Weak Goldbach

Here is an example showing that even simple elementary looking problems can lead to difficult proofs. Harald Helfgott has proven in 2014 that Every odd integer larger than 5 is the sum of three primes. The proof is available on the arxiv, had been accepted in a journal but Helfgott decided to write a book about it instead giving more details. Indeed, this is a mile stone in Mathematics. It seems as if experts in the field believe however that there is still a large way from the weak Goldbach problem to the actual Goldbach problem stating that every even number larger than 2 is a sum of two primes.

• The paper of Helfgott (2014)
• Helfgotts book

Here is a movie about Helfgott: Apropos number theory, here are my own famous open problems in number theory: And (also a shameless plug), here is an Goldbach conjecture for Gaussian primes.