You’ll often get the same answer whether you use Google, Qwant, Wolfram Alpha (which specializes in calculating mathematical problems) or the chat bot Web app Cleverbot. Adams was friends with Pink Floyd guitarist David Gilmour and came up with the title of the band's … Forty-two is a Catalan number. And Langdarma, who ruled from 836 to 842 A.D. The paper reporting their findings concluded that the question of the existence of a solution for numbers below 1,000 remained open only for 33, 42, 74, 114, 165, 390, 579, 627, 633, 732, 795, 906, 921 and 975. Like other computational number theorists who work in arithmetic geometry, he was aware of the “sum of three cubes” problem. But when he turned to solve for 42, Booker found that the computing needed was an order of magnitude higher and might be beyond his supercomputer’s capability. The number 42 also appears in different forms in the film Spider-Man: Into the Spider-Verse. People who have never heard of Douglas Adams know it. Discover world-changing science. By Xbox explorer Finious. The puzzle is an illustration consisting of 42 multi-coloured balls, in 7 columns and 6 rows. The problem is stated as follows: What integers n can be written as the sum of three whole-number cubes (n = a3 + b3 + c3)? “You wait and wait and just when you’re at the point of giving up, the number shows up,” said Sutherland. Principal research scientist Andrew Sutherland and a colleague at the University of Bristol have  solved a decades-old math problem known as the “summing of the three cubes.” The team found the answer with the help of the platform the Charity Engine, “which utilizes idle, unused computing power from over 500,000 home PCs to create a crowdsourced and environmentally conscious supercomputer,” writes David Grossman for Popular Mechanics. Ancient Tibet had 42 rulers. Toward the end of the book, the supercomputer Deep Thought reveals that the answer to the “Great Question” of “Life, the Universe and Everything” is “forty-two.”. In a 2016 preprint paper, Sander Huisman, now at the University of Twente in the Netherlands, pressed on and found a solution for 74: (–284,650,292,555,885)3 + (66,229,832,190,556)3 + (283,450,105,697,727)3. Check out our douglas adams 42 selection for the very best in unique or custom, handmade pieces from our shops. Catalan numbers were first mentioned, under another name, by Swiss mathematician Leonhard Euler, who wanted to know how many different ways an n-sided convex polygon could be cut into triangles by connecting vertices with line segments. As a result, the carbon footprint of this computation — related to the electricity our computations caused the PCs in the network to use above and beyond what they would have used, in any case — is lower than it would have been if we had used a supercomputer.”. Computers participating in the Charity Engine network of personal computers, calculating for the equivalent of more than one million hours, showed: 42 = (–80,538,738,812,075,974)3 + 80,435,758,145,817,5153 + 12,602,123,297,335,6313. However, Adams found Alice in Wonderland utterly terrifying when it was read to him as a child, hated the book as a result, and issued a definitive no. Such is the enduring interest in Douglas Adams’s story that it is due to be adapted into a new television series by Hulu, a streaming service. This sum of three cubes puzzle, first set in 1954 at the University of Cambridge and known as the Diophantine Equation x3+y3+z3=k, challenged mathematicians to find solutions for numbers 1-100. No simple known formula provides the nth element of this sequence. With smaller numbers, this type of equation is easier to solve: for example, 29 could be written as 33 + 13 + 13, while 32 is unsolvable. For example: In ancient Egyptian mythology, during the judgment of souls, the dead had to declare before 42 judges that they had not committed any of 42 sins. The sequence corresponds to entry A020988 in The On-Line Encyclopedia of Integer Sequences (OEIS), created by mathematician Neil Sloane. Ryan Mandelbaum writes for Gizmodo about the efforts of principal research scientist Andrew Sutherland and others to use a crowd-sourced supercomputer to solve a math problem that scientists have been working on since the 1950s. Some propose that it was chosen because 42 is 101010 in binary code, others have pointed out that light refracts through a water surface by 42 degrees to create a rainbow, and others have commented that light requires 10−42 seconds to cross the diameter of a proton. Yet, as the computer points out, the question itself was vaguely formulated. Adams – who died, aged 49, 10 years ago this May – had launched the world's greatest universal joke. 1 Summary 2 Alias names 3 Discovered 4 Planets & Moons 5 Starships 6 Multi-Tools 7 Location information 7.1 Coordinates 7.2 Portal Glyphs 7.3 Navigation Images 8 Space station 9 Additional Info 10 Gallery Douglas Adams FIN42 is a star system in the No Man's Sky universe. In base 2, the nth element may be specified by repeating 10 n times (1010 ... 10). You can explore the properties of various numbers on Wikipedia. As if.) It would be very exciting to find another solution for k=3.”. The number 42 is especially significant to fans of science fiction novelist Douglas Adams’ “ The Hitchhiker’s Guide to the Galaxy, ” because that number is the answer given by a supercomputer to “the Ultimate Question of Life, the Universe, and Everything.” Booker also wanted to … The conjecture that solutions exist for all integers n that are not of the form 9m + 4 or 9m + 5 would appear to be confirmed. Many other references and allusions to it can be found, for example, in the Wikipedia entry for “42 (number).”. All this is amusing, but it would be wrong to say that 42 is really anything special mathematically. Sutherland is also a fan of Douglas Adams, so the project was irresistible. What makes a number particularly interesting or uninteresting is a question that mathematician and psychologist Nicolas Gauvrit, computational natural scientist Hector Zenil and I have studied, starting with an analysis of the sequences in the OEIS. Catalan numbers are named after Franco-Belgian mathematician Eugène Charles Catalan (1814–1894), who discovered that c(n) is the number of ways to arrange n pairs of parentheses according to the usual rules for writing them: a parenthesis is never closed before it has been opened, and one can only close it when all the parentheses that were subsequently opened are themselves closed. Booker devised an ingenious algorithm and spent weeks on his university’s supercomputer when he recently came up with a solution for 33. As a practical matter, the difficulty in making this calculation is that for a given n, the space of the triplets to be considered involves negative integers. ", International team launches vast atlas of mathematical objects, More about MIT News at Massachusetts Institute of Technology, Abdul Latif Jameel Poverty Action Lab (J-PAL), Picower Institute for Learning and Memory, School of Humanities, Arts, and Social Sciences, View all news coverage of MIT in the media. All orders are custom made and most ship worldwide within 24 hours. Binary representations, base thirteen, Tibetan monks are all complete nonsense. For integers below 1,000, only 114, 390, 579, 627, 633, 732, 921 and 975 remain to be solved. © 2021 Scientific American, a Division of Springer Nature America, Inc. Support our award-winning coverage of advances in science & technology. Since the first such school was created in France in 2013 there has been a proliferation of private computer-training institutions in the “42 Network,” whose name is a clear allusion to Adams’s novels. All were eventually solved, or proved unsolvable, using various techniques and supercomputers, except for two numbers: 33 and 42. Consider the example of 16, which is double the cube of 2. Note that for some integer values of n, the equation n = a3 + b3 + c3 has no solution. MIT researchers grow structures made of wood-like plant cells in a lab, hinting at the possibility of more efficient biomaterials production. An obvious question, which indeed has been asked, is whether the use of 42 in Adams’s books had any particular meaning for the author. The cases of 165, 795 and 906 were also solved recently. Booker also wanted to know the answer to 42. From that point, Douglas Adams’s number was the last positive integer lower than 100 whose representation as a sum of three integer cubes was unknown. For p = 1, we get: Note that for n = 3, as of August 2019, only two solutions were known: A question that naturally follows is: Is there at least one solution for every nonprohibited value? Otherwise, the main difference between the search for 33 and the search for 42 would be the size of the search and the computer platform used. Forty-two is also a “practical” number, which means that any integer between 1 and 42 is the sum of a subset of its distinct divisors. “Well, any computer *can* solve the problem, provided you are willing to wait long enough, but with roughly half a million PCs working on the problem in parallel (each with multiple cores), we were able to complete the computation much more quickly than we could have using the Bristol machine (or any of the machines here at MIT),” says Sutherland. Douglas Adams FIN42 is a star system in No Man's Sky. You cannot get a sum of 4 or 5 (= –4). 2. “42” Is the meaning of life, the universe and everything. While it is conjectured that there should be infinitely many solutions, despite more than 65 years of searching we know only the easy solutions that were already known to Mordell. These numbers are extremely rare, much more so than prime numbers: only 14 of the former are lower than one billion. For the sum of cubes, some solutions may be surprisingly large, such as the one for 156, which was discovered in 2007: 156 = 26,577,110,807,5693 + (−18,161,093,358,005)3 + (−23,381,515,025,762)3. The formula for this sequence is a(n) = (2/3)(4n – 1). Thanks to a generous offer from UK-based Charity Engine, Booker and Sutherland were able to tap into the computing power from over 400,000 volunteers’ home PCs, all around the world, each of which was assigned a range of values for d. The computation on each PC runs in the background so the owner can still use their PC for other tasks. “One then enumerates values for d and checks each of the possible x, y, z associated to d. In the attempt to crack 33, the search bound B was 1016, but this B turned out to be too small to crack 42; we instead used B = 1017 (1017 is 100 million billion). The new version of the computer is Earth. In the binary system, or base 2, 42 is written as 101010, which is pretty simple and, incidentally, prompted a few fans to hold parties on October 10, 2010 (10/10/10). Could lab-grown plant tissue ease the environmental toll of logging and agriculture? The sequence b(n), which is the sum of the powers of six, corresponds to entry A105281 in OEIS. Such is the case for all integers n that are expressible as 9m + 4 or 9m + 5 for any integer m (e.g., 4, 5, 13, 14, 22, 23). Booker and Sutherland say there are 10 more numbers, from 101-1000, left to be solved, with the next number being 114. Booker says he received many offers of help to find the answer, but instead he turned to his friend Andrew "Drew" Sutherland, a principal research scientist in the Department of Mathematics. That is, are there three cubes whose sum is 42? The method of using Charity Engine is similar to part of the plot surrounding the number 42 in the "Hitchhiker" novel: After Deep Thought’s answer of 42 proves unsatisfying to the scientists, who don’t know the question it is meant to answer, the supercomputer decides to compute the Ultimate Question by building a supercomputer powered by Earth … in other words, employing a worldwide massively parallel computation platform. Shortly afterwards his sister, Susan, was born three years later followed by the divorce of their parents in 1957, as his mother then went to live in an RSPCA shelter in Brentwood with his grandparents. It had to be a number, an ordinary, smallish number, and I chose that one. Examples include Amelia Earhart’s disappearance over the Pacific in 1937 and the daring escape of inmates Frank Morris and John and Clarence Anglin from Alcatraz Island in California in 1962. Read on to find out more about the whole situation. (The fact that the kilometer had not yet been defined at that time only makes the connection all the more astonishing.). To find out what happens next, you’ll have to read Adams’s books. In one instance, the series suggests that 42 is the answer to the question “What do you get if you multiply six by nine?” That idea seems absurd because 6 x 9 = 54. The difficulty appears so daunting that the question “Is n a sum of three cubes?” may be undecidable. For n = 1, there is the obvious solution: 93 + (–6)3 + (–8)3 = 729 + (–216) + (–512) = 1. The Lowest Crime Rates in 42 Douglas Adams. It was discovered in 1908 by mathematician A. S. Werebrusov. As noted in a review of the book on The Independent, there are 42 lines per page in the Gutenberg … But in base 13, the number expressed as “42” is equal to (4 x 13) + 2 = 54. “It’s very gratifying.”. Often you hear it as a simple namecheck, a gently conclusive "Douglas Adams", … Understanding antibodies to avoid pandemics, An intro to the fast-paced world of artificial intelligence, Designing in a pandemic to fight a pandemic. Computers tried but had been unable to crack the problem. There have been many theories from fans in an attempt to explain why the number 42 was chosen, and what secret meaning it may hold. / (n! “There are four very easy solutions that were known to the mathematician Louis J. Mordell, who famously wrote in 1953, ‘I do not know anything about the integer solutions of x3 + y3 + z3 = 3 beyond the existence of the four triples (1, 1, 1), (4, 4, -5), (4, -5, 4), (-5, 4, 4); and it must be very difficult indeed to find out anything about any other solutions.’ This quote motivated a lot of the interest in the sum of three cubes problem, and the case k=3 in particular. MIT News | Massachusetts Institute of Technology, The answer to life, the universe, and everything, Mathematics researcher Drew Sutherland helps solve decades-old sum-of-three-cubes puzzle, with help from "The Hitchhiker's Guide to the Galaxy. It seems that Douglas Adams was right after all: the answer to Life, the Universe and everything, is 42. Here are some of them: The number is the sum of the first three odd powers of two—that is, 21 + 23 + 25 = 42. In 1936 German mathematician Kurt Mahler proposed an infinite number of them. A team led by Andrew Sutherland of MIT and Andrew Booker of Bristol University has solved the final piece of a famous 65-year old math puzzle with an answer for the most elusive number of all: 42. This website is managed by the MIT News Office, part of the MIT Office of Communications. Booker and Sutherland discussed the algorithmic strategy to be used in the search for a solution to 42. The number 42 is the tale’s signature joke. If, for example, you ask your search engine variations of the question “What is the answer to everything?” it will most likely answer “42.” Try it in French or German. If we could prove such undecidability, that would be a novelty. Here you will read about a popular alternate theory and where and how Douglas Adams explained that it is very smart but not what he had had in mind. Subscribers get more award-winning coverage of advances in science & technology. The Gutenberg Bible, the first book printed in Europe, has 42 lines of text per column and is also called the “Forty-Two-Line Bible.”, According to a March 6 Economist blog post marking the 42nd anniversary of the radio program The Hitchhiker’s Guide to the Galaxy, which preceded the novel, “the 42nd anniversary of anything is rarely observed.”, An obvious question, which indeed has been asked, is whether the use of 42 in Adams’s books had any particular meaning for the author. “With these large-scale computations you pour a lot of time and energy into optimizing the implementation, tweaking the parameters, and then testing and retesting the code over weeks and months, never really knowing if all the effort is going to pay off, so it is extremely satisfying when it does.”. It’s at the origin of a multitude of jokes and winks exchanged between initiates. In 1936, for example, Alan Turing showed that no algorithm can solve the halting problem for every possible computer program. Douglas himself attended Brentwood School after passing their entrance exam before going onto learn at the prestigious Cambridge University where he graduated with a B.A. When it was applied to the “sum of three cubes” problem, 42 was more troublesome than all the other numbers below 100. Why couldn't Bristol's supercomputer solve this problem? Structural biologist Pamela Björkman shared insights into pandemic viruses as part of the Department of Biology’s IAP seminar series. The density of these numbers also tends toward zero at infinity. 42 is a special number because it is the funniest of all numbers. The number 42 was difficult, but it is not the final step! Scientific American is part of Springer Nature, which owns or has commercial relations with thousands of scientific publications (many of them can be found at, the 42nd anniversary of anything is rarely observed, The On-Line Encyclopedia of Integer Sequences, explore the properties of various numbers. This article originally appeared in Pour la Science and was reproduced with permission. For example, c(3) = 5 because the possible arrangements of three pairs of parentheses are: ( ( ( ) ) ); ( ) ( ) ( ); ( ( ) ) ( ); ( ( ) ( ) ); ( ) ( ( ) ). In other words, the cube of an integer modulo 9 is –1 (= 8), 0 or 1. The nth element of the sequence is given by the formula c(n) = (2n)! Moreover our interest holds even if the mystery is based on a joke. 24. Deep Thought takes 7.5 million years to calculate the answer to the ultimate question. Hitchhiker’s conspiracy theorists cite Lewis Carroll as an influence in Adams using 42 as the answer to life, the universe and everything. His answer, posted in the online discussion group alt.fan.douglas-adams, was succinct: “It was a joke. The answer came in a 2020 preprint, the result of a huge computational effort coordinated by Booker and Andrew Sutherland of the Massachusetts Institute of Technology. We thus say that n = 9m + 4 and n = 9m + 5 are prohibited values. It is an element in the sequence a(n), which is the sum of n odd powers of 2 for n > 0. For integers less than 100, just three enigmas remained: 33, 42 and 74. If there was no solution, that conclusion would provide a genuinely compelling rationale for the mathematical significance of 42: it would be the first number for which a solution appeared possible but none had been found. That, too, will take time. The reference to base 13 in Adams’s answer requires a more indirect explanation. 7. And like the two preceding sequences, the density of numbers is null at infinity. For any integer p: By multiplying each term of these equations by the cube of an integer (r3), we deduce that there are also infinitely many solutions for both the cube and double the cube of any integer. The numbers 41 and 43, for example, are also elements of many sequences. “For the most part, we are using computational resources that would otherwise go to waste,” says Sutherland. “When you're sitting at your computer reading an email or working on a spreadsheet, you are using only a tiny fraction of the CPU resource available, and the Charity Engine application, which is based on the Berkeley Open Infrastructure for Network Computing (BOINC), takes advantage of this. For any integer p: This proposition may be proved using the remarkable identity: An infinite set of solutions is also known for n = 2. Aside from a theoretical connection to Kolmogorov complexity (which defines the complexity of a number by the length of its minimal description), we have shown that the numbers contained in Sloane’s encyclopedia point to a shared mathematical culture and, consequently, that OEIS is based as much on human preferences as pure mathematical objectivity. The marathon distance of 42.195 kilometers corresponds to the legend of how far the ancient Greek messenger Pheidippides traveled between Marathon and Athens to announce victory over the Persians in 490 B.C. And the two had worked together before, helping to build the L-functions and Modular Forms Database (LMFDB), an online atlas of mathematical objects related to what is known as the Langlands Program. The first practical numbers are 1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66 and 72 (sequence A005153 in OEIS). Douglas Adams, the “master of wacky words and even wackier tales” (Entertainment Weekly) once again boggles the mind with a completely unbelievable story of ghosts, time travel, eccentric computer geniuses, Samuel Taylor Coleridge, the end of the world, and—of course—missing cats. Jean-Paul Delahaye is a professor emeritus of computer science at the University of Lille in France and a researcher at the Research Center in Computer Science, Signal and Automatics of Lille (CRIStAL). Years of volumes and hundreds of essays, published by the MIT Press since 2003, are now freely available. www.godtype.com/2014/05/rational-prophets-humanity-douglas-adams-godtype Associate Professor Michael Short's innovative approach can be seen in the two nuclear science and engineering courses he’s transformed. To illustrate how difficult it is to find solutions to the equation n = a3 + b3 + c3, let’s see what happens for n = 1 and n = 2. “He’s a world’s expert at this sort of thing,” Booker says. Computer scientists and mathematicians recognize the appeal of the number 42 but have always thought that it was a simple game that could be played just as well with another number. The puzzle is an illustration consisting of 42 multi-coloured balls, in 7 columns and 6 rows. They ran a number of computations at a lower capacity to test both their code and the Charity Engine network. “All opinions are not equal. The number 42 is especially significant to fans of science fiction novelist Douglas Adams’ “The Hitchhiker’s Guide to the Galaxy,” because that number is the answer given by a supercomputer to “the Ultimate Question of Life, the Universe, and Everything.”. That calculation is not the only other solution. To answer that question, mathematicians started by taking the nonprohibited values 1, 2, 3, 6, 7, 8, 9, 10, 11, 12, 15, 16 ... (A060464 in OEIS) and examining them one by one. Apart from allusions to 42 deliberately introduced by computer scientists for fun and the inevitable encounters with it that crop up when you poke around a bit in history or the world, you might still wonder whether there is anything special about the number from a strictly mathematical point of view. “There is a single integer parameter, d, that determines a relatively small set of possibilities for x, y, and z such that the absolute value of z is below a chosen search bound B,” says Sutherland. And for such integers, how do you find a, b and c? In two years, the MIT Quest for Intelligence has allowed hundreds of students to explore AI in its many applications. Adams’s mysterious number even inspired a 2011 book, 42: Douglas Adams’ Amazingly Accurate Answer to Life, the Universe and Everything, by Peter Gill. As Booker found with his solution to 33, they knew they didn’t have to resort to trying all of the possibilities for x, y, and z. 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