I matematici sono vicini a scoprire il più grande mistero che si nasconde dietro i numeri primi

This article is just horrendous.

>They then turned to the Gowers norm, a tool from a seemingly unrelated branch of mathematics, to bridge the gap between rough primes and actual primes.

Gowers norm is used in lots of disciplines, including number theory, extensively. It was indeed introduced for combinatorial considerations (as a very effective bounding norm) but currently you can even find it in some discrete stochastic application. It’s just wrong.

Actually an interesting part of paper is the the comparison of two summing procedures in given fields and concluding that those fields have prime characteristic (ergo the characteristic is a prime number to some power) and then they reduce the possibilities to exactly one possibility (minus shift) using (more or less standard, if very time-consuming) asymptotic analysis. A fascinating paper, but its core idea is very different to what the “journalist” presented. Yes, the comparison of sums is done by this norm, but it’s like saying that the “core or proof for *some analysis theorem* is triangle inequality”. It’s technically correct and completely misses the novel argument which is indeed there. The novel part is definitely not in the use of some norm (c’mon, you learn it during Analysis 1, do better)