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Sum-of-Three-Cubes Problem Solved for ‘Stubborn’ Number 33:
A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years.
Mathematicians long wondered whether it’s possible to express the number 33 as the sum of three cubes — that is, whether the equation 33 = x³+ y³+ z³ has a solution. They knew that 29 could be written as 3³ + 1³ + 1³, for instance, whereas 32 is not expressible as the sum of three integers each raised to the third power. But the case of 33 went unsolved for 64 years.
Now, Andrew Booker, a mathematician at the University of Bristol, has finally cracked it: He discovered that (8,866,128,975,287,528)³ + (–8,778,405,442,862,239)³ + (–2,736,111,468,807,040)³ = 33.
Booker found this odd trio of 16-digit integers by devising a new search algorithm to sift them out of quadrillions of possibilities. The algorithm ran on a university supercomputer for three weeks straight. (He says he thought it would take six months, but a solution “popped out before I expected it.”) When the news of his solution hit the internet earlier this month, fellow number theorists and math enthusiasts were feverish with excitement. According to a Numberphile video about the discovery, Booker himself literally jumped for joy in his office when he found out.
Why such elation? Part of it is the sheer difficulty of finding such a solution. Since 1955, mathematicians have used the most powerful computers they can get their hands on to search the number line for trios of integers that satisfy the “sum of three cubes” equation k = x³ + y³ + z³, where k is a whole number. Sometimes solutions are easy, as with k = 29; other times, a solution is known not to exist, as with all whole numbers that leave behind a remainder of 4 or 5 when divided by 9, such as the number 32.
[...]33 was an especially stubborn case: Until Booker found his solution, it was one of only two integers left below 100 (excluding the ones for which solutions definitely don’t exist) that still couldn’t be expressed as a sum of three cubes. With 33 out of the way, the only one left is 42.
Next up is 42? Where have I seen that number before?
(Score: 5, Funny) by DannyB on Wednesday March 27 2019, @02:54PM (2 children)
I recently watched a Numberphile video [youtube.com] showing a math teacher attempting to find a way to cut a ham sandwich in half. It took almost six minutes to present a way to do it.
I don't think it's that hard of a problem.
New problem . . .
Teacher: I am going to teach you how to evenly cut a round cake so that it may be eaten by any number of people. The two requirements are:
1. The cut cake pieces must be extremely close to equal in size.
2. There must be nobody who complains that their piece is too small.
First, you take 360 degrees and divide by the number . . . .
Student: (interrupting) Your approach is too complicated. If three people were wanting to eat the cake, a much simpler solution would be to cut the cake in half (as closely as possible) and shoot the third person. That way both conditions (1) and (2) are satisfied.
Teacher: Ah, but your approach required an additional tool, the gun.
Student: My method can be simplified by using only one tool, the knife. The third person is stabbed instead of shot. Whether this step is performed before or after cutting the cake is a matter of preference.
Teacher: I see your approach is simpler and worthy of a Fields medal.
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(Score: 2) by Osamabobama on Wednesday March 27 2019, @10:16PM (1 child)
I wonder how many people throughout history have stabbed somebody in order to win a Fields medal...
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(Score: 2) by DannyB on Thursday March 28 2019, @03:06PM
I don't believe the fields medal existed at the time of the guy who shot Galois. But then that was not a stabbing.
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