The number 42 holds a special place in the hearts of science fiction fans, primarily due to Douglas Adams’s “The Hitchhiker’s Guide to the Galaxy.” In this comedic and philosophical series, a supercomputer named Deep Thought famously calculates the answer to “the Ultimate Question of Life, the Universe, and Everything” to be, quite simply, 42. But what was the ultimate question in Hitchhiker’s Guide?
But beyond its fictional significance, 42 also presented a real-world challenge to mathematicians. A long-standing puzzle known as the sum of three cubes problem, or the Diophantine Equation x³+y³+z³=k, asked mathematicians to find integer solutions for k ranging from 1 to 100. For decades, 42 remained one of the most elusive numbers in this puzzle. Finally, a team led by Andrew Sutherland of MIT and Andrew Booker of Bristol University cracked the code, finding the solution to the seemingly simple equation.
The Three Cubes Problem: A Mathematical Odyssey
The three cubes problem, first posed in 1954, challenges mathematicians to express numbers as the sum of three cubed integers. For instance, 29 can be expressed as 3³ + 1³ + 1³. However, some numbers proved stubbornly resistant to solution. Through the years, mathematicians have solved or proven unsolvable equations using supercomputers and advanced algorithms. But two numbers proved particularly difficult: 33 and 42.
Booker, driven by a desire to solve the mystery of 42, developed a clever algorithm. After successfully finding a solution for 33 using his university’s supercomputer, he turned his attention to 42. However, he soon realized that the computational power required was significantly greater, potentially exceeding his supercomputer’s capabilities. This is where Andrew Sutherland entered the picture.
Andrew Sutherland and Massively Parallel Computation
Sutherland, a principal research scientist at MIT, is an expert in massively parallel computations. He famously broke the record in 2017 for the largest Compute Engine cluster. He utilized 580,000 cores on Preemptible Virtual Machines. His expertise in this area made him the perfect partner to tackle the challenge of 42.
Booker and Sutherland worked together to refine the algorithmic strategy for finding a solution. They built upon the approach used to solve for 33. This involved identifying a parameter, d, that narrows down the possibilities for x, y, and z. They then enumerated values for d and checked the associated x, y, and z values within a certain search bound.
Charity Engine: Harnessing Planetary-Scale Computing
The primary difference between solving for 33 and 42 was the sheer scale of the computation. To overcome this hurdle, Booker and Sutherland partnered with Charity Engine, a UK-based organization that harnesses the combined computing power of over 400,000 volunteer home PCs worldwide. This allowed them to distribute the computational workload across a massive network, significantly accelerating the search for a solution.
Sutherland, a self-proclaimed fan of Douglas Adams, appreciated the irony of using a planetary-scale computer to solve a problem connected to The Hitchhiker’s Guide to the Galaxy. The novel describes a supercomputer powered by Earth being built to compute the Ultimate Question, mirroring the real-world use of Charity Engine.
The Solution to the Ultimate Question… Equation
After months of computation, the team finally received the email confirming the solution:
42 = (-80538738812075974)³ + 80435758145817515³ + 12602123297335631³
The discovery was a significant achievement. It demonstrated the power of distributed computing and resolved a long-standing mathematical puzzle.
Beyond 42: The Quest Continues
While the solution to 42 was a major victory, the journey isn’t over. There are still ten numbers between 101 and 1000 that remain unsolved in the three cubes problem, with 114 being the next target. However, both Booker and Sutherland are even more intrigued by a related, computationally challenging problem: finding more solutions for the sum of three cubes equaling 3.
The pursuit of solutions to these mathematical puzzles highlights the ongoing quest to understand the fundamental properties of numbers. It also speaks to the power of collaboration, ingenuity, and the relentless pursuit of knowledge. So, while we now know one answer relating to “what was the ultimate question in Hitchhiker’s Guide”, the broader exploration of mathematical mysteries continues to captivate and inspire.
