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Two Mathematicians Solve Old Math Riddle, Possibly the Meaning of Life

pgmrdlm shares a report from Live Science: In Douglas Adams’ sci-fi series “The Hitchhiker’s Guide to the Galaxy,” a pair of programmers task the galaxy’s largest supercomputer with answering the ultimate question of the meaning of life, the universe and everything. After 7.5 million years of processing, the computer reaches an answer: 42. Only then do the programmers realize that nobody knew the question the program was meant to answer. Now, in this week’s most satisfying example of life reflecting art, a pair of mathematicians have used a global network of 500,000 computers to solve a centuries-old math puzzle that just happens to involve that most crucial number: 42. The question, which goes back to at least 1955 and may have been pondered by Greek thinkers as early as the third century AD, asks, “How can you express every number between 1 and 100 as the sum of three cubes?” Or, put algebraically, how do you solve x^3 + y^3 + z^3 = k, where k equals any whole number from 1 to 100? This deceptively simple stumper is known as a Diophantine equation, named for the ancient mathematician Diophantus of Alexandria, who proposed a similar set of problems about 1,800 years ago. Modern mathematicians who revisited the puzzle in the 1950s quickly found solutions when k equals many of the smaller numbers, but a few particularly stubborn integers soon emerged. The two trickiest numbers, which still had outstanding solutions by the beginning of 2019, were 33 and — you guessed it — 42. Using a computer algorithm to look for solutions to the Diophantine equation with x, y and z values that included every number between positive and negative 99 quadrillion, mathematician Andrew Booker, of the University of Bristol in England, found the solution to 33 after several weeks of computing time.

Since his search turned up no solutions for 42, Booker enlisted the help of Massachusetts Institute of Technology mathematician Andrew Sutherland, who helped him book some time with a worldwide computer network called Charity Engine. “Using this crowdsourced supercomputer and 1 million hours of processing time, Booker and Sutherland finally found an answer to the Diophantine equation where k equals 42,” reports Live Science. The answer: (-80538738812075974)^3 + (80435758145817515)^3 + (12602123297335631)^3 = 42.


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