I haven't read it yet, but this looks like a fairly accessible (but still technical) explanation of the argument: http://www.ams.org/journals/notices/201605/rn

I haven't read it yet, but this looks like a fairly accessible (but still technical) explanation of the argument: http://www.ams.org/journals/notices/201605/rnoti-p508.pdf http://www.ams.org/journals/notices/201605/rnoti-p508.pdf