(AG) Reading Rainbow: Get Your Books!

So there's an Algebraic Geometry reading group at this subreddit.

If you're up for this, it looks like you'll have to buy the Beltrametti et al book on your own.  But if you're looking to pick up the other books, and maybe you also want to score an Introduction to Commutative Algebra with some solution manuals on the side... I know a guy... (the blogger gestures down a nearby alley)

Follow the link after the break...

Discord in the Axioms

You've all heard about Gödel's Second Incompleteness theorem, right?  If a theory with a finite list of axioms contains the basis for arithmetic, this theory cannot produce statements about its own consistency without contradicting itself.  So we can't ever prove such a theory's consistency; we can only take solace in the notion that we haven't found any contradictions yet.  Kind of a bummer.

Way back in September, the distinguished Ed Nelson, a math professor at Princeton, claimed to have found an inconsistency in Peano Axions--one of the most widely used formalizations of arithmetic--and distributed a sketch of his proof through a math mailing list.  It's hard to get more basic than this: these are axioms that establish the existence of zero, all the common rules for how the equals sign works, your ability to add one to a number that already exists, and (Nelson thought this last one was the culprit) the validity of proof-by-induction.  There might be some question about whether certain bits of modern set theory are inconsistent, but arithmetic?  Nelson was really going for the balls here.