I actually would like to give it a shot, even though I know that it's way too far beyond my level. But after googling Henry Andrew Pogorzelski, no pdf's came out.
I think he should have written a paper explaining in easier term what he does. E.g "First I will map the integers into a group defined by X and Y, it makes the work easier because that group has some interesting properties like... Then I show how the Goldback conjecture translates onto my group, then, etc."
I know this is easier to be said than to be done, but on the other hand the Goldback conjecture is so simple that there have to be ways to break down its demonstration (or attempts of) into understandable steps, each steps being once again broken down, etc. and each stage introducing new layers of complexity. That way, instead of claiming "I proved the Goldback conjecture, here is the proof, just check those 1000 pages", he could have said "I proved X, Y and Z, and we can see how together they can be added up to prove the actual conjecture", with X, Y and Z (and probably lots of others) being smaller results that experts could challenge or assert.
EDIT: TL;DR: If a mathematician claims to prove a long time unproven claim such as Goldbach conjecture, it belongs to him to do the vulgarisation works so even schmucks like me can have a remove idea of how he did it.
I think he should have written a paper explaining in easier term what he does. E.g "First I will map the integers into a group defined by X and Y, it makes the work easier because that group has some interesting properties like... Then I show how the Goldback conjecture translates onto my group, then, etc."
I know this is easier to be said than to be done, but on the other hand the Goldback conjecture is so simple that there have to be ways to break down its demonstration (or attempts of) into understandable steps, each steps being once again broken down, etc. and each stage introducing new layers of complexity. That way, instead of claiming "I proved the Goldback conjecture, here is the proof, just check those 1000 pages", he could have said "I proved X, Y and Z, and we can see how together they can be added up to prove the actual conjecture", with X, Y and Z (and probably lots of others) being smaller results that experts could challenge or assert.
EDIT: TL;DR: If a mathematician claims to prove a long time unproven claim such as Goldbach conjecture, it belongs to him to do the vulgarisation works so even schmucks like me can have a remove idea of how he did it.