Computers As a Novel Mathematical Reality: IV. The Goldbach Problem

this part I pursue the discussion of the role of computers in additive number theroy. I sketch the definitive solution of the ternary = odd Goldbach conjecture, not in one of its 20th century asymptotric reformulations, but in its original 17th century form. Namely, that every odd number n > 5 is a sum of three positive rational primes. This problem was only solved in 2013-2014 by Harald n = p(1) + p(2) + p(3) Helfgott, and there is no chance that it could have been obtained without the use of computers. Apart from that, I discuss the status of the binary = even Goldbach conjecture and partial results leading towards its solution, as well as some further related problems.