Buzz
The number 42 was the last remaining integer below 100 that had not been solved as the sum of three cubes. MytourEarlier this year, Andrew Booker, a professor at the University of Bristol in the U.K., made headlines by solving the problem of expressing the number 33 as the sum of three cubes.
Now, Booker, alongside Massachusetts Institute of Technology professor Andrew Sutherland, has achieved a breakthrough by solving the Diophantine Equation (x^3+y^3+z^3=k) for the previously unsolved number 42, the final integer under 100 to be conquered.
As outlined in this University of Bristol press release, Booker and Sutherland relied on the computational power of Charity Engine to perform the extensive calculations needed. The platform enlists global volunteers to install an app on their PCs (over 400,000 participated), pooling their unused processing power to create a virtual supercomputer. The same software that solved the problem for the number 33, as detailed by Booker in the journal "Research in Number Theory," was used to crack the case for 42. Charity Engine generates funds by offering its services, supporting causes like CARE, Oxfam, and others.
The solution, discovered after more than a million hours of computation, is as follows:
X = -80538738812075974 Y = 80435758145817515 Z = 12602123297335631
In this Numberphile YouTube segment, Booker provides insights into how the problem was successfully resolved:
As Booker mentions in the video, their work isn't done. Next, they aim to tackle the number 114. Additionally, he is curious to explore whether a third solution exists for the number 3, a question originally posed by mathematician Louis Mordell in the 1950s.
Solving for 42 holds a unique cultural significance. Enthusiasts of Douglas Adams' 1979 novel "The Hitchhiker's Guide to the Galaxy" will recognize it as the answer provided by the supercomputer Deep Thought to the meaning of life, the universe, and everything. In Lewis Carroll's "Alice's Adventures in Wonderland," the King of Hearts references the famous Rule Forty-two, which mandates that anyone taller than a mile must exit the court. Additionally, 42 was the jersey number of Jackie Robinson, the Brooklyn Dodgers player who broke Major League Baseball's color barrier in 1947. In 1997, acting commissioner Bud Selig permanently retired the number 42, ensuring no other player could wear it.
According to British IT publication The Register, there are still 12 numbers under 1,000 for which solutions as the sum of three cubes remain undiscovered by mathematicians.
