The August 6, 2010, a c ESEARCHERS Indian his 39-year made elements ( evidence of more than 100 pages still being verified, with apparently he doubts at this stage) a demonstration of one of the most important mathematical algorithms: P \u0026lt;> ; NP - ie: are there problems for which it is easy to verify if a solution is necessary, but very difficult to find a solution.
To give a more romantic: is it the same capabilities, and possibly a little method to appreciate a symphony or Mozard "Being and Nothingness" and to write them?
P stands for problems whose solutions can be found consistently in a while "short" compared to the length of the problem. For example, sort the items in a list of size N can be done in less time than N ^ 2 (just for example through the list to find the smallest, then travel the rest of the list to seek the second smallest, etc. ...).
NP means problems for which there is no systematic method to solve them in time "short" (they require an exponential time with problem size, ie it becomes very quickly too long to solve, even for a computer), then it is possible to check if a solution is good in a short time. For example, in what order to put bags of different sizes to fill in as much as possible the trunk of a car is a difficult problem: apart from trying all solutions, there is no simple way to ensure rapid success in all cases. It's complicated with 10 suitcases, very difficult with 100,000 bags.
To determine whether a problem is in NP, it is not enough to have a hard time finding a solution: for example, solving the Rubiks Cube is difficult for many people (although it is easy to see if it has been resolved or not), but there simple solutions and automation to solve . Researchers who have studied these issues and have identified a set of problems "NP-complete" , both difficult to resolve, such that if one of them was resolved (that to say whether a simple and systematic resolution was found), then a simple method for each problem "NP" could be inferred.
If P is not equal to NP, this means that exist problems whose solution is easy to verify but for which no one ever found a simple solution to solve them. Currently, we know now lot of hard problems to solve , but nobody is on - unless the demonstration of N = NP is done - there is a simple method for their solution. For example: Fill a bag or box, find the shortest route possible through a list of cities, Tetris, manage schedules ...
Currently, most scientists believe that P \u0026lt;> NP, remains to be seen whether the demonstration Vinay Deolalikar holds ( it can take time , as was the case with Fermat's theorem, and require further evidence being provided) ... Even in the opposite case it has confirmed the exceptional power of India in the IT field, and the strength of the American model of "war for talent" ...
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