Solved one of the greatest mathematical problems in history after 150 years

It took 150 years and there are two physicists, one Italian and one American, to solve one of the greatest mathematical problems in history, namely the Riemann conjecture which allows us to predict, with great accuracy, the distribution of prime numbers.

Lsolution thanks to Italy and the USA

The result, published in the Journal of Statistical Mechanics, it is due to the physicists Giuseppe Mussardo, of the International School of Advanced Studies (Sissa), and Andrè Leclair of Cornell University. Surprisingly, the two physicists were able to find the solution to the mystery using the laws of probability that regulate chaotic movements, such as those of gas atoms. It took three years of research to get there. “It was a real tour de force, in the data analysis of an incredibly large set of prime numbers, the basic constituents of arithmetic, the real atoms of mathematics,” said the two physicists.

Bernhard Riemann and his theory

Not even Riemann himself, who had presented his theory in an article at the Berlin Academy of Sciences in 1859, had not been able to prove his conjecture. “At the heart of Riemann’s argument – says Mussardo – there was a conjecture about the location of an infinite number of zeros in the complex plane of a particular function, known today as the Riemann function, which, however, he was not able to try”.

The mystery solved

The puzzle was solved using the rules that control the movements of disordered systems, such as those of gas atoms that incessantly collide with each other, the so-called Brownian motions “The fact that the explanation of the Riemann conjecture comes from physics, or mechanics statistics and the surprising connections of this discipline with a genuinely mathematical field such as that of number theory, does nothing but reveal – concludes Mussardo – the great unity of scientific knowledge and increase the amazement in front of such a profound fact “.