> I like geometry. Let's start with Hilbert's axioms > for Euclidean > geometry and prove a couple theorems and a couple > statements that > look like they are theorems but are demonstrably > false. >
Good luck. It has been my experience that even the most trivial geometric proofs starting from formal axioms are very long and tedious indeed. I cannot recommend it for the beginner. Better to start with the simplest possible systems, e.g. logic and set theory that are the basis for EVERY branch of mathematics.
Dan Download my DC Proof 2.0 software at http://www.dcproof.com Also see "The Barber Paradox Video"
