Field's medal level maths is unbelievably complicated.

More or Less on BBC radio 4 sent a highly qualified reporter (alex belos of alex's adventures in numberland) to the ceremony in Hyderabad, India and even the deleagates - professional mathematicians and science writers admitted to only understanding a tiny fraction of the lectures/seminars given. Cedric Villani, one of the winners described advanced maths as having developed into different languages; and if you cannot speak the language you have no chance of understanding anything - there are barriers and chasms that cannot be crossed by an outsider. If I remember correctly Cedric Villani admitted he was able to comprehend rough ideas in only 20 percent of the papers - and this is a fields medallist!

I have found some of the blogs maintained by maths academics particularly useful - perhaps try searching the blogosphere and when you find an academic in the right field just ask nicely for some help. This exact approach worked for me on a different topic a few months ago; most academics will point you to basic learning books and advise how to progress in a subject.

Good Luck - and to get you going this is a very basic summary of Ngo's work

The little lemma that could