Abstract:
The ternary Goldbach conjecture (1742) asserts that every odd number
greater than 5 can be written as the sum of three prime numbers.
Following the pioneering work of Hardy and Littlewood, Vinogradov
proved (1937) that every odd number larger than a constant $C$ satisfies
the conjecture. In the years since then, there has been a succession
of results reducing $C$, but only to levels much too high for a
verification by computer up to $C$ to be possible ($C>10^{1300}$). (Works by
Ramare and Tao have solved the corresponding problems for six and five
prime numbers instead of three.) My recent work proves the conjecture.
We will go over the main ideas of the proof.
