Abstract:
Here we describe the definitive solution of the ternary = odd Goldbach problem, not its
cheaper XX century asymptotic versions, but its original XVIII century absolute form.
This is the statement that every odd natural number n>5 can be presented as the sum
n=p1+p2+p3 of three natural primes. A solution of this problem was finalised by Harald
Helfgott in 2013–2014 and could not have been obtained without the use of computers.
In the talk, I discuss the history of this classical problem, both its statement and impact,
and the ideas that eventually lead to its solution. The literature is full of gross historical
mistakes. In particular, it is claimed that as early as 1930 Schnirelmann has proven that
each integer is the sum of s<800.000 primes. In reality, he has never proven any such
thing. The first similar results, with much worse bounds for s, were only published in
the 1960-ies. From a psychologically viewpoint, the confusion between the Schnirelmann
constant S and the absolute Schnirelmann constant s is easily explained by the fact that
the first credible bound for Schnirelmann constant S was only published in 1936, while
already in 1937 Ivan Vinogradov obtained the bound S<=4 [as a matter of comparison,
Helfgott established that even s<=4]. I sketch a possible chain of events that could have
lead to the fictitious 800.000 primes. Apart from that, I plan to describe the role of computers
in the definitive solution of the odd Goldbach problem, the status of the binary = even
Goldbach problem and the known partial results towards its solution, as well as some
related problems.
*) Zoom ID: 893-744-395-05, password mkn
