One of my classmates was telling me that it is an open question whether every 3-manifold can be triangulated. This was rather surprising. He said that the question as far as he remember is settled only for 4-manifold where answer is negative. If this is the case, can somebody shed some light why this problem is so hard?
Post Closed as "off topic" by Franz Lemmermeyer, J.C. Ottem, Andrew Stacey, Qiaochu Yuan, S. Carnahan♦