The biggest mathematical proof in the world weighs 200 TB
The problem of Pythagorean Boolean triples is solved by the Stampede supercomputer
Supercomputer Stampede from the University of Texas - Austin
A team of scientists has announced a solution to the mathematical problem of Boolean Pythagorean triples. The solution was obtained using the supercomputer Stampede of the University of Texas - Austin. But its volume is 200 TB. This is as much as the digitized materials of the Library of Congress would occupy. Compressed proof takes 68 GB. It will take about 30,000 hours of computer time to deploy the data array and verify the solution. If we talk about the verification of the decision by man, but this is simply impossible - the whole life is not enough to perform such work without the help of a computer.
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This is not the first such solution - now quite often mathematically problems (especially in combinatorics) are solved with the help of the most powerful computer systems, because a person is simply unable to perform such work. Everything is good, but a person cannot verify the correctness of the decision, too much work. The previous record on the bulk of the solution belonged to 13 GB of evidence, published in 2014. 200 TB and completely out of the ordinary.
The problem of the Pythagorean Boolean triples has occupied the minds of mathematicians for many years. In 1980, Ronald Graham was even offered a cash reward (as much as $ 100) for this important task. And only now the team of specialists behind the decision received these funds. And the wording of the problem is as follows. Is it possible to dye every positive natural number red or blue, so that the triple natural numbers a, b and c satisfying the Pythagorean theorem a 2 + b 2 = c 2 would not be painted the same color. For example, take the Pythagorean trio 3,4 and 5. If 3 and 5 are colored blue, then the number 4 must be red.
In an article published on May 3 , scientists argue that up to 7824, all Pythagorean triples can satisfy the condition of the problem. Since the number 7825 this is no longer possible. There are 10 2300 ways to color triples in different colors up to the number 7825. To come to this solution, scientists took 2 days of computer time, with the work of 800 processors of the Stampede system. After this decision was confirmed using another computer program.
The problem of the Pythagorean triples is one of many related to Ramsey Theory . This is a branch of mathematics that studies the conditions under which a certain order must appear in arbitrarily formed mathematical objects. Tasks in Ramsey’s theory usually sound in the form of the question “how many elements must there be in some object in order for a given condition to be guaranteed to exist or a given structure to exist”.
Despite the fact that the computer solved the problem, it did not provide an answer to the question why the number 7825 is so significant, or why staining triples in different colors is generally possible. And this is the perennial problem of machine evidence. They may be true, but is it math?
Supercomputer Stampede from the University of Texas - Austin
A team of scientists has announced a solution to the mathematical problem of Boolean Pythagorean triples. The solution was obtained using the supercomputer Stampede of the University of Texas - Austin. But its volume is 200 TB. This is as much as the digitized materials of the Library of Congress would occupy. Compressed proof takes 68 GB. It will take about 30,000 hours of computer time to deploy the data array and verify the solution. If we talk about the verification of the decision by man, but this is simply impossible - the whole life is not enough to perform such work without the help of a computer.
')
This is not the first such solution - now quite often mathematically problems (especially in combinatorics) are solved with the help of the most powerful computer systems, because a person is simply unable to perform such work. Everything is good, but a person cannot verify the correctness of the decision, too much work. The previous record on the bulk of the solution belonged to 13 GB of evidence, published in 2014. 200 TB and completely out of the ordinary.
The problem of the Pythagorean Boolean triples has occupied the minds of mathematicians for many years. In 1980, Ronald Graham was even offered a cash reward (as much as $ 100) for this important task. And only now the team of specialists behind the decision received these funds. And the wording of the problem is as follows. Is it possible to dye every positive natural number red or blue, so that the triple natural numbers a, b and c satisfying the Pythagorean theorem a 2 + b 2 = c 2 would not be painted the same color. For example, take the Pythagorean trio 3,4 and 5. If 3 and 5 are colored blue, then the number 4 must be red.
In an article published on May 3 , scientists argue that up to 7824, all Pythagorean triples can satisfy the condition of the problem. Since the number 7825 this is no longer possible. There are 10 2300 ways to color triples in different colors up to the number 7825. To come to this solution, scientists took 2 days of computer time, with the work of 800 processors of the Stampede system. After this decision was confirmed using another computer program.
The problem of the Pythagorean triples is one of many related to Ramsey Theory . This is a branch of mathematics that studies the conditions under which a certain order must appear in arbitrarily formed mathematical objects. Tasks in Ramsey’s theory usually sound in the form of the question “how many elements must there be in some object in order for a given condition to be guaranteed to exist or a given structure to exist”.
Despite the fact that the computer solved the problem, it did not provide an answer to the question why the number 7825 is so significant, or why staining triples in different colors is generally possible. And this is the perennial problem of machine evidence. They may be true, but is it math?
Source: https://habr.com/ru/post/394679/
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