I did not have the impression the proof uses a surprising and novel contribution of fields. I think the proof uses standard application techniques of algebraic

I did not have the impression the proof uses a surprising and novel contribution of fields. I think the proof uses standard application techniques of algebraic number theory towards discrete geometry. If you have a quote substantiating what you said I would be curious. I know these articles write that it used deep algebraic number theory techniques, which is true, but it may also just be the standard in the field.