Buzz
For 64 years, mathematicians have struggled to express 33 as the sum of three cubes. Recently, Andrew Booker, a Reader in Pure Mathematics at the University of Bristol, has cracked the equation, leaving only the number 42 unsolved in this domain. (Source: Wikimedia Commons)If you’re a fan of trivia, you might recognize the number 33 as the former jersey number of Kareem Abdul-Jabbar, or perhaps from the cryptic label on Rolling Rock beer bottles. It’s also the country code for France if you’re dialing internationally.
But unless you’re deeply interested in the number 33, you may not be aware that for over six decades, mathematicians have been grappling with whether it's possible to express 33 as the sum of three cubes (the equation being 33 = x³ + y³ + z³). For a more detailed discussion, check out this Quanta Magazine article.
This problem is an example of a Diophantine equation, where all variables must be whole numbers. Some numbers lend themselves easily to this kind of equation. For instance, as explained by Massachusetts Institute of Technology professor Bjorn Poonen in a 2008 paper, the number 29 can be expressed as the sum of the cubes of 3, 1, and 1. On the other hand, for 30, the three cubes are all 10-digit numbers, and two of them are negative integers. Math has its quirks like that.
Finding a way to express 33 as the sum of three cubes has been an incredibly difficult challenge. That is, until recently, when Andrew Booker, a Princeton graduate and Reader in Pure Mathematics at the University of Bristol in the UK, worked out a solution.
In a YouTube video by Numberphile, Booker shares how, after watching a video on solving the three cubes problem for 74, he was inspired to take on 33 himself.
In the end, he developed a new, more efficient algorithm that was a significant improvement over what mathematicians had been using until then.
"It probably looks like I’ve made things a lot more complicated," he humorously remarked in the video while writing out his calculations on a large brown sheet of paper.
In order to process the data, he employed a network of robust computers — utilizing 512 central processing unit (CPU) cores simultaneously — referred to as Blue Crystal Phase 3. Upon returning to his office one morning after dropping his children off at school, he saw the breakthrough on his screen. 'I leaped for joy,' he said, reflecting on the moment.
The three values are 8,866,128,975,287,5283; - 8,778,405,442,862,2393; and -2,736,111,468,807,0403.
In the Numberphile video, Booker shares that his next step is to use the same method for solving the mystery of the three cubes that sum up to 42, another number that has so far proven unsolvable. '42 is the next 33,' he jokes, adding a lighthearted touch to his pursuit.
