Stories
Slash Boxes
Comments

SoylentNews is people

posted by Fnord666 on Friday September 13 2019, @08:26PM   Printer-friendly
from the for-all-values-of-everything<113 dept.

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.

Source: https://www.extremetech.com/computing/298112-life-the-universe-and-math-42-proven-to-be-the-sum-of-3-cubes


Original Submission

 
This discussion has been archived. No new comments can be posted.
Display Options Threshold/Breakthrough Mark All as Read Mark All as Unread
The Fine Print: The following comments are owned by whoever posted them. We are not responsible for them in any way.
  • (Score: 3, Touché) by DannyB on Friday September 13 2019, @09:16PM (15 children)

    by DannyB (5839) Subscriber Badge on Friday September 13 2019, @09:16PM (#893856) Journal

    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.
    Starting Score:    1  point
    Moderation   +1  
       Touché=1, Total=1
    Extra 'Touché' Modifier   0  
    Karma-Bonus Modifier   +1  

    Total Score:   3  
  • (Score: 0) by Anonymous Coward on Friday September 13 2019, @09:28PM (4 children)

    by Anonymous Coward on Friday September 13 2019, @09:28PM (#893859)

    "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)

      by Anonymous Coward on Friday September 13 2019, @09:30PM (#893860)

      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

        by Anonymous Coward on Friday September 13 2019, @10:10PM (#893877)

        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)

      by FatPhil (863) <pc-soylentNO@SPAMasdf.fi> on Friday September 13 2019, @11:19PM (#893900) Homepage
      "brute force it"

      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

        by Anonymous Coward on Friday September 13 2019, @11:56PM (#893908)

        Oh, wow, we're so impressed.

  • (Score: 2) by legont on Saturday September 14 2019, @12:40AM (1 child)

    by legont (4179) on Saturday September 14 2019, @12:40AM (#893932)

    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

      by Mer (8009) on Saturday September 14 2019, @07:07AM (#893997)

      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)

    by captain normal (2205) on Saturday September 14 2019, @04:35AM (#893977)

    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

      by martyb (76) Subscriber Badge on Saturday September 14 2019, @09:54AM (#894020) Journal

      Is a negative number really a cube?

      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

      by Anonymous Coward on Saturday September 14 2019, @11:54AM (#894038)

      Is a negative number really a cube?

      Never been inside a TARDIS have you?

  • (Score: 3, Funny) by martyb on Saturday September 14 2019, @09:24AM

    by martyb (76) Subscriber Badge on Saturday September 14 2019, @09:24AM (#894014) Journal

    Why didn't the summary simply include the three cubes?

    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

    by martyb (76) Subscriber Badge on Saturday September 14 2019, @10:06AM (#894022) Journal

    Why didn't the summary simply include the three cubes? Even within a spoiler tag.

    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

    dc -e '60k _80538738812075974 3 ^  80435758145817515 3 ^   12602123297335631 3 ^ f  + + f'
    which outputs:
    2001387454481788542313426390100466780457779044591
    520412211582497361738652718463552780369306583065875
    -522413599036979150280966144853653247149764362110424
    42
    Q.E.D.

    --
    Wit is intellect, dancing.
  • (Score: 3, Informative) by janrinok on Saturday September 14 2019, @11:02AM (2 children)

    by janrinok (52) Subscriber Badge on Saturday September 14 2019, @11:02AM (#894025) Journal

    I guess you didn't read TFS then....

    For years, mathematicians have worked to demonstrate that x3+y3+z3 = k, where k is defined as the numbers from 1-100. By 2016, researchers had demonstrated that this theory held true in all cases except for two unproven exceptions: 33 and 42. The formal theory, as expressed by Roger Heath-Brown in 1992, is that every k unequal to 4 or 5 modulo 9 has infinitely many representations as the sum of three cubes. By closing this particular gap, we’ve now proven that all numbers below 113 fit this theory.

    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

      by janrinok (52) Subscriber Badge on Saturday September 14 2019, @11:04AM (#894026) Journal
      s/thing/think/
    • (Score: 0) by Anonymous Coward on Tuesday September 17 2019, @01:25PM

      by Anonymous Coward on Tuesday September 17 2019, @01:25PM (#895126)

      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].