2019, @11:04AM
(Score: 0) by Anonymous Coward on Tuesday September 17 2019, @01:25PM
These are very informative. View in order (or just jump to the third for the punchline): 1 [youtube.com], 2 [youtube.com], and 3 [youtube.com].