What is the answer to
Video What’s the Answer A workforce led by Andrew Sutherland of MIT and Andrew Booker of Bristol College has solved the last piece of a famous math puzzle 65 years ago with answers for many elusive catch: 42. 42 is especially important to followers of novelist Douglas Adams’ sci-fi novel “A Guide to the Galaxy,” as that number is the answer given by one supercomputer for “The Final Question of Life, the Universe, and Everything”. Reading: What is the answer toBooker also wants to know the answer to 42. That is, are there three cubes whose sum is 42? This sum of three cubes puzzle, first laid out in 1954 at Cambridge University and commonly known as the Diophantine Equation x3 + y3 + z3 = okay, challenges mathematicians to explore choices for numbers 1-100. For smaller numbers, any such equation is easier to solve: for example, 29 can be written as 33 + 13 + 13, while 32 is unsolvable. All were eventually solved or proved unsolvable using different methods and supercomputers, besides 2 numbers: 33 and 42. When turned to solving for 42, Booker discovered that the requirements of the computer were to an order of magnitude greater and possibly beyond the functionality of his supercomputer. Booker says he’s had a lot of help finding the answer, but instead turned to his good friend Andrew “Drew” Sutherland, a principal analytical scientist with the Department of Numerology. “He’s the world’s expert on this sort of thing,” says Booker. Like various computational quantity theorists working in the field of arithmetic geometry, he was aware of the “sum of three cubes” disadvantage. And the two have worked together before, for the construction of the Modular and L Functions Database (LMFDB), an internet atlas of mathematical objects associated with what is commonly known. called the Langlands Program. Sutherland said: “I was delighted when Andy asked me to join him on this project. Read more: what is an inverted fontanel | Top Q & ABooker and Sutherland mentioned the algorithmic technique used to find the answer to 42. When Booker found out along with his answer to 33, they knew they didn’t need to try. all the prospects for x, y and z. “There is a single integer parameter, d, that defines a relatively small set of possibilities for x, y, and z such that the absolute value of z is below the chosen search limit B, ‘ said Sutherland. “Then one enumerates the values of d and examines each possible x, y, z value that is related to d. In an attempt to crack 33, the search limit for B was 1016, but this B turned out to be too small to crack 42; Instead, we use B = 1017 (1017 is 100 million billion). In contrast, the main difference between search 33 and search 42 will be the size of the search and the computer platform used. Thanks to a generous offer from the UK-based Charity Company, Booker and Sutherland were able to harness the computing power from more than 400,000 volunteers’ home computers around the world, one each of which is assigned a series of values for d. Per-PC computation runs in the background so owners can still use their PCs for other tasks. number 42 in the novel “Hitchhiker”: After Deep Thought’s answer to 42 displeased scientists, who didn’t know the question it was supposed to answer, the supercomputer decided to calculate the Last Question together by building an Earth-powered supercomputer… In other words, using a worldwide parallel computing platform. “This is another reason why I really enjoy running this calculation on the Charity Engine – we actually used a planet-scale calculator to solve a long-standing open-ended question whose answer is 42. ” They ran various calculations with mitigations to test each of their codes and the Charity Tools community. They then use various optimizations and diversifications to make the code more suitable for widely distributed computing, as opposed to computation running on a supercomputer, Sutherland said. comedy show “Well, any computer *can* solve the problem, as long as you’re willing to wait long enough, but with about half a million computers solving the problem in parallel (each with multiple core), we were able to complete the calculation of Sutherland say much faster than we could with a Bristol machine (or any machine here at MIT). “For the most part, we’re using computational resources that would otherwise go to waste,” says Sutherland. “When you are sitting at your computer reading email or working on a spreadsheet, you are using only a fraction of the available CPU resources and the Charity Engine application, based on the Berkeley Open Infrastructure for Network Computing ( BOINC ), take advantage of this. As a result, the carbon footprint of this calculation – relative to the amount of electricity we calculate caused the PCs in the network to use above and beyond what they would use, in any case – is lower than with the level if we use a supercomputer. “Sutherland and Booker ran the calculations for months, yet the last profitable run was completed in just a few weeks. When the email from Charity Engine arrived, it gave the first reply for x3 + y3 + z3 = 42:42 = (-80538738812075974) ^3 + 80435758145817515^3 + 12602123297335631^3 “When I heard the news, it was definitely a Sutherland said. “With these large-scale computations, you pour a lot of time and energy into optimizing the implementation, tweaking the parameters, and then testing and retrying the code for weeks and months, no matter what. never really know if all the effort will pay off, so Booker and Sutherland say that there are 10 remainders, 101-1000, left to solve, with the next number being 114. : yes or there are no further solutions for the sum of three cubes for 3. “There are four very easy solutions that were known in 1953 by the mathematician Louis J. Mordell, who famously wrote in 1953, in 1953,” I do not know nothing about integer solutions of x3 + y3 + z3 = 3 other than the existence of four triples (1, 1, 1), (4, 4, -5), (4, -5, 4), (– 5, 4, 4) ; and it’s really hard to find any other solution. ‘ This quote has fueled a great deal of interest in the problem of the sum of three cubes, and the k = 3 case in particular. Although it is conjectured that an infinite number of solutions are required, despite more than 65 years of searching, we know only the easy solutions that Mordell already knew. It would be interesting to find another solution to k = 3.” Read more: What do pink and green make up
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