Heh. I was not prepared for the punchline that this "only" goes from 4^k to 3.993^k. I mean, they're creating a whole new form of proof that will almost certainly allow further decreases, and they generously aren't holding back until they make a bigger dent, but it just intuitively feels like the true value has got to be way, way smaller.<p>(On a side note, I am so often stunned by the quality of articles on Quanta Magazine. I sorta thought this type of quality writing was dead and gone from the freely accessible web.)