Does the proof by Maryna S. Viazovska that the E8 sphere packing is optimal use a computer?
Asked
Active
Viewed 41 times
0
-
What do you mean by "use"? It is clear from reading the paper that some computing is done to get some coefficients, but then a rigorous proof follows. What's the question? – Randall Apr 09 '19 at 15:50
-
Maybe I should have said "require a computer". Does it require a computer or could it be done by hand? Should we call it a "computer-assisted proof" ? Yes I see the coefficients near the end of the paper, they look like they require a computer. – Gary McGuire Apr 09 '19 at 16:00
-
I would guess so. You could ask Doron Zeilberger. If he says it's useless then you know no computer was involved. – Randall Apr 09 '19 at 16:08
-
I only did a quick scan, so maybe a I missed something, but there was nothing that required a computer that I could see. Yes, a computer was used to handle some calculations, but the result of those calculations can be reasonalby checked by hand. A computer-assisted proof is one where you supply an algorithm to the computer that will come to a conclusion that is too difficult to even verify by hand. If this were such a proof, the author would need to prove that the algorithm - if correctly implemented and producing a result - would produce a correct result. There is no such discussion here. – Paul Sinclair Apr 10 '19 at 01:39