My professor was lecturing today and he made this statement which I was unable to verify. (I worded it nicer)
There is no map which is both smooth and onto from $S^1$ to $S^1$$\times$ $S^1$.
When he said this he included the original "one can clearly see" statement which is usually when the most people seem to be confused in his class. Thus, I was hesitant to ask why. So, please no one lecture me on the fact that I should have asked anyway. If it is really that obvious, I would rather look stupid here than in class :)