An undergraduate degree wouldnt get you to the level required to understand the proof; generally you dont cover things like differential geometry/manifolds/algebraic topology until masters/phd level. However its possible to get a very rough idea about what sort of questions are being asked in modern geometry/topology/etc without going extremely deep into the mathematics, and some universities do teach very basic courses to final year undergraduates (either on their own, or as part of a class on general relativity)
Unless you are willing to devote several months/years of study, your best bet would probably be to try and find a popscience book that explains it in relatively nontechnical terms.ast Theorem, so I imagine you'll start to see more on the Poincare conjecture springing up in the next few years (if there arent any already) Ive never read it so I'm not recommending it specifically, but you want something like this: http://www.amazon.com/The-Poincare-C...are+conjecture
If you already had a Masters/MSci/PhD in pure mathematics then you might be able to approach it on a more technical level through this (which again I havent read): http://www.amazon.com/Ricci-Poincare...are+conjecture
Last edited by poohat; 29-06-2012 at 18:19.