Up til now my math-blog reading has been limited to Scott Aaronson’s Shtetl-Optimized (entertaining) and BitTorrent creator Bram Cohen’s LiveJournal (always glad to help). But Leland McInnes’ The Narrow Road is the kind of math blog you can sit down and have a drink with, because the posts are long and you probably aren’t going to fully grasp them anyway though it’s fun to try. McInnes is a mathematician completing his Ph.D. in pro-finite Lie rings. A pro-finite Lie ring, in case you cheated your way through abstract math, “is a compact Hausdorff topological Lie ring such that the open ideals of finite index form a neighbourhood base of 0.” But don’t let that scare you away. McInnes’ manifesto, If We Taught English the Way We Teach Math, is the best thing I’ve read today. You too can blame your elementary school teacher for focusing too much on the details and neglecting to instill in you an appreciation for the beauty and wonder of “the art of abstraction.” Then you can start at the beginning of Mr. McInnes’ blog and catch up.
2 Comments
His blog is good stuff, and interesting to a curious non-mathematician such as myself, but can anyone actually explain what a lie ring even is? I can’t find any sort of meaning in the doctorate-level equations of wikipedia and elswhere, and as a lazy/american high school student I need some vague definition using words (it doesn’t even have to be totally accurate, just an outline of possible applications).
Any help would be appreciated.
I have no idea what a Lie ring is, honestly. As McInnes likes to point out, the problem with math is that the levels of abstraction increase exponentially the deeper you go. If you miss a level you’re screwed. But I think if you stick with McInnes’ blog (the printable version makes good bedtime reading), he’ll eventually get to it. He’s currently exploring different algebras, which means he might get to Lie algebra soon. Maybe you should email him though about the applications of his work.