The super-difficult problem that existed for decades has been solved, the solution weighs 200TB

Huge capacity just to contain the solution to a problem. Is it really that difficult?

Many of us must have spent many years studying through level 1, level 2 and level 3 to get rid of Maths (and then go to University and have to do with Advanced Mathematics). Do you think the math homework delivered after every lesson is sweet? So look at this problem here, to solve it, it takes 3 mathematicians and 200 terabytes of capacity just to contain the solution, that's got a supercomputer to help!

You calculate, 1 terabyte contains 337,920 copies of War and Peace , the novel by Lev Tolstoi, the longest set of novels in human history, so how much 200 terabytes will contain so many words.

How difficult is this problem, but the solution is so great? It was a mathematical problem centered around Pythagoras's theorem (or we still know it under the Py-theoretic theorem), first introduced by mathematics professor Ronald Graham in the 1980s. is the wrong variable of the trio of Pythagoras (Boolean Pythagorean Triples) , so this math problem is "sweet" that Graham has suspended 100 USD for anyone to solve (1980!).

This math problem revolves around the Pythagoras theorem: a ^ 2 b ^ 2 = c ^ 2 . Where a and b are the two right angles of a right triangle, and c is the hypotenuse.

Recipe of Pythagoras theorem.

Explain the name of this math problem:

Bolean is a variable of true or false value.

As for Pythagoras Triples , there are positive integers called Pythagoras trio that will always be correct when applied to Pythagoras's formula: 3 ^ 2 4 ^ 2 = 5 ^ 2; 8 ^ 2 15 ^ 2 = 17 ^ 2. They are called Pythagoras positive integers.

And imagine that all positive integers in the alphanumeric table will be colored either red or blue. Graham came up with the question: is it possible to color all integers or green or red, so that there are no trio of pythagoras of the same color. And 100 USD will be rewarded for anyone who solves the problem (Well, with 100 USD, we can pay for 1 drive with 1 terabyte capacity).

Ronald Graham, the teacher who gave us the problem that could not be solved for decades.

This mathematical problem is difficult: a positive integer can be in many different Pythagoras Triads. For example, number 5, we have the sequence 3-4-5 which is the Pythagoras Triad, but so does the sequence 5-12-13. Applying Graham's condition, if the number 5 of the first sequence is green, then the second sequence must also be green, so numbers 12 and 13 must be red.

As far as the condition Graham proposes, the greater the numbers and the problem starts to arise. If number 12 must be red in the sequence 5-12-13, the numbers that will contain the number 12 will then be required to wear a certain color.

Marijn Heule mathematicians from the University of Texas, Victor Marek from the University of Kentucky, and Oliver Kullmann from Swansea University in England worked together to solve this problem. They installed a number of tests and computational techniques into the Stampede supercomputer at the University of Texas, so that it could narrow the "color" range to 102.3 trillion dong (hundred trillion, That's a total of 25 "0" numbers for you.

Seamless Stampede supercomputer is used to solve this difficult problem.

The supercomputing set of 800 powerful microprocessors took up to two days to "rip" all the other tests, and it could only be feasible until 7,824. Starting from 7,825 onwards is impossible to satisfy Graham's requirements.

So the 3 mathematicians (with a supercomputer) solved the math problem that has existed for this decade, and Ronald Graham also kept his promise, rewarding "post- prize " money 100 USD for 3 brothers.

The three mathematicians of the three mathematicians have created a 68 gigabyte compression version for any young man who has a good processor with 30,000 hours of free time to download, reconstruct and verify the problem. . But if you have 30,000 hours of real time, there is also another problem, people can't read those algorithms.

In fact, the trio had to "ask" another computer program to verify their results, and finally 7,824 was the correct number. Ronald Graham was also pleased with the verification of this number.

Numbers from 1 to 7,824 can be colored because they satisfy Graham's condition.But from 7,825 onwards, no number is satisfied.

But many people believe that people cannot read the results, so it is not convincing enough. Although it is not proven that it is wrong, it does not solve the problem to the end. Why is it not feasible to start from 7,825 onwards? We cannot explain it, but it is only said by the supercomputer.

Later on, people can understand the meaning of numbers with us as well as the whole universe if all math problems are solved by such machines. The fact is that this problem is too difficult to solve, maybe also have to use a certain supercomputer to get involved.