Russian scientist Alexander Zhulanov proposed a new approach to one of the seven "Millennium Prize Problems" – the P versus NP problem. Currently, mathematicians are trying to understand whether a complex problem can be solved as quickly as a ready-made answer can be verified. Zhulanov's work was published in the scientific journal "Information Processes" of the Institute for Information Transmission Problems of the Russian Academy of Sciences.

The "Millennium Prize Problems" are seven crucial mathematical problems formulated by the Clay Mathematics Institute in 2000. A prize of $1 million is offered for the solution to each of them. The list includes the Riemann Hypothesis, the Hodge Conjecture, the Birch and Swinnerton-Dyer Conjecture, the P versus NP problem, the Navier-Stokes equations, Yang-Mills theory, and the Poincaré Conjecture. The latter was eventually proven by Grigori Perelman, while the other six are officially still considered unsolved.

Zhulanov's work is dedicated to the P versus NP problem and is related to the so-called symmetric traveling salesman problem. In it, one needs to find the shortest closed route between given points such that each point is visited exactly once.

This problem belongs to the class of NP-hard problems. Therefore, the existence of an exact algorithm that would solve its general case in polynomial time would imply P = NP.

The method proposed by the scientist is based on dynamic modeling of signals that simultaneously propagate from all vertices of the graph. The algorithm analyzes the order of visiting these vertices and gradually discards routes that cannot be the shortest.

The IITP RAS emphasizes that the publication of the article itself does not mean the P versus NP problem has been solved. Specialists still need to verify the mathematical proof, look for possible counterexamples, and ensure that the algorithm works correctly for any valid initial data.

However, the results can already be independently verified. The author provided program code that allows mathematicians to audit and check the stated time characteristics of the algorithm in practice.

If the correctness of the method is confirmed, it can find application in optimizing complex logistics networks, creating new molecules, and developing artificial intelligence systems. In particular, according to Dmitry Repin, chief researcher at IITP RAS, the algorithm could potentially help create "explainable AI" that will make fewer errors and reduce "hallucinations" in neural networks.