The mathematical problem of the millennium has not yet been solved
The mathematical problem of the millennium has not yet been solved
This hypothesis, one of the most famous mathematical problems in the world, was raised by Bernd Riemann almost 160 years ago and consists of studying the distribution of zeros of the Zeta function of Riemann, closely related to the theorem of the distribution of prime numbers.
"The idea with this hypothesis is to try to establish how many prime numbers can be smaller than a given number", says Professor Agustín Moreno, from the Mathematics Department of the National University of Colombia (UN), Ph. D. in Theory of Representation , Theory of Numbers and Cryptography.
As explained by the teacher, this hypothesis is included within the seven problems of the millennium whose solution rewards the Clay Institute of Mathematics of EE. UU with a million dollars.
These same prime numbers are the keys since the seventies, in public key cryptographic systems such as the RSA in which its creators -Rivest, Shamir and Adleman- developed an algorithm based on prime numbers and the current difficulty to factor integers.
"In the RSA cryptographic system the prime numbers used are secret. We have a natural number n, which is the product of two cousins P and Q, which are secret. The n is published, in such a way that any message encrypted with this method can be obtained with that value and another number, also public, that is part of the RSA key ", explains the teacher.
The solution of the Riemann hypothesis would imply obtaining with high precision the prime numbers smaller or equal than n, with which efficient algorithms would be obtained that can find in a reasonable time the cousins that constitute the RSA key, the same ones that are also used to generate digital signature schemes widely used today to verify user authentication in systems such as the DIAN.
Michael Atiyah, professor emeritus at the University of Edinburgh in the United Kingdom. (Photo: DICYT)
Since the number n is public, if the Riemann hypothesis is solved and an algorithm is found to factor it, this would open up the RSA cryptographic system, something like facilitating the access of anyone to a keychain with all the keys of your house and the capacity to identify which one specifically opens the front door.
"The impact on cryptography has to do with the knowledge that we can have of the prime numbers up to a certain value and in this way recognize those keys that are used in cryptographic systems of public key or generation of digital signature schemes", clarifies the Professor Moreno.
The author of the possible solution to the Riemann hypothesis, Michael Atiyah, professor emeritus of the University of Edinburgh in the United Kingdom, is one of the mathematicians of greater recognition in recent times. As such, he has received the two most important recognitions within the field: the Fields Medal, in 1966, and the Abel Prize, in 2004.
Due to the recognition obtained by this 89-year-old professor during his career, the scientific world paid special attention to the 45-minute conference at the Laureate Forum, held in Heidelberg, Germany, in which he made a simple demonstration of this problem.
However, for experts from the U.N. Like Professor John Alexander Cruz of the Department of Mathematics, the problem is not yet solved.
In his concept, although when such a statement comes from such an important mathematician, it is taken more seriously than that of the many scientists who have previously claimed to have the solution to the hypothesis - drawn by the million dollar reward - not yet it can be said that there is a demonstration.
"What exists is the declaration of an important mathematician saying that he demonstrated a result and we must begin to evaluate that statement," said Professor Cruz.
On the other hand the ex-rector of the UN, Professor Ignacio Mantilla Prada, evaluate if the demonstration is correct or it will not take at least two months, so that the specialists evaluate if the work of professor Atiyah was sufficient, free of errors and correct, or insufficient or erroneous test of the conjecture. (Source: UN / DICYT)
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