/sci/ - Science & Math

Topologists don't actually think in terms of proofs, that's a common misconception. Handwavy techniques are all that it it takes. For example, in topology to prove S^n and S^m are not homeomorphic it's enough to say that an embedding of it into R^k separates it into two components only for the appropriate k. You don't actually need to prove it because it's intuitively obvious. We've localized the topological nastiness from of the problem into an extremely particular and uninteresting situation. Such is the goal of topology