A mathematician from India claims to be the solution of the Millennium

In general, the objectives of the millennium is hard to expect that it will be easy to understand. As it is written on the website of the Institute Clay ... Now that hundreds or even thousands of mathematicians were unable to cope with these problems, so they really impossibly.

However, as time at the Clay Institute, presented a very accessible description of what the human language does the phrase ... We use this explanation. Suppose that you face the challenge to settle the students in the dormitory, and a hundred places available and willing to settle down - four hundred. In addition, the management of a flat top of a list of pairs of students, which in any case can not settle with. It is obvious that after the settlement is completed, you can easily check whether all the conditions, but that's up to the task in a reasonable time is extremely difficult - the number of options to choose from hundreds of students from the four higher than the number of atoms in the universe.

Such problems are called problems of the class of NP, and very difficult to solve the ... But the fact that the problem, the correct answer to that is easy to check ( in our case, just checking the list received from the leadership ) really can not be solved in a relatively short period of time using, for example, some clever algorithm, not strictly proved. In the language of mathematicians, the absence of such evidence is recorded as a question mark in the formula 'P = NP?'. As the reader has already guessed, the problem of complexity class P can be solved in an adequate time ( scientists use the term ...

Another example of the problem complexity classes NP - is assembling a mosaic Blind. You can easily determine whether all the pieces are placed, but that's to get, say, the Mona Lisa of the thousands of colorful pieces, fingering their various combinations, are not so simple.

For the first time the question of equality or inequality of the classes P and NP at the same time wondered just two math - Stephen Cook (Stephen Cook) and Leonid Levin in 1971. Since then, scientists have unsuccessfully tried to answer it. Statements of evidence, can we still put an equal sign between P and NP are expected not only to researchers who are interested in only the fundamental aspects of mathematics ( question for them is a truly topical ). This task is extremely important for the Millennium professionals involved in computing theories and data encryption.

Interest in the latter, generally speaking, should be separated by any person who has ever paid for any of their online shopping with credit card. When you send your card details to the address of the store, they go there in an encrypted form, and encryption is often not in complicated patterns, which we all know from the books about spies. In modern ciphers use large numbers - the transmitted information is encoded by a huge number of digits ( the so-called key), and the opening of this code, an attacker would have to spend so much time that this problem will lose all meaning.

But - if P does turn out to equal NP, it means that an attacker can find a way to reveal the code quickly and steal information about your card. Or the secret KGB documents. Or whatever.

To reassure those who immediately ran to cancel your cards, make a reservation, that to date most mathematicians believe that the complexity classes P and NP are not equal. However, these assumptions are not supported by rigorous evidence, and based on experience - so far nobody has been able to solve the problem of complexity class NP in polynomial time.
While the article is an Indian mathematician has not been published in peer-reviewed journal ( although, for example, articles Grigory Perelman, for which the Clay Institute Millennium Prize awarded him, has never been published ), and he emphasizes that it is only a preliminary version and the final version will . So the formal mathematics who wish to publicly evaluate the evidence, must wait for the final text. But informally, many of them have already begun to study the article Deolalikara and some have already criticized the approach used by scientists.

But the staff at the Massachusetts Institute of Technology (MIT) Scott Aaronson (Scott Aaronson) acted differently - he promised to give Deolalikaru 200 thousand dollars, if it turns out that his proof of the true. Aaronson explained his action this way: ... By these words it is difficult to add something.

Irina Yakutenko.


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